Copyright notice

This bibliography is copyright 2000 by Donald E. Hooley.  You may copy it
electronically or in printed form for your personal use.  Sale of electronic or
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1970 - 2000 Topic Index 
for the College Mathematics Journal

0 	Precalculus Mathematics (also see 9)

0.1 		Arithmetic (also see 9.3)

Remedial or Developmental? Confusion over Terms,  Don Ross,  1:2,  1970, 
27-31,  1.2
Two-Pan Weighings,  Chris Burditt,  3:2,  1972,  80-81,  C
Cyclically Permuted Code: A Variation on Binary Arithmetic,  J. Maurice
Kingston,  5:1,  1974,  29-36
Computation of Repeating Decimals, James E. McKenna, 7:2, 1976, 55-58
Smith Numbers, A. Wilansky, 13:1, 1982, 21, 9.3
Cryptology: From Caesar Ciphers to Public-Key Cryptosystems, Dennis Luciano and
Gordon Prichett, 18:1, 1987, 2-17, 7.2, 9.3
What's Significant about a Digit?, David A. Smith, 20:2, 1989, 136-139, C, 9.6
FFF #85. Unto Everyone That Hath Shall Be Given, John W. Kenelly, 26:1, 1995, 36, F
Number Words in English, Steven Schwartzman, 26:3, 1995, 191-195
The Mathematical Judge: A Fable, William G. Frederick and James R. Hersberger, 26:5, 1995, 377-381, 1.1
The Square of Any Odd Number is the Difference Between Two Triangular Numbers (Proof Without Words), Roger B. Nelsen, 27:2, 1996, 118, C, 9.3
Fractions with Cycling Digit Patterns, Dan Kalman, 27:2, 1996, 109-115, 9.3
FFF #112. United in Purpose, Bruce Yoshiwara, 28:2, 1997, 119, F
FFF #121. A Case of Black and White - But Not So Much Black, Peter Rosenthal, 28:5, 1997, 377, F
FFF #125. Effects of Changing Temperature, Dave Trautman, 29:1, 1998, 35, F
More Coconuts, Sidney H. Kung, 29:4, 1998, 312-313, C, 9.3


0.2 		Algebra

Mathematics, A Solitary Game, Olof Hanner, 1:2, 1970, 5-16, 4.1
Gog and Gug, Howard W. Eves, 1:1, 1970, 8, C
The Irrationality of Certain Numbers, Peter A. Lindstrom, 1:1, 1970, 30-31, 9.3
A Computer-Oriented Multiplication Algorithm, John Peterson, 1:2, 1970, 106, C
A Geometric Approach to the Orders of Infinity, Harold L. Schoen, 3:2, 1972,
74-76, C, 9.5
Pascal's k-Simplex, Dale Woods and Mary Jane Kohlenberg, 4:3, 1973, 38-43
Teaching Inequalities Involving Absolute Values, Frances W. Lewis, 4:2, 1973,
87-90, C
Maximize x(a-x), L. H. Lange, 5:1, 1974, 22-24, 0.7, 5.1.4
A Geometric Approach to Linear Programming in the Two-Year College, Pat Semmes,
5:1, 1974, 37-40, 9.10
A Further Note on the Orders of Infinity, Harold L. Schoen, 5:1, 1974, 80-81,
C, 9.5
Investigations of Linear and Reciprocal Functions by the Line-to-Line
Technique, David R. Duncan and Bonnie H. Litwiller, 6:2, 1975, 2-7, 0.7
Distributivity with Respect to All Four Rational Operations, Myles Greene, 6:2,
1975, 10-12
Mathematical Induction: If Student k Understands It, Will Student K + 1?,
Judith L. Gersting, 6:2, 1975, 18-20, 0.9
Easter Revisited, Daniel T. Bleck, 6:3, 1975, 38-40
Functional NotationAn Intuitive Approach, Ann D. Holley, 7:3, 1976, 14-15, 1.2
Finding Super Accurate Integers, Pasquale Scopelliti and Herbert Peebles, 7:3,
1976, 52-54, 0.7, 9.6
Mathematics and Computing without Computers, William S. Dorn, 8:2, 1977,
101-105
The Perfect Curve: at Least for Grades, Lawrence Sher, 8:3, 1977, 148-152
Operational and Intuitive Algebra, Betsey Whitman and Donald Cook, 8:3, 1977,
155-161
Stirling's Triangle of the First Kind-Absolute Value Style, Hugh Ouellette and
Gordon Bennett, 8:4, 1977, 195-202, 6.3
An Elementary Construction of the Common Log Tables, James H. Jordan, 8:5,
1977, 274-278
Fractions Without Quotients: Arithmetic of Repeating Decimals, Richard Plagge,
9:1, 1978, 11-15
Applicable Mathematics in Two Year Colleges, Ralph Mansfield, 9:3, 1978,
148-153
Completing the SquareA Laboratory Approach, Charles G. Moore, 9:4, 1978,
215-218
Stirling's Numbers of the Second KindProgramming Pascal's and Stirling's
Triangles, Satish K. Janardan and Konanur G. Janardan, 9:4, 1978, 243-248, 6.3
Some Pre-Calculus Algebra, John Staib, 10:2, 1979, 89-95
The Discovery of a Generalization: An Example in Problem Solving, Hugh
Ouellette and Gordon Bennett, 10:2, 1979, 100-106, 0.3
Polygonal Roots, Barnabas B. Hughes, 10:5, 1979, 313-318, 0.7
Distance from a Point to a Line, Warren B. Gordon, 10:5, 1979, 348-349, C
A Technique for Determining When a General Quadratic Expression is Factorable,
Leo Chosid, 10:5, 1979, 354-355, C, 0.7
Luddhar's Method of Solving a Cubic Equation with a Rational Root, R. S.
Luthar, 11:2, 1980, 107-110, 0.7
Computer Solution of Alphametics, Sarah Brooks, 11:2, 1980, 111-114
Why Not Teach Synthetic Multiplication?, Kenneth R. Kundert, 11:2, 1980,
121-122, C
A Precalculus Approximation of n!, Norman Schaumberger, 11:3, 1980, 202-204, C,
5.4.2
An Error-Detecting Check by Substitution, Charles G. Moore, 11:5, 1980,
326-327, C
A "Proof" that M=N, W. Thurmon Whitley, 12:3, 1981, 211, C
Inventor's Paradox, Man-Keung Siu, 12:4, 1981, 267, C
Misguided Mathematical Maxim-Makers, Betsy Darken Smith, 12:5, 1981, 309-316,
1.2
A Classroom Approach to Pythagorean Triples, Norman Schaumberger, 13:1, 1982,
61-62, C
Selection of a Fair Currency Exchange Rate, Allen J. Schwenk, 13:2, 1982,
154-155, C, 0.8
An Alternate Method for Solving Radical Equations, Bill Bompart, 13:3, 1982,
198-199, C
The Thrills of Abstraction, P. R. Halmos, 13:4, 1982, 243, 1.2
Isomorphisms on Magic Squares, Ali R. Amir-Moez, 14:1, 1983, 48-51, 5.4.1, 9.2,
9.3, 9.4
A Logarithm Algorithm for Four-Function Calculators, David Cusick, 14:4, 1983,
322, 5.3.2
The Address Problem, Michael Tennor, 14:5, 1983, 407-414, 9.3
Approximation of Square Roots, Leon Wejntrob, 14:5, 1983, 427-430, 0.7, 9.6
Antisubmarine Warfare: Passive vs. Active Sonar, L. Whitt and K. Wilk, 14:5,
1983, 434-435, C
Is the Venn Diagram Good Enough?, Mou-Liang Kung and George C. Harrison, 15:1,
1984, 48-50, 9.1
A Geometrical Interpretation of the Weighted Mean, Larry Hoehn, 15:2, 1984,
135-139, 0.4, 7.3
On Problems with Solutions Attainable in More Than One Way, Jean Pedersen and
George Polya, 15:3, 1984, 218-228, 0.4, 5.4.2
Complex Roots Made Visible, Alec Norton and Benjamin Lotto, 15:3, 1984,
248-249, C, 0.7
Pythagorean Systems of Numbers, Joseph Wiener, 15:4, 1984, 324-326, C, 0.4, 9.3
An Approach to Problem-Solving Using Equivalence Classes Modulo n, James E.
Schultz and William F. Burger, 15:5, 1984, 401-405, 9.3
The Factorial Triangle and Polynomial Sequences, Steven Schwartzman, 15:5,
1984, 424-426, C, 5.4.1, 6.3
Right Triangles with Perimeter and Area Equal, William Parsons, 15:5, 1984,
429, C, 0.4
What Do I Know? A Study of Mathematical Self-Awareness, Philip J. Davis, 16:1,
1985, 22-41, 9.3
Nested Polynomials and Efficient Exponential Algorithms for Calculators, Dan
Kalman and Warren Page, 16:1, 1985, 57-60, C, 0.7, 9.6
Behold! The Arithmetic-Geometric Mean Inequality, Roland H. Eddy, 16:3, 1985,
208, C, 0.3
Instances of Simpson's Paradox, Thomas R. Knapp, 16:3, 1985, 209-211, C, 7.3
Approximating Solutions for Exponential Equations, Norman Schaumberger, 16:3,
1985, 211-212, C
Graphing the Complex Roots of a Quadratic Equation, Floyd Vest, 16:4, 1985,
257-261, C , 0.7, 9.5
A New Divisibility Algorithm, Joseph Whittaker, 16:4, 1985, 268-276, 9.3
A Discrete Look at 1 + 2 + ... + n, Loren C. Larson, 16:5, 1985, 369-382, 0.9,
3.1, 3.2, 5.4.2, 6.3
Routine Problems, Sherman Stein, 16:5, 1985, 383-385, 5.1.5, 1.2
A Babylonian Geometrical Algebra, James K. Bidwell, 17:1, 1986, 22-31, 0.3
Irrationality Made Easy, Robert Bumcrot, 17:3, 1986, 243-244, C
The Change of Base Formula for Logarithms, Chris Freiling, 17:5, 1986, 413, C,
5.3.2
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 4.1,
5.1.2, 5.1.5, 5.2.3, 5.2.4, 5.2.5
Behold! The Graphs of f and f inverse are Reflections about the Line y=x, Ayoub
B. Ayoub, 18:1, 1987, 52, C, 5.3.2
Powers and Roots by Recursion, Joseph F. Aieta, 18:5, 1987, 411-416, 0.7, 6.3
FFF #1. The Zero Function, Ed Barbeau, 20:1, 1989, 49-50, F (also 20:2, 1989,
133)
FFF #5.  A Howler about Products of Logarithms, Ed Barbeau, 20:3, 1989, 226, F
(also 20:4, 1989, 318 and 21:3, 1990, 218)
FFF #7. An Exponential Equation, Ed Barbeau, 20:4, 1989, 317, F (also 20:5,
1989, 404)
Quick Function Evaluation, Daniel S. Yates, 21:1, 1990, 51, C, 5.1.5
FFF #25. Solving an Inequality, Ed Barbeau, 21:4, 1990, 303, F
Geometrical and Graphical Solutions of Quadratic Equations, E. John Hornsby,
Jr., 21:5, 1990, 362-369, 0.4
China's 1989 National College Entrance Examination, Bart Braden, 21:5, 1990,
390-393, 0.4, 0.6, 1.2
FFF #38. How to Solve a Quadratic Equation, Ed Barbeau, 22:2, 1991, 132, F
(also 24:4, 1993, 345)
FFF #39. The End Justifies the Mean, Ed Barbeau, 22:3, 1991, 220, F
FFF #40. Perron's Paradox, Ed Barbeau, 22:3, 1991, 221, F, 9.1 (also 23:3,
1992, 205 and 24:3, 1993, 231)
FFF #42. A Characterization of Finite Geometric Sequences, Ed Barbeau, 22:3,
1991, 221, F
Positivity from Evaluation of a Single Point, Henry Mark Smith, 22:3, 1991,
230-231, C, 5.1.5
FFF #46. A Straightforward Cancellation, Ed Barbeau, 22:5, 1991, 403-404, F,
3.2
FFF #49. Two Transcendental Equations, Ed Barbeau, 23:1, 1992, 36, F, 5.3.2
FFF #52. An Application of the Cauchy-Schwartz Inequality, Ed Barbeau, 23:2,
1992, 142, F, 9.5
Infinitely Many Different Quartic Polynomial Curves, Nitsa Movshovitz-Hader and
Alla Shmukler, 23:3, 1992, 186-195, 0.7
The Joy of Mathematics: A Mary P. Dolciani Lecture, Peter Hilton, 23:4, 1992,
274-281, 1.2
A Serendipitous Application of the Pythagorean Triplets, Susan Forman, 23:4,
1992, 312-314, C, 9.3
Commutativity of Polynomials, Shmuel Avital and Edward Barbeau, 23:5, 1992,
386-395, 6.3, 0.7
FFF. Matrices and the TI-81 Graphics Calculator, Constance J. Gardner, 24:1,
1993, 64, F, 4.1
FFF #58. A Rational Combination of Two Transcendentals, Ed Barbeau, 24:3, 1993,
229, F, 5.3.2
FFF #59. A Formula that Works Only for n=1, Ed Barbeau, 24:3, 1993, 229-230, F,
0.9
FFF #60. A Two-Valued Function, Ed Barbeau, 24:3, 1993, 230, F, 5.3.2
FFF #65. Solving a Cubic, Ed Barbeau, 24:4, 1993, 344, F, 0.7
FFF #67. A Superficial Volume Problem, Randall K. Campbell-Wright, 25:1, 1994,
35, F
FFF #70. Reading a Calculator Display, Sandra Z. Keith, 25:1, 1994, 36, F,
5.1.3
Approaches to the Formula for the nth Fibonacci Number, Russell Jay Hendel,
25:2, 1994, 139-142, C, 4.5, 5.4.2, 9.3, 9.5
Extending Bernoulli's Inequality, Ronald L. Persky, 25:3, 1994, 230, C, 9.5
FFF #84. A Method for Solving a Cubic Equation, Ed Barbeau, 26:1, 1995, 35-36, F, 0.7
FFF #86. Watch Your Ears!, Bruce Yoshiwara, 26:1, 1995, 36, F
FFF #87. Do You Know How to Split the Atom?, Milt Eisner, 26:1, 1995, 37, F
The Product of Four (Positive) Numbers in Arithmetic Progression is Always the Difference of Two Squares (Proof Without Words), Roger B. Nelsen, 26:2, 1995, 131, C
A Geometric Approach to Linear Functions, Jack E. Graver, 26:5, 1995, 389-394, C, 0.4, 6.3
FFF #97. A Surd Equation, Ed Barbeau, 27:1, 1996, 45, F (see also 27:3, 1996, 204-205)
FFF #105. The Remainder Theorem, Richard Laatsch, 27:4, 1996, 282, F, 9.4
FFF #113. The Disappearing Solution, Ed Barbeau, 28:2, 1997, 120, F
FFF #120. A Quick (?) Proof of Irrationality, Richard Askey, 28:4, 1997, 286, F
Visualizing the Complex Roots of Quadratics (Proof Without Words), Shaun Pieper, 28:5, 1997, 359, C, 0.7
FFF #124. The Number of Tickets Sold, Robert W. Vallin, 29:1, 1998, 34-35, F
FFF.  Distributing Addition over Multiplication, S. R. S. Sastry, 29:3, 1998, 221, F
FFF #136. Surprising Symmetry, David Wells, 29:5, 1998, 407, F


0.3 		Synthetic geometry

Kepler's explanation of the Timaeus associations, Howard Eves, 1:2, 1970, 31,
C, 2.2
Shapes of the Future, Victor Klee, 2:2, 1971, 14-27, 3.1
Plaited Platonic Puzzles, Jean J. Pedersen, 4:2, 1973, 23-37
Partitions of the Plane, Nathan Hoffman, 5:2, 1974, 71-73, C, 3.1
Some Insight into the Convex Quadrilateral, Benjamin Greenberg, 5:3, 1974,
14-17
A Finite FieldA Finite Geometry and Triangles, Marc Swadener, 5:3, 1974, 22-26,
9.4
Polygons, Both Perfect and Regular, Richard L. Francis, 6:2, 1975, 20-21
Some Consequences of a Property of the Centroid of a Triangle, Norman
Schaumberger, 8:3, 1977, 142-144
Guessing and Proving, George Polya, 9:1, 1978, 21-27
The Discovery of a Generalization: An Example in Problem Solving, Hugh
Ouellette and Gordon Bennett, 10:2, 1979, 100-106, 0.2
Geometry is Alive and Well: The Coxeter Symposium in Toronto, Jean J. Pedersen,
11:1, 1980, 19-25, 1.2
Circles and Spheres, G.D.Chakerian, 11:1, 1980, 26-41
On Sets of Points in the Plane and A Property of the Binomial Coefficients,
Ross Honsberger, 11:2, 1980, 116-119, 9.3
Inscribed Figures of Maximum Area: A Geometric Approach for a Geometric
Problem, Peter Renz, 11:2, 1980, 147-149
The Pentagram and the Discovery of an Irrational Number, James R. Choike, 11:5,
1980, 312-316, 2.2
Euclid's 'Elements' -excerpts from a 1660 edition, 12:2, 1981, 117, 5.3.2,
5.3.3
>From an Inequality to Inversion, Man-Keung Siu, 12:2, 1981, 149-151, C
A Space-Filling Torus, Dan Wheeler and David Sklar, 12:4, 1981, 246-248
An Equal Ratio Property for Convex Polygons, K.R.S.Sastry, 13:4, 1982, 270, C
The Euler Line: A Vector Approach, Norman Schaumberger, 13:5, 1982, 329-331, C
Commadino's Theorem, Norman Schaumberger, 13:5, 1982, 331, C
The Butterfly Problem and Other Delicacies from the Noble Art of Euclidean
GeometryPart I, Ross Honsberger, 14:1, 1983, 2-8, 0.4
The Steiner-Lehmus Theorem as a Challenge problem, Ken Seydel and Carl Newman,
14:1, 1983, 72-75, 0.4, 0.6
Some Unusual Locus Problems, Shephen B. Maurer, 14:2, 1983, 146-153
The Butterfly Problem and Other Delicacies from the Noble Art of Euclidean
GeometryPart 2, Ross Honsberger, 14:2, 1983, 154-158, 0.4
How to Make a Bank Shot, Richard C. Bollinger, 14:2, 1983, 169-170, C
How Big is a Point?, Richard J. Trudeau, 14:4, 1983, 295-300
The Construction of Integral Cevians, Charles G. Moore, 14:4, 1983, 301-308
A Tiling of the Plane with Triangles, Paul T. Mielke, 14:5, 1983, 377-381, 9.2,
9.3
On the Radii of the Inscribed and Escribed Circles of Right TrianglesA Second
Look, Calvin T. Long, 14:5, 1983, 382-389
Ellipses from a Circular and Spherical Point of View, Alden R. Partridge, 14:5,
1983, 436-438, 0.5
Behold! The Arithmetic-Geometric Mean Inequality, Roland H. Eddy, 16:3, 1985,
208, C, 0.2
The International Mathematical Olympiad Training Session, Cecil Rousseau and
Gregg Patruno, 16:5, 1985, 362-365, 2.2, 9.3
A Babylonian Geometrical Algebra, James K. Bidwell, 17:1, 1986, 22-31, 0.2
Three Ways to Maximize the Area of an Inscribed Quadrilateral, Leroy F. Meyers,
17:3, 1986, 238-239, 5.5
Behold! The Vertex Angles of a Star Sum to 180 degrees, Fouad Nakhli, 17:4,
1986, 338, C
Geometry of the Rational Plane, Larry Cannon, 17:5, 1986, 392-402
The Geometric Supposer: An Intellectual Prosthesis for Making Conjectures,
Judah L. Schwartz and Michal Yerushalmy, 18:1, 1987, 58-65, 0.10
The Generalized Polygonal Cycloid, Duane W. DeTemple, 19:5, 1988, 417-419, C
Equality in Overlapping Gravitational Fields, Howard K. Justice, 20:1, 1989,
27-31
Pythagorean Theorem: aa' + bb' = cc', Enzo R. Gentile, 20:1, 1989, 58, C
Hippocrates and Archytas Double the Cube: A Heuristic Interpretation, Barnabas
B. Hughes, 20:1, 1989, 42-48, 2.1
FFF #2. The Steiner-Lehmus Theorem, Ed Barbeau, 20:1, 1989, 50, F (also 20:2,
1989, 133 and 21:3, 1990, 218)
Surface Area of a Cone, Herb Holden, 20:5, 1989, 432, C
FFF #23. A Luney Way to Square the Circle, Ed Barbeau, 21:4, 1990, 302-303, F
(also 22:1, 1991, 41 and 22:5, 1991, 405)
Trisection of an Angle in an Infinite Number of Steps, Eric Kincanon, 21:5,
1990, 393, C
FFF #27. Trisecting an Angle with Ruler and Compasses, Ed Barbeau, 21:5, 1990,
394-395, F (also 22:1, 1991, 41 and 23:2, 1992, 143)
Two Surprising Theorems on Cavalieri Congruence, Howard Eves, 22:2, 1991,
118-124, 2.2
A Theorem about Right Triangles, Roland H. Eddy, 22:5, 1991, 420, C
Misconceptions about the Golden Ratio, George Markowsky, 23:1, 1992, 2-19, 2.1,
2.2
Geometry: A Gateway to Understanding, Peter Hilton and Jean Pedersen, 24:4,
1993, 298-317, 9.3
A "Very Pleasant Theorem", Roger Herz-Fischler, 24:4, 1993, 318-324, 2.2
The Geometer's Sketchpad and Cabri-Geometre (software review), Dennis DeTurck,
24:4, 1993, 370-376, 0.4, 0.10
Two Trisectrices for the Price of One Rolling Coin, Jack Eidswick, 24:5, 1993,
422-430, 0.4, 9.7
Tangents to Conics, Eccentrically, Frederick Gass, 25:1, 1994, 43-45, C, 0.5
Kepler Orbits More Geometrico, Andrew Lenard, 25:2, 1994, 90-98, 5.5
A Three-Circle Theorem, R. S. Hu, 25:3, 1994, 211, C
Nothing New Under the Sun (The "Three-Circle Theorem"), H. Guggenheimer, 26:1, 1995, 10
FFF. The Spirit Is Willing But the Ham Is Rotten, John Kinloch and Rick Norwood, 26:1, 1995, 37, F
Functions of a Curve: Leibniz's Original Notion of Functions and Its Meaning for the Parabola, David Dennis and Jere Confrey, 26:2, 1995, 124-131, 0.5, 2.2
Angle Trisection by Fixed Point Iteration, L. F. Martins and I. W. Rodrigues, 26:3, 1995, 205-208, 9.6
FFF #89. A Case of Irregularity, Herb Bailey, 26:3, 1995, 221-222, F ( see also 27:4, 1996, 284)
Inductive Tiling of the Plane by Penrose Aperiodic Rhombi (by picture), Dean Clark and E. R. Suryanarayan, 26:4, 1995, 266-267, C
The 9-Point Circle Is in Fact a 12-Point Circle (by picture), Jingcheng Tong and Sidney H. Kung, 26:5, 1995, 371, C
Volume of a Frustrum of a Square Pyramid (Proof Without Words), S. H. Kung, 27:1, 1996, 32, C
Geometry Class (Peom), JoAnne Growney, 27:2, 1996, 143, C
The Moise Plane, James R. Boone, 27:3, 1996, 182-185, 9.7
Behold: The Pythagorean Theorem, Frank Burk, 27:5, 1996, 407, C
A Concurrency Theorem and Geometer's Sketchpad, Larry Hoehn, 28:2, 1997, 129-132, C
Tiling with Squares and Parallelograms (proof by picture), Alfinio Flores, 28:3, 1997, 171, C
Putting the Pieces Together: Understanding Robinson's Nonperiodic Tilings, Aimee Johnson and Kathleen Madden, 28:3, 1997, 172-181, 3.3
FFF.  The Pup Tent Problem, Ed Barbeau, 29:3, 1998, 220-221, F
A Law of Sines (proof without words), Sidney H. Kung, 29:3, 1998, 221, C
Prelude to Musical Geometry, Brian J. McCartin, 29:5, 1998, 354-370, 9.4, 9.7


0.4		Analytic geometry

An Interesting Practical Application of Solid Analytic Geometry, W.K.Viertel,
9:5, 1978, 273-275
Geometry via Physics, Ross Honsberger, 10:4, 1979, 271-276
Distance from a Point to a Line, K.R.S.Sastry, 12:2, 1981, 146-147, C
A Classroom Approach to x^2 + y^2 + z^2 = w^2, Norman Schaumberger, 12:5, 1981,
331-332, C
An Application of Convex Coordinates, J.N.Boyd and P.N.Raychowdhury, 14:4,
1983, 348-349, C
An Analytic Approach to the Euler Line, Johathan W. Lewin, 15:1, 1984, 52-53, C
The Fractal Geometry of Mandelbrot, Anthony Barcellos, 15:2, 1984, 98-114, 9.8
A Geometrical Interpretation of the Weighted Mean, Larry Hoehn, 15:2, 1984,
135-139, 0.2, 7.3
On Problems with Solutions Attainable in More Than One Way, Jean Pedersen and
George Polya, 15:3, 1984, 218-228, 0.2, 5.4.2
Proving Heron's Formula Tangentially, David E. Dobbs, 15:3, 1984, 252-253, C,
0.6
Pythagorean Systems of Numbers, Joseph Wiener, 15:4, 1984, 324-326, C, 0.2, 9.3
Distance From a Point to a Line, Abdus Sattar Gazdar, 15:4, 1984, 328-329, C
Right Triangles with Perimeter and Area Equal, William Parsons, 15:5, 1984,
429, C, 0.2
A Nonstandard Solution to a Standard Problem, Florence S. Gordon, 17:1, 1986,
74, C
Angling for Pythagorean Triples, Dan Kalman, 17:2, 1986, 167-168, C, 9.3
Geometric Parametrization of Pythagorean Triples, Alvin Tirman, 17:2, 1986,
168, C
Three Ways to Maximize the Area of an Inscribed Quadrilateral, Leroy F. Meyers,
17:3, 1986, 238-239, 5.5
A Pretrigonometry Proof of the Reflection Property of the Ellipse, Zalman P.
Usiskin, 17:5, 1986, 418, C
Behold! The Pythagorean Theorem via Mean Proportions, Michael Hardy, 17:5,
1986, 422, C
Drawing the Line Segment Connecting Two Points, Harley Flanders, 18:1, 1987,
53-57, 3.3, 8.1
Heron's Area Formula, Roger C. Alperin, 18:2, 1987, 137-138, C
Equiangular Lattice Polygons and Semiregular Lattice Polyhedra, Paul R. Scott,
18:4, 1987, 300-306
A Rational Approach to Lattice Polygons, Warren Page, 18:4, 1987, 316-317, C
Some Properties of Polygons Inside a Circle, Larry Hoehn, 18:5, 1987, 397-401
Newton's nth Root Method Without Derivatives, David A. Smith, 18:5, 1987,
403-406, C, 0.7
An Unexpected Appearance of the Golden Ratio, George Manuel and Amalia
Santiago, 19:2, 1988, 168-170, C, 5.1.1
Behold! Two Extremum Problems and the Arithmetic-Geometric Mean Inequality,
Paolo Montuchi and Warren Page, 19:4, 1988, 347, C, 5.1.4
The Generalized Polygonal Cycloid, Duane W. DeTemple, 19:5, 1988, 417-419, C
Pythagorean Theorem: aa' + bb' = cc', Enzo R. Gentile, 20:1, 1989, 58, C
FFF #3. Tangency by Double Roots, Ed Barbeau, 20:2, 1989, 132, F (also 20:3,
1989, 227)
To View an Ellipse in Perspective, Charles G. Moore, 20:2, 1989, 134-136, C,
0.5
The Root Mean SquareArithmetic MeanGeometric MeanHarmonic Mean Inequality,
Roger B. Nelsen, 20:3, 1989, 231, C, 9.5
On the Radial Packing of Circles in the Plane, P. D. Weidman and K. Pfendt,
21:2, 1990, 112-120, 9.7
Harmonic, Geometric, Arithmetic, Root Mean Inequality, Sidney Kung, 21:3, 1990,
227, C, 9.5
Triangles with Integer Sides and Sharing Barrels, David Singmaster, 21:4, 1990,
278-285, 9.3
Geometrical and Graphical Solutions of Quadratic Equations, E.John Hornsby,
Jr., 21:5, 1990, 362-369, 0.2
China's 1989 National College Entrance Examination, Bart Braden, 21:5, 1990,
390-393, 0.2, 0.6, 1.2
Triquetras and Porisms, Dana N. Mackenzie, 23:2, 1992, 118-131
Optimal Locations, Bennett Eisenberg and Samir Khabbaz, 23:4, 1992, 282-289,
3.1, 9.9
Single Equations Can Draw Pictures, Keith M. Kendig, 22:2, 1991, 134-139, C,
0.5, 5.1.5, 5.6.1, 5.6.2
Investigating Spirolaterals Through LOGO, William Fisher and Richard Campbell,
22:2, 1991, 148-159
Triangles in a Lattice Parabola, K.R.S.Sastry, 22:4, 1991, 301-306
FFF #66. An Equilateral Property of Altitudes, Ed Barbeau, 24:4, 1993, 344, F
The Geometer's Sketchpad and Cabri-Geometre (software review), Dennis DeTurck,
24:4, 1993, 370-376, 0.3, 0.10
Two Trisectrices for the Price of One Rolling Coin, Jack Eidswick, 24:5, 1993,
422-430, 0.3, 9.7
A Geometrical Exploration Concluded, James N. Boyd and P.N.Raychowdhury, 25:2,
1994, 155-156
Cutting Corners: A Four-gon Conclusion, S. C. Althoen and K. E. Schilling and M. F. Wyneken, 25:4, 1994, 266-279, 0.5, 9.5
The Arithmetic Mean-Geometric Mean Inequality (Proof by Picture), Sidney H. Kung, 26:1, 1995, 38, C
A Geometric Approach to Linear Functions, Jack E. Graver, 26:5, 1995, 389-394, C, 0.2, 6.3
How to Kick a Field Goal, Daniel C. Isaksen, 27:4, 1996, 267-271
An Application of Elementary Geometry in Functional Analysis, Ji Gao, 28:1, 1997, 39-42, 9.5
Area and Perimeter, Volume and Surface Area, Jingcheng Tong, 28:1, 1997, 57, C, 5.1.3
The Arithmetic Mean - Geometric Mean Inequality (proof by picture), Sidney H. Kung, 28:2, 1997, 88, C
A Stronger Triangle Inequality, Herbert R. Bailey and Robert Bannister, 28:3, 1997, 182-186
Paths of Minimum Length in a Regular Tetrahedron, Richard A. Jacobson, 28:5, 1997, 394-397, C, 5.7.1
The Brahmagupta Triangles, Raymond A. Beauregard and E. R. Surynarayan, 29:1, 1998, 13-17, 9.3
A Sharp Triangle Inequality, Murray S. Klamkin, 29:1, 1998, 33, C
Geometric Characterization of the Shortest Path in a Tetrahedron, Sergey Markelov, 29:2, 1998, 150-151, C


0.5		Conic sections

A Simple Proof of the Reflection Property for Parabolas, R.H.Cowen, 7:2, 1976,
59-60, C, 5.1.3
Three-D Pictures from Your Computer-Linked Plotter, Charles John Acker and Joe
Frank Allison, 9:5, 1978, 303-308
An Ellipse Problem Beyond the Reach of Calculus, Ivan Niven, 10:3, 1979,
162-168, 0.6
Stories in Combinatorial Geometry, Ross Honsberger, 10:5, 1979, 344-347, 3.2
The Curve Parallel to a Parabola is not a Parabola: Parallel Curves, F. Max
Stein, 11:4, 1980, 239-246, 0.7
An Analytic Geometry Approach to the Least Squares Line of Best Fit, Stewart
Venit and Richard Katz, 11:4, 1980, 270-272, 7.3
Conic Section or Degenerate FormA Simple Test, Stewart Venit, 11:5, 1980,
316-319
Generalized Cycloids: Discovery via Computer Graphics, Sheldon P. Gordon, 13:1,
1982, 22-27
Chords of the Parabola, Herb Holden, 13:3, 1982, 186-190
Roots of Polynomials and Loci, Ali R. Amir-Moez, 14:4, 1983, 313-317, 5.6.1
Ellipses from a Circular and Spherical Point of View, Alden R. Partridge, 14:5,
1983, 436-438, 0.3
Deriving the Equations of the Ellipse and Hyperbola, John C. Huber and Joseph
Wiener, 15:1, 1984, 58-59, C
Reflection Property of the Ellipse and the Hyperbola, Michael K. Brozinsky,
15:2, 1984, 140-142, C
Geometric Procedures for Graphing the General Quadratic Equation, Duane W.
DeTemple, 15:4, 1984, 313-323, 0.7
Constructing the Foci and Directrices of a Given Ellipse, Charles G. Moore,
16:2, 1985, 122-128
Area of a Parabolic Region, R. Rozen and A. Sofo, 16:5, 1985, 400-402, C, 5.2.6
A Pretrigonometry Proof of the Reflection Property of the Ellipse, Zalman P.
Usiskin, 17:5, 1986, 418, C, 0.4
FFF #4. Area of an Ellipse, Ed Barbeau, 20:2, 1989, 132-133, F, 5.6.1 (also
20:3, 1989, 227)
To View an Ellipse in Perspective, Charles G. Moore, 20:2, 1989, 134-136, C,
0.4
Moire Fringes and the Conic Sections, M. R. Cullen, 21:5, 1990, 370-378, 5.7.1
Single Equations Can Draw Pictures, Keith M. Kendig, 22:2, 1991, 134-139, C,
0.4, 5.1.5, 5.6.1, 5.6.2
A Carpenter's Ellipse, Elliot Winston, 22:4, 1991, 311-312, C
Stacking Ellipses, Richard E. Pfiefer, 22:4, 1991, 312-313, C
Visualization of Limits and Limits of Visualization: Student Research Projects,
Lee H. Minor, 23:1, 1992, 48-51, 0.4, 5.1.3
Rotation of AxexNot Just for Conics, Steven Schonefeld, 23:5, 1992, 418-425,
5.6.1
FFF #59. A Puzzling Graph, Richard L. Francis, 24:1, 1993, 63, F
Stacking Ellipses Revisited, Calvin Jongsma, 24:5, 1993, 453, C
Tangents to Conics, Eccentrically, Frederick Gass, 25:1, 1994, 43-45, C, 0.3
Isaac Newton: Credit Where Credit Won't Do, Robert Weinstock, 25:3, 1994, 179-192, 2.2, 5.1.3, 5.4.3, 5.6.1
Newton's Orbit Problem: A Historian's Response, Curtis Wilson, 25:3, 1994, 193-200, 2.2, 6.4
In Defense of Newton: A Physicist's View, A. P. French, 25:3, 1994, 206-209, 2.2, 5.6.1
Newton's Principia and Inverse-Square Orbits, N. Nauenberg, 25:3, 1994, 212-221, 2.2, 6.4, 6.5
Robert Weinstock's Response to Nauenberg, Robert Weinstock, 25:3, 1994, 221-222, 2.2
Cutting Corners: A Four-gon Conclusion, S. C. Althoen and K. E. Schilling and M. F. Wyneken, 25:4, 1994, 266-279, 0.4, 9.5
Functions of a Curve: Leibniz's Original Notion of Functions and Its Meaning for the Parabola, David Dennis and Jere Confrey, 26:2, 1995, 124-131, 0.3, 2.2
Cylinder and Cone Cutting, Michael R. Cullen, 28:2, 1997, 122-123, C
Doughnut Slicing, Wolf von Ronik, 28:5, 1997, 381-383, C, 5.6.2


0.6 		Trigonometry (also see 5.3)

Factoring Functions, J.C.Bodenrader, 2:1, 1971, 23-26, 5.1.2, 3.2, 9.1
An Interesting Correspondence and Its Consequence, Sidney Penner, 2:1, 1971,
40-44
Pascal's Triangle, Karl J. Smith, 4:1, 1973, 1-13, 3.2, 9.2
A "Doodling" Inequality, Benjamin Greenberg, 4:1, 1973, 78-79, C
A Classroom Theorem on Trigonometric Irrationalities, Norman Schaumberger, 5:1,
1974, 73-76, C
Square Functions, Helmer Junghans, 5:2, 1974, 15-18, 0.7
A Set of Trigonometric Inequalities with Applications to Maxima and Minima,
Norman Schaumberger, 5:3, 1974, 26-30, 5.1.4
A Generator of Trigonometric Identities, Aron Pinker, 5:4, 1974, 54-55, C
Mathematical Astronomy, Vincent J. Motto, 6:1, 1975, 21-26
Closing the Loopholes, Morton Bloomfield and Frank Lasak, 6:2, 1975, 42-44, C
An Interesting Use of Generating Functions, Aron Pinker, 6:4, 1975, 39-45,
5.4.2, 9.5
Closing the Loopholes in "Closing the Loopholes", Gene Zirkel, 7:3, 1976,
55-58, C
Another Note on "Closing the Loopholes", Larry F. Bennett, 7:3, 1976, 56-58, C
Quasi-Pythagorean Triples for an Oblique Triangle, Kay Dundas, 8:3, 1977,
152-155, 9.3
Geometric Proofs of the Formulas for Sin(x+y) and Cos(x+y), Norman
Schaumberger, 10:1, 1979, 35, C
An Ellipse Problem Beyond the Reach of Calculus, Ivan Niven, 10:3, 1979,
162-168, 0.5
Why Can't We Trisect an Angle This Way?, David Beran, 10:3, 1979, 199-200, C
Products of Sines, Zalman Usiskin, 10:5, 1979, 334-340
Geometric Interpretations of Sin(phi1)+Sin(phi2)=1, Charles Muses, 10:5, 1979,
350-351, C
A Formula for Sin (A+B), Simon J. Lawrence, 11:2, 1980, 125-126, C
Formulas for sin(x+y) and cos(x+y), Robert Geist, 11:2, 1980, 126, C
Trigonometric Solutions to the Quadratic Equation, Leo Chosid, 11:5, 1980,
330-331, C
A Coordinate Geometry Evaluation of ABS(tan(A-B)), Norman Schaumberger, 12:1,
1981, 52-54, C
Applying Complex Arithmetic, Herbert L. Holden, 12:3, 1981, 190-194, 5.3.1,
9.3, 9.5
Visual Application of Sin(theta1 + theta2) = Sin(theta1)Cos(theta2) +
Cos(theta1)Sin(theta2), Gerald E. Gannon, 12:3, 1981, 206, C
Sum Formulas for Sine and Cosine, Dan Kalman, 14:1, 1983, 55-56, C
The Steiner-Lehmus Theorem as a Challenge Problem, Ken Seydel and Carl Newman,
14:1, 1983, 72-75, 0.4
Approximation to an Angle Trisection, Glen Peterson, 14:2, 1983, 166-167, C
Integer-Sided Triangles with One Angle Twice Another, R.S.Luthar, 15:1, 1984,
5-56, C, 9.3
Proving Heron's Formula Tangentially, David E. Dobbs, 15:3, 1984, 252-253, C,
0.4
Approximate Angle Trisection, David Gauld, 15:5, 1984, 420-422, C, 5.4.2
Generalized Pythagorean Triples, W.J.Hildebrand, 16:1, 1985, 48-52, 5.5, 9.3
Pitfalls in Graphical Computation, or Why a Single Graph Isn't Enough, Franklin
Demana and Bert K. Waits, 19:2, 1988, 177-183, 5.1.5
The Fundamental Periods of Sums of Periodic Functions, James Caveny and Warren
Page, 20:1, 1989, 32-41, 9.5
The Double-Angles Formulas, Roger B. Nelsen, 20:1, 1989, 51, C
Lattices of Trigonometric Identities, Willeam E. Rosenthal, 20:3, 1989,
232-234, C, 5.2.3
Where There is Pattern, There is Significance, Lloyd Olson, 20:4, 1989, 321, C
FFF #11. A New Trigonometric Identity, Ed Barbeau, 20:5, 1989, 404, F (also
22:2, 1991, 132-133)
(Sin x)^2: A Sheep in Wolf's Clothing, Mark E. Saul, 21:1, 1990, 43-44, C,
5.1.5
FFF #18. Glide-Reflection to Sine Curve, Ed Barbeau, 21:3, 1990, 216, F
China's 1989 National College Entrance Examination, Bart Braden, 21:5, 1990,
390-393, 0.2, 0.4, 1.2
Trigonometric Identities through Calculus, Herb Silverman, 21:5, 1990, 403, C,
5.3.1
A Productive Error in a Trigonometry Text, Lee H. Minor, 22:4, 1991, 315-318, C
FFF #54. A Degree of Differentiation, Ed Barbeau, 23:3, 1992, 203, F, 5.1.3
(also 23:4, 1992, 306 and 24:4, 1993, 345)
FFF.  A 21-41-50 Triangle, Ed Barbeau, 23:4, 1992, 304, F
Cos(s-t) from the Distance Formula, Gilbert Strang, 23:4, 1992, 333, C
The Half-Angle Formula for Cotangent, Fen Chen, 23:5, 1992, C
The Half-Angle Formulas for the Tangent, Sidney H. Kung, 25:3, 1994, 205, C
A Simple Geometric Proof of the Addition Formula for the Sine, Jeffrey Li-chieh Ho, 25:3, 1994, 229-230, C
An Early Iterative Method for the Determination of Sine of One Degree, Farhad Riahi, 26:1, 1995, 16-21, 2.1
cos(x+y) (Proof Without Words), Sidney H. Kung, 26:2, 1995, 145, C
The Double-Angle Formulas via the Laws of Sines and Cosines, Sidney H. Kung, 27:2, 1996, 155, C
A Complex Approach to the Laws of Sines and Cosines, William V. Grounds, 27:2, 1996, 108, C, 9.5
A Law of Cosines (Proof Without Words), S. H. Kung and Jingcheng Tong, 27:3, 1996, 219, C
FFF #122. On Not Identifying Equations and Identities, Richard Askey, 28:5, 1997, 377-379, F
Trigonometric Identity: The Difference of Two Sines or Two Cosines (proof without words), Yukio Kubayashi, 29:2, 1998, 133, C
Trigonometric Identity: The Sum of Two Sines or Two Cosines (proof without words), Yukio Kubayashi, 29:2, 1998, 157, C
Undersampled Sine Waves, J. C. Derderian and Enriqueta Rodriguez-Carrington, 29:3, 1998, 213-218, 5.1.5
FFF #130. Forces with a Given Resultant, Don Curran, 29:4, 1998, 301-302, F
FFF #133. Identifying the Angle, K. R. S. Sastry, 29:5, 1998, 405-406, F



0.7 		Elementary theory of equations

Maximize x(a-x), L.H.Lange, 5:1, 1974, 22-24, 0.2, 5.1.4
Square Functions, Helmer Junghans, 5:2, 1974, 15-18, 0.6
Investigations of Linear and Reciprocal Functions by the Line-to-Line
Technique, David R. Duncan and Bonnie H. Litwiller, 6:2, 1975, 2-7, 0.2
A Precalculus Unit on Area Under Curves, Samuel Goldberg, 6:4, 1975, 29-35,
5.4.2
Several Hyperbolic Encounters, L.H.Lange, 7:1, 1976, 2-6
Identities, Inequalities and Equations: A Computer-Graphical Approach, Thomas
M. Green, 7:1, 1976, 33-37
Finding Super Accurate Integers, Pasquale Scopelliti and Herbert Peebles, 7:3,
1976, 52-54, 0.2, 9.6
Can This Polynomial Be Factored?, Harold L. Dorwart, 8:2, 1977, 67-72, 9.4
Polygonal Roots, Barnabas B. Hughes, 10:5, 1979, 313-318, 0.2
Luddhar's Method of Solving a Cubic Equation with a Rational Root, R.S.Luthar,
11:2, 1980, 107-110, 0.2
Continued Fractions and Iterative Processes, Jean H. Bevis and Jan L. Boal,
13:2, 1982, 122-127, 9.5
Approximation of Square Roots, Leon Wejntrob, 14:5, 1983, 427-430, 0.2, 9.6
Complex Roots Made Visible, Alec Norton and Benjamin Lotto, 15:3, 1984,
248-249, C, 0.2
Nested Polynomials and Efficient Exponential Algorithms for Calculators, Dan
Kalman and Warren Page, 16:1, 1985, 57-60, C, 0.2, 9.6
Graphing the Complex Roots of a Quadratic Equation, Floyd Vest, 16:4, 1985,
257-261, C, 0.2, 9.5
Transitions, Jeanne L. Agnew and James R. Choike, 18:2, 1987, 124-133, 5.1.3,
5.6.1, 9.10
Newton's nth Root Method Without Derivatives, David A. Smith, 18:5, 1987,
403-406, C, 0.4
Powers and Roots by Recursion, Joseph F. Aieta, 18:5, 1987, 411-416, 0.2, 6.3
Parameter-generated Loci of Critical Points of Polynomials, F. Alexander
Norman, 19Z:3, 1988, 223-229, 5.1.5, 9.5
Graphing the Complex Zeros of Polynomials Using Modulus Surfaces, Cliff Long
and Thomas Hern, 20:2, 1989, 98-105, 9.5, 5.1.5
Finding Rational Roots of Polynomials, Don Redmond, 20:2, 1989, 139-141, C, 9.3
A Zero-Row Reduction Algorithm for Obtaining the gcd of Polynomials, Sidney H.
Kung and Yap S. Chua, 21:2, 1990, 138-141, 4.1, 9.4
Algorithms for Evaluation of Polynomials, J.J.Price, 21:5, 1990, 404-405, C
Reading Bombelli's x-purgated Algebra, Abraham Arcavi and Maxim Bruckheimer,
22:3, 1991, 212-219, 2.2
Euler and the Fundamental Theorem of Algebra, William Dunham, 22:4, 1991,
282-293, 2.2
Infinitely Many Different Quartic Polynomial Curves, Nitsa Movshovitz-Hader and
Alla Shmukler, 23:3, 1992, 186-195, 0.2
Commutativity of Polynomials, Shmuel Avital and Edward Barbeau, 23:5, 1992,
386-395, 0.2, 6.3
Individualized Computer Investigations for Calculus, Sheldon P. Gordon, 23:5,
1992, 426-428, C, 5.1.4, 5.1.5
FFF #65. Solving a Cubic, Ed Barbeau, 24:4, 1993, 344, F, 0.2
Roots of Cubics via Determinants, Robert Y. Suen, 25:2, 1994, 115-117, 4.2
FFF #84. A Method for Solving a Cubic Equation, Ed Barbeau, 26:1, 1995, 35-36, F, 0.2
A Genuine Application of Synthetic Division, Descartes' Rule of Signs, and All That Stuff, Dwight D. Freund, 26:2, 1995, 106-110, 0.8
The Hyperbolic Number Plane, Garret Sobczyk, 26:4, 1995, 268-280, 9.5
Critical Points of Polynomial Families, Elias Y. Deeba, Dennis M. Rodriquez, and Ibrahim Wazir, 27:4, 1996, 291-295, C, 5.1.5
Newton's Method for Resolving Affected Equations, Chris Christensen, 27:5, 1996, 330-340, 5.1.2, 5.4.3
Bounding the Roots of Polynomials, Holly P. Hirst and Wade T. Macey, 28:4, 1997, 292-295, C, 5.1.5
Visualizing the Complex Roots of Quadratics (Proof Without Words), Shaun Pieper, 28:5, 1997, 359, C, 0.2
Who Cares if X2 + 1 = 0 Has a Solution?, Viet Ngo and Saleem Watson, 29:2, 1998, 141-144, C, 5.2.5, 5.4.2, 6.2
A Simple Solution of the Cubic, Dan Kalman and James White, 29:5, 1998, 415-418, C


0.8 		Business mathematics

A Question of Interest, Ann D. Holley, 9:2, 1978, 81-83
Classroom Applications of the Inexpensive Hand-Held Calculator, Bert K. Waits,
9:3, 1978, 162-166
Algorithms for Finding Maturity Value in Compound Interest Problems, Jane I.
Robertson, 9:4, 1978, 249-251, C
Another Question of Interest, Stanley G. Wayment, 11:4, 1980, 252-254
Compounding Energy Savings, Leo Chosid, 12:1, 1981, 56-57, C
Guessing and AlgorithmA Case for Interpolation, Denis R. Lichtman, 12:3, 1981,
199-203
Selection of a Fair Currency Exchange Rate, Allen J. Schwenk, 13:2, 1982,
154-155, C, 0.2
Income Tax Averaging and Convexity, Michael Henry and G.E.Trapp, Jr., 15:3,
1984, 253-255, 5.1.5, 5.7.1, 9.5
Income Averaging Can Increase your Tax Liability, Gino T. Fala, 16:1, 1985,
53-55, C, 9.5
Both a Borrower and a Lender Be, William Miller, 16:4, 1985, 284, C, 6.1
Arithmetic Progression and the Consumer, John D. Baildon, 16:5, 1985, 395-397,
C, 5.4.1
A Case of True Interest, Soo Tang Tan, 17:3, 1986, 247-248, C, 5.4.2
A Hidden Case of Negative Amortization, Bert K. Waits and Franklin Demana,
21:2, 1990, 121-126, 6.3
FFF. Dollars and Sense, Stuart E. Mills, 24:5, 1993, 446-448, F
A Genuine Application of Synthetic Division, Descartes' Rule of Signs, and All That Stuff, Dwight D. Freund, 26:2, 1995, 106-110, 0.7
How Much Money Do You (or Your Parents) Need for Retirement?, James W. Daniel, 29:4, 1998, 278-283, 7.2
How Much Should You Pay for a Derivative?, Bennett Eisenberg, 29:5, 1998, 412-414, C

 
0.9		Techniques of proof (including mathematical induction)

Good Induction versus Bad Induction, from Howard Eves, 1:2, 1970, 16, C
If...Some Suggestions on Presenting the Connector "if...then", Aaron Seligman,
1:2, 1970, 22-26, 9.1
Some Applications of the Law of the Contrapositive, Morton J. Hellman, 4:3,
1973, 86-88, C, 9.1
Mathematical Induction: If Student k Understands It, Will Student k + 1?,
Judith L. Gersting, 6:2, 1975, 18-20, 0.2
The Well-Ordering Principle as an Alternative to Mathematical Induction in Our
Lower Division Recursive Formula Proofs, Orrin G. Cocks, 7:1, 1976, 13-14
A Helpful Device: or One More Use for Pascal's Triangle, Robert Rosenfeld, 8:3,
1977, 188-191, C, 5.4.2
A Note on the Principle of Mathematical Induction, Charles M. Bundrick and
David L. Sherry, 9:1, 1978, 17-18
Mathematical Induction, or "What Good is All This Stuff if We Are Going to
Assume It's True Anyway?", Leonard G. Swanson and Rodney T. Hansen, 12:1, 1981,
8-12
A Discrete Look at 1 + 2 + ... + n, Loren C. Larson, 16:5, 1985, 369-382, 0.2,
3.1, 3.2, 5.4.2, 6.3
A Division Game: How Far Can You Stretch Mathematical Induction?, William H.
Ruckle, 18:3, 1987, 212-218, 3.2, 9.9
Behold! (1x2)+(2x3)+ . . . +nx(n+1) = (1/3)([(n+1)^3 - (n+1)], Ali R.
Amir-Moez, 18:4, 1987, 318, C
Sum of Squares (Proof by Picture), Pi-Chun Chuang, 20:2, 1989, 123, C
Product of k^k times k! (Proof by Picture), Edward T. A. Wang, 20:2, 1989, 152,
C
Sum of Squares (Proof by Picture), Sidney H. Kung, 20:3, 1989, 205, C
FFF. Equal Integers, Ed Barbeau, 22:2, 1991, 133, F (also 23:1, 1992, 38)
FFF. Four Weighings, Ed Barbeau, 22:2, 1991, 133, F
FFF #45. All Powers of x are Constant, Ed Barbeau, 22:5, 1991, 403, F, 5.1.2
FFF #59. A Formula that Works Only for n=1, Ed Barbeau, 24:3, 1993, 229-230, F,
0.2
FFF. Which Balls are Actually There?, Ruma Falk, 26:1, 1995, 37, F
Count the Dots: 1+2+...+n = [n(n+1)]/2 (proof by picture), S. J. Farlow, 26:3, 1995, 190, C
Sum of Alternating Series (proof by picture), Guanshen Ren, 26:3, 1995, 213, 5.4.2
FFF #92. An Inductive Fallacy, Adrian Riskin and William Stein, 26:5, 1995, 382, F
MAD Property of Medians: An Induction Proof, Eugene F. Schuster, 26:5, 1995, 387-389, C, 7.3
FFF #94. Every Second Square is the Same, Allen J. Schwenk, 27:1, 1996, 44, F
FFF #103. Polynomial Detection, Ed Barbeau, 27:2, 1996, 118, F
FFF #118. Rabbits Reproduce; Integers Don't, Annie and John Selden, 28:4, 1997, 285, F
FFF #119. Yet Another Perplexing Proof by Induction, P. D. Johnson and Martin Schlam, 28:4, 1997, 285-286, F
Weighing Coins: Divide and Conquer to Detect a Counterfeit, Mario Martelli and Gerald Gannon, 28:5, 1997, 365-367, 3.3
A Discrete Intermediate Value Theorem, Richard Johnsonbaugh, 29:1, 1998, 42, C, 3.3


0.10		Software for precalculus mathematics

A Mathematics Software Database, R.S.Cunningham and David A. Smith, 17:3, 1986,
255-266, 3.4, 4.8, 5.8, 6.7, 7.4, 9.11
The Geometric Supposer: An Intellectual Prosthesis for Making Conjectures,
Judah L. Schwartz and Michal Yerushalmy, 18:1, 1987, 58-65, 0.3
A Mathematics Software Database Update, R.S.Cunningham and David A. Smith,
18:3, 1987, 242-247, 3.4, 4.8, 5.8, 6.7, 7.4, 9.11
The Compleat Mathematics Software Database, R.S.Cunningham and David A. Smith,
19:3, 1988, 268-289, 3.4, 4.8, 5.8, 6.7, 7.4, 9.11
Mathematics by Machine with Mathematica@, Alan Hoenig, 21:2, 1990, 146-149
IBM Software for Finite Mathematics, Part I, Joan Wyzkoski Weiss, 22:3, 1991,
248-254
Derive@, A Mathematical Assistant, Jeanette R. Palmiter, 23:2, 1992, 158-161
IBM Software for Finite Mathematics, Part II, Joan Wyzkoski Weiss, 23:3, 1992,
241-246
The Geometer's Sketchpad and Cabri-Geometre (software review), Dennis DeTurck,
24:4, 1993, 370-376, 0.3, 0.4
Converge, Version 4.0 (Software Review), Lawrence G. Gilligan, 26:1, 1995, 58-63, 5.8
Toolkit for Interactive Mathematics, review by L. Carl Leinbach, 26:2, 1995, 152-156, 5.8
Software Review: f(g) Scholar, David C. Arney and Daniel J. Arney, 26:5, 1995, 401-403, 4.8, 5.8
EXP, Version 3.02 for Windows, Jon Wilkin, 27:1, 1996, 68-73, 9.11


1	Mathematics Education

1.1		Teaching techniques and research reports

A Statistical Analysis of Multiple-Choice Examinations in Mathematics, Bert K.
Waits and Larry C. Elbrink, 1:1, 1970, 25-29
Programmed Instruction in Elementary Algebra: An Experiment, Margaret L. Lial,
1:2, 1970, 17-21
New Results of Research Comparing Programmed and Lecture-Text Instruction,
Maurice E. Nott, 2:1, 1971, 19-22
Two-Year College Faculty Participation in Professional Mathematics
Organizations, John B. Davis and T.J.Pignani, 2:1, 1971, 53-57
An Experiment in Teaching Elementary Algebra, Donald Perry, 2:2, 1971, 40-46
The Crossover Mathematics Program at Milwaukee Area Technical College, Keith J.
Roberts and Leo E. Michels, 2:2, 1971, 47-50
A Design for Class Testing Mathematics Textbook Materials, Karl G. Zahn, 3:2,
1972, 29-32
Academic Qualifications of North Carolina's Community College Professors,
Phillip E. Johnson, 3:2, 1972, 33-36
Do Students Learn From and Like An Audio-Tutorial Course in Freshman
Mathematics?, Peter M. Wilson, 3:2, 1972, 37-41
A Look at That 1971 MAA Information Services Survey, Lester H. Lange, 3:2,
1972, 56-69
The Effects of a Laboratory on Achievement in College Freshman Mathematics,
Cameron Douthitt, 4:1, 1973, 55-59
Student Evaluation of Mathematics Instruction, Bert K. Waits and Larry C.
Elbrink, 4:2, 1973, 59-66
A Study: Using CUPM Recommendations As Criteria of the Academic Preparation of
Two-Year College Teachers, Donald Perry, 4:2, 1973, 67-71
Achievement, Aptitude and Attitude in Mathematics, Anthony N. Behr, 4:2, 1973,
72-74
An Audio-Tutorial Method of Instruction vs. the Traditional Lecture-Discussion
Method, Shelba Jean Morman, 4:3, 1973, 56-61
The Contract Method vs. the Traditional Method of Teaching Developmental
Mathematics to Underachievers: A Comparative Analysis, Wayne L. Miller, 5:2,
1974, 45-49
Some Research Support for A Second Chance for Beginning Algebra Students, Paul
W. Merritt, 5:2, 1974, 50-54
A Mastery Approach to Mathematical Literacy, Judith Harle Hector, 6:2, 1975,
22-27
Research and Development of Synchronized Slide-Tape Units for a Mathematics
Laboratory, Eddie R. Williams and Harold W. Mick, 7:2, 1976, 28-33
Flow Charts in Mathematics Classes for Elementary School Teachers, Janet E.
Ford and Douglas B. McLeod, 8:1, 1977, 15-19
A Look at General Education Mathematics Programs, Charles D. Friesen, 9:4,
1978, 218-221
Developing Skills in College AlgebraA Mastery Approach, William E. Haver, 9:4,
1978, 282-287
The Two-Year Colleges and the Graduate Schools: The Teachers' Perspective,
Robert McKelvey, 10:2, 1979, 136
1978 AMS Survey: Two-Year College Report, Wendell Fleming, 10:2, 1979, 143
1979 AMS Survey: Two-Year College Report, Wendell Fleming, 11:3, 1980, 222
A Classroom Experiment Involving Basic Mathematics and Women, Pansy Waycaster
Brunson, 14:4, 1983, 318-324
What Makes Mathematics Lessons Easy to Follow, Understand, and Remember?, Nira
Hativa, 14:5, 1983, 398-406
Collegiate Mathematics Education Research: What Would That Be Like?, Annie
Selden and John Selden, 24:5, 1993, 431-445
Graphing Calculators in Calculus, Anita E. Solow, 25:3, 1994, 235-239
Asking Good Questions about Differential Equations, Paul Davis, 25:5, 1994, 394-400, 1.2, 6.1
Assessing the Quantitative Skills of College Juniors, Steven F. Bauman and William O. Martin, 26:3, 1995, 214-220
The Mathematical Judge: A Fable, William G. Frederick and James R. Hersberger, 26:5, 1995, 377-381, 0.1


1.2		Courses and programs

First-Year MathematicsA Challenging Variable, June P. Wood, 1:1, 1970, 8-13
The Summer Developmental Mathematics Program at Kalamazoo Valley Community
College, Fred Toxopeus, 1:1, 1970, 14-16
An Integrated Physics-Calculus Course, Herbert D. Peckham, 1:1, 1970, 17-24
Progress Report on Articulation in Illinois, R. David Gustafson and Arnold
Wendt, 1:1, 1970, 37-40
Junior College Cooperative Program in Colorado, James C. Davis and Ralph H.
Niemann, 1:1, 1970, 41-43
The Use of the Computer in Mathematics Instruction, Albert E. Hickey, 1:1,
1970, 44-54
A New Graduate Degree for Mathematics Teachers, Jon M. Laible, 1:1, 1970, 55-58
A Curriculum Suggestion for Teaching College Arithmetic, Stanley Schmidt, 1:1,
1970, 92
Remedial or Developmental? Confusion over Terms, Don Ross, 1:2, 1970, 27-31,
0.1
Who's Committed? Who's Involved?, Carol Kipps, 1:2, 1970, 32-35
Mini-Math: A Progam of Short Courses, Larry D. Carter, 1:2, 1970, 36-38
Calculus and the Computer: An Evaluation by Participants, Gary G. Bitter, 1:2,
1970, 41-49
Two-Year Colleges and Post-Secondary Education in Western Europe, Ralph
Mansfield, 1:2, 1970, 50-55
Spring Retreat for Community College Mathematics Teachers in Washington, Phil
Heft and Charles Ainley, 1:2, 1970, 56-57
Lower Columbia College Mathematics Laboratory, Richard Spangler, 2:1, 1971,
27-31
Calculus as an Experimental Science, R.P.Boas, 2:1, 1971, 36-39
Mathematics for the Undergraduate Physics Major, Mary L. Boas, 2:1, 1971, 49-52
Committing Curricular Heresy, Paul Lawrisuk, 2:1, 1971, 58-64
Calculus and the ComputerCRICISAM, William Stark, 2:2, 1971, 51-54
The MAA and the Mathematics Teacher in the Two-Year College, Joseph Hashisaki,
2:2, 1971, 63-68
The Fredonia Plan for Preparing Two-Year College Teachers, Charles R. Colvin,
2:2, 1971, 69-73
Basic Mathematics for Collegesthe CUPM Recommendations, J.A.Jones, 2:2, 1971,
87-94
"Sample" Tests for Students, June P. Wood, 3:1, 1972, 14-15
Developmental Mathematics: Self-Instruction with Mathematics Laboratory, Joanna
S. Burris and Lee Schroeder, 3:1, 1972, 16-22
Conference Proceedings: Teaching Mathematics to Occupational and Developmental
Students, Lawrence L. Mitchell, 3:1, 1972, 42-47
The Mathematics Laboratory and the Single Student, Ralph C. Williams, 4:1,
1973, 40-47
A Doctorate for the Two-Year College Instructor?, H. Vernon Price, 4:1, 1973,
48-50
Group-Based Instruction: The Best Chance for Success?, John Wagner and Howard
Jones, 4:1, 1973, 51-54
Another Challenge in the Classroom, Jack M. Robertson, 4:2, 1973, 48-54
A Flexible Response to Open Admissions, Anthony Giangrasso, 4:2, 1973, 55-58
Mathematics for the Captured Student, S.K.Stein, 4:3, 1973, 62-71
The Man-Made World: Cultural vs. Remedial Mathematics, Ralph Mansfield, 5:1,
1974, 9-21
Innovative Evaluation, Margaret Maxfield, 5:1, 1974, 47-52
A Bibliography of Literature: Mathematics Education in the Junior and Community
Colleges, Nancy F. Carter and Marc Swadener, 5:1, 1974, 53-59
Improving General Education Mathematics, William Mitchell, 5:2, 1974, 32-38
Nonlab, Nonprogrammed, and Nonlecture: Any Chance?, Donald R. Horner, 5:2,
1974, 39-41
Mini-Calculus, Joseph C. Bodenrader, 5:2, 1974, 74, C
Pills: Mathematics Instructional Models, Louise Dyson and Edward B. Wright,
5:3, 1974, 31-33
Logic: A Logical Elective, William M. Setek Jr., 5:3, 1974, 39-40
Bubbles, Frank O. Armbruster and Jean J. Pedersen, 5:3, 1974, 34-38
A Working Model for Inservice Training, Michael A. Topper, 5:4, 1974, 16-17
A Suggested Recruiting Project: Math Contests, Donald Perry and Wayne L.
Miller, 5:4, 1974, 19-21
A Doctor's Degree for Community College TeachersWhy?, Lewis H. Coon, 5:4, 1974,
22-26
Instructional Videocassettes in Mathematics, Bert K. Waits, 5:4, 1974, 27-30
Survival of the Two-Year College Mathematics Teacher, Peter A. Lindstrom, 6:1,
1975, 11-13
Leonardo, His Rabbits and Other Curiosa, Clyde A. Bridger, 6:1, 1975, 14-20
Factoring Functions and Relations, Thomas J. Brieske, 6:3, 1975, 8-12, 9.4
Note on Teaching the Implication, David Beran, 6:3, 1975, 18-19
MathematicsIs It Any of Your Business?, Ralph Mansfield, 6:3, 1975, 20-26, 9.1,
3.1
A Survey of Mathematics Programs, Nancy F. Carter, 6:4, 1975, 14-16
Small Groups: An Alternative to the Lecture Method, Julian Weissglass, 7:1,
1976, 15-20
A Search for Trends Among Mathematics Programs in Small Colleges, Andrew
Sterrett, 7:1, 1976, 21-23
A New Approach for Computer Mathematics, Clifford L. Conrad and Nancy J. Conrad
and Harry B. Higley, 7:2, 1976, 34-39
Functional NotationAn Intuitive Approach, Ann D. Holley, 7:3, 1976, 14-15, 0.2
History in the Mathematics Curriculum, Gerald E. Lenz, 7:3, 1976, 27-28
The Open University, Helen B. Siner, 7:3, 1976, 28-32
Modularizing Liberal Arts Mathematics: An Experiment, William F. Steger and
Gretchen Willging, 7:3, 1976, 33-37
Basic Algebra in a Balanced Lecture-Program Format, Corrinne J. Brase and
Charles H. Brase, 7:4, 1976, 13-17
The Doctor of Arts Degree in Mathematics:  University of Illinois at Chicago
Circle, Irwin K. Feinstein, 7:4, 1976, 18-20
Getting the Students Involved in the Elementary Statistics Course, Larry J.
Stephens, 8:1, 1977, 19-21
Discovery Method Algebra at the University of Washington, Square Partee and
Eric Halsey, 8:1, 1977, 27-29
The Community College Basic Mathematics Course, Barbara J. Lederman, 8:1, 1977,
29-35
What's It Good for?, Nancy F. Carter, 8:2, 1977, 79-80
The Sequencing of Instructional Activities in Written Materials, Donald Cohen,
8:2, 1977, 81-87
The Construction and Uses of CATIA, a Computerized Mathematics Testbank,
Charles R. Burton and Wanda A Marosz, 8:4, 1977, 212-216
A Transfer Level Computer Calculus Sequence, Robert C. Sanger, 8:4, 1977,
216-218
Two Factors Involved in Successful Individualized Mathematics Programs, Michael
E. Greenwood, 8:4, 1977, 219-222
Why and How to Use Small Groups in the Mathematics Classroom, Judith L. Gersing
and Joseph E. Kuczkowski, 8:5, 1977, 270-274
A Rational Approach to Fractions, John Pace, 9:3, 1978, 154-158
Introductory Mathematics and the Adult Woman Student, Carolyn T. MacDonald,
9:3, 1978, 158-161
Experiment and Conjecture in Mathematics: A Discovery Course for College
Freshmen and Sophomores, Benjamin Burrell and Jessie Ann Engle and Henry C.
Nixt, 9:4, 1978, 210-215
The Role of the Instructor in the Individualized Classroom, Gail B. Mounteer
and Robert J. Cermele, 9:4, 1978, 276-281
The Anatomy of the Stupid Error, Charles G. Moore, 9:4, 1978, 309-310, C.
Exams Can Leverage Learning, Warren Page, 10:1, 1979, 38, C.
HomeworkA Problem with a Solution, Alban J. Roques, 10:2, 1979, 116, C
Mathematics in Seventeen Three-Hour Lessons: A Challenge, Ann D. Holley, 10:3,
1979, 191-192
More on Guessing and Proving, George Polya, 10:4, 1979, 255-258
Jazz, Literature, and the Teaching of Mathematics, Ralph P. Boas, 10:4, 1979,
264-265
Questions in the RoundAn Effective Barometer of Understanding, Warren Page,
10:4, 1979, 278-279, C
Super Bat Meets the Word Problem, Dave Logothetti, 10:5, 1979, 371
Geometry is Alive and Well: The Coxeter Symposium in Toronto, Jean J. Pedersen,
11:1, 1980, 19-25, 0.3
Applications of Intermediate Algebra: A Possible Alternative, J. Michael
Shaughnessy, 11:2, 1980, 94-101
Math Anxiety: Some Suggested Causes and Cures: Part 1, Peter Hilton, 11:3,
1980, 174-188
Math Anxiety: Sume Suggested Causes and Cures: Part 2, Peter Hilton, 11:4,
1980, 246-251
Mathematics by Fiat?, Philip J. Davis, 11:4, 1980, 255-263
Fixed Point IterationAn Interesting Way to Begin a Calculus Course, Thomas
Butts, 12:1, 1981, 2-7, 5.1.1, 9.6
Mathematical Proof: What It Is and What It Ought to Be, Peter Renz, 12:2, 1981,
83-103
A Digression on Proof, Yu I. Manin, 12:2, 1981, 104-107
The Nature of Proof: Limits and Opportunities, Kenneth Appel and Wolfgang
Haken, 12:2, 1981, 118-119
Computer Use to Computer Proof: A Rational Reconstruction, Thomas Tymoczko,
12:2, 1981, 120-125
Teachers, Clocks, and Students, Sherman K. Stein, 12:3, 1981, 195-198
Shouldn't We Teach GEOMETRY?, Branko Grunbaum, 12:4, 1981, 232-237
The Thrills of Abstraction, P.R.Halmos, 13:4, 1982, 243-251, 0.2
A First Course in Continuous Simulation, Richard Bronson, 13:5, 1982, 300-310,
9.10
Imbedding the Metric, John D. Neff, 14:3, 1983, 197-202
Toward a Common Understanding of the Content of College Preparatory
Mathematics, Joan R. Leitzel, 14:3, 1983, 206-209
Nonnumeric Computer Applications to Algebra, Trigonometry, and Calculus, David
R. Stoutemyer, 14:3, 1983, 233-239
SSD Persistence: A Mathematical System for Student Investigation, John
Scheding, 14:4, 1983, 309-312, 9.3
Integrating Writing into the Mathematics Curriculum, Dorothy Goldberg, 14:5,
1983, 421-424
Zork, RAMS and the Curse of Ra: Computo, ergo sum, Curt Suplee, 15:2, 1984,
158-159
Will Discrete Mathematics Surpass Calculus in Importance?, Anthony Ralston,
15:5, 1984, 371-373
Responses to: Will Discrete Mathematics Surpass Calculus, Saunders MacLane and
Daniel H. Wagner and Peter J. Hilton and R. L. Woodriff and Daniel J. Kleitman
and Peter D. Lax, 15:5, 1984, 373-380
The Introductory Mathematics Curriculum: Misleading, Outdated, and Unfair, Fred
Roberts, 15:5, 1984, 383-385
Responses to the Introductory Mathematics Curriculum, William F. Lucas and
R.W.Hamming and David Tall and Robert E. Davis and Wade Ellis, Jr. and Patrick
Thompson and John Mason and Richard K. Guy, 15:5, 1984, 386-397
FORUM: The Algorithmic Way of Life is Best, Stephen B. Maurer, 16:1, 1985, 2-5
Responses to the FORUM on the Algorithmic Way of Life, R.G.Douglas and Bernhard
Korte and Peter Hilton and Peter Renz and Craig Smorynski and J.M.Hammersley
and P.R.Halmos, 16:1, 1985, 5-21
Testing Understanding and Understanding Testing, Jean Pedersen and Peter Ross,
16:3, 1985, 178-185, 0.2, 5.1.2, 5.2.2
Routine Problems, Sherman Stein, 16:5, 1985, 383-385, 0.2, 5.1.5
Interactive Graphics for Multivariable Calculus, Michael E. Frantz, 17:2, 1986,
172-181, 5.1.1, 5.1.4, 5.7.1
A Mathematics Software Database, R.S.Cunningham and David Smith, 17:3, 1986,
255-266
Computer Algebra Systems in Undergraduate Mathematics, Don Small, John Hosack
and Kenneth Lane, 17:5, 1986, 423-433, 5.1.4, 5.1.5, 5.2.2, 5.4.2
Should Mathematicians Teach Statistics?, David S. Moore, 19:1, 1988, 3-7, 7.3
Should Mathematicians Teach Statistics (2)?, A. Blanton Godfrey, 19:1, 1988,
8-11, 7.3
No! But Who Should Teach Statistics?, Judith Tanur, 19:1, 1988, 11-12, 7.3
Statistics Teachers need Experience With Data, R. Gnanadesikan and
J.R.Kettenring, 19:1, 1988, 12-14, 7.3
The Mathematicians' Statistics Has a Subsidiary Role, Barbara A. Bailar, 19:1,
1988, 14-15, 7.3
Growth and Advances in Statistics, Frederick Mosteller, 19:1, 1988, 15-16, 7.3
Statistician, Examine Thyself: Response, Gudmund R. Iversen, 19:1, 1988, 16-18,
7.3
It's Not "By Whom" But Rather "How", John E. Freund, 19:1, 1988, 18-19, 7.3
The Need for Good Teaching of Statistics, Henry L. Alder, 19:1, 1988, 20-21,
7.3
Let the Experts Teach and Judge, David L. Hanson, 19:1, 1988, 21-24, 7.3
Who Teachers What to Whom?, Michail Reed, 19:1, 1988, 24-26, 7.3
What Should the Introductory Statistics Course Contain?, Gerald J. Hahn, 19:1,
1988, 26-30, 7.3
Mathematics is Only One Tool that Statisticians Use, Ronald D. Snee, 19:1,
1988, 30-32, 7.3
Reaction to Responses to "Should Mathematicians Teach Statistics?", David S.
Moore, 19:1, 1988, 32-35, 7.3
Readers' Responses to the January 1988 Forum: "Should Mathematicians Teach
Statistics?", Joseph B. Kadane and William A. Golomsky and Daniel A. Sankowsky
and Benjamin M. Perles, 19:2, 1988, 164-165, 7.3
A Computer in the Classroom: The Time is Right, David P. Kraines and David A.
Smith, 19:3, 1988, 261-267
Teaching with CAL: A Mathematics Teaching and Learning Environment, James E.
White, 19:5, 1988, 424-443, 5.1.5
The Simplex Method of Linear Programming on Microcomputer Spreadsheets, Frank
S. T. Hsiao, 20:3, 1989, 153-160, 9.9
Copyright Law As It Applies to Computer Software, Michael Gemignani, 20:4,
1989, 332-338
Learning Mathematics Through Writing: Some Guidelines, J.J.Price, 20:5, 1989,
393-401
Notational Collisions, J. Hillel, 20:5, 1989, 418-422, C, 4.1
Graphing with the HP-28S, John Selden and Annie Selden, 20:5, 1989, 423-432,
5.1.5
Sum the Alternating Harmonic Series, Dave P. Kraines and Vivian Y. Kraines and
David A. Smith, 20:5, 1989, 433-435, C, 5.4.2
Taylor Polynomials, David P. Kraines and Vivian Y. Kraines and David A. Smith,
20:5, 1989, 435-436, C, 5.4.2
Calculus Quiz, David P. Kraines and Vivian Y. Kraines and David A. Smith, 20:5,
1989, 437-438, C, 5.1.5
What's an Assignment Like You Doing in a Course Like This? Writing to Learn
Mathematics, George D. Gopen and David A. Smith, 21:1, 1990, 2-19
Let's Teach Philosophy of Mathematics!, Reuben Hersh, 21:2, 1990, 105-111
Proofs by -Tion, John S. Robertson, 21:3, 1990, 220-222, C
Student Research Projects: Self-esteem in Mathematics, Herbert S. Wilf, 21:4,
1990, 274-277, 9.3
Recruitment and Retention of Students in Undergraduate Mathematics, Miriam P.
Cooney and Jacqueline M. Dewar and Patricia Clark Kenschaft and Vivian Kraines
and Brenda Latka and Barbara LiSanti, 21:4, 1990, 294-301
A Mathematical Field Day, S.C.Althoen and M.F.Wyneken, 21:5, 1990, 379-383
China's 1989 National College Entrance Examination, Bart Braden, 21:5, 1990,
390-393, 0.2, 0.4, 0.6
Forward Homework, Raymond A. McGivney, 21:5, 1990, 400-402, C
Teaching about Fractals, Stephen J. Willson, 22:1, 1991, 56-59
Physical Demonstrations in the Calculus Classroom, Tom Farmer and Fred Gass,
23:2, 1992, 146-148, C, 5.2.1, 6.1
The Joy of Mathematics: A Mary P. Dolciani Lecture, Peter Hilton, 23:4, 1992,
274-281, 0.2
How Should We Introduce Integration?, David M. Bressoud, 23:4, 1992, 296-298,
5.2.1
Gems of Exposition in Elementary Linear Algebra, David Carlson and Charles R.
Johnson and David Lay and A. Duane Porter, 23:4, 1992, 299-303, 4.1, 4.5, 4.7
Studying Students Studying Calculus: A Look at the Lives of Minority
Mathematics Students in College, Uri Treisman, 23:5, 1992, 362-372
The Growing Importance of Linear Algebra in Undergraduate Mathematics, Alan
Tucker, 24:1, 1993, 3-9
Teaching Linear Algebra: Must the Fog Always Roll In?, David Carlson, 24:1,
1993, 29-40, 4.1
The Linear Algebra Curriculum Study Group Recommendations for the First Course
in Linear Algebra, David Carlson and Charles R. Johnson and David C. Lay and A.
Duane Porter, 24:1, 1993, 41-46, 4.1, 4.3, 4.2, 4.5
A Computer Lab for Multivariate Calculus, Casper R. Curjel, 24:2, 1993,
175-177, C, 5.7.1, 8.3
Old Calculus Chestnuts: Roast, or Light a Fire?, Margaret Cibes, 24:3, 1993,
241-243, C, 5.1.4
Great Problems of Mathematics: A Summer Workshop for High School Students,
Reinhard C. Laubenbacher and Michael Siddoway, 25:2, 1994, 112-114
A Note from the Guest Editor and other ODE Resources, Beverly H. West, 25:5, 1994, 362-363
New Directions in Elementary Differential Equations, William E. Boyce, 25:5, 1994, 364-371, 6.2, 6.4
What It Means to Understand A Differential Equation, John H. Hubbard, 25:5, 1994, 372-384, 6.1, 6.2, 6.4
Teaching Differential Equations with a Dynamical Systems Viewpoint, Paul Blanchard, 25:5, 1994, 385-393, 6.1, 6.2, 6.4
Asking Good Questions about Differential Equations, Paul Davis, 25:5, 1994, 394-400, 1.1, 6.1
The Computer-oriented Calculus Course at Rensselaer Polytechnic Institute, William E. Boyce and Joseph G. Ecker, 26:1, 1995, 45-50
Mathematics Education: A Case for Balance, George E. Andrews, 27:5, 1996, 341-348
Mathematics Education: A Response to Andrews, David M. Mathews, 27:5, 1996, 349-353
George Andrews Replies, George Andrews, 27:5, 1996, 354-355
Is Mathematics Necessary?, Underwood Dudley, 28:5, 1997, 360-364


2	History of Mathematics

2.1		History of mathematics before 1400

The origin of our word "sine", Howard Eves, 1:1, 1970, 93, C
On the origin of ">" and "<", Howard Eves, 1:1, 1970, 94, C
The Genesis and Development of Set Theory, Phillip E. Johnson, 3:1, 1972, 55-62
An Informal History of Formal Proofs: From Vigor to Rigor?, Klaus Galda, 12:2,
1981, 126-140
Hippocrates and Archytas Double the Cube: A Heuristic Interpretation, Barnabas
B. Hughes, 20:1, 1989, 42-48, 0.3
Misconceptions about the Golden Ratio, George Markowsky, 23:1, 1992, 2-19
The Algorists vs. the Abacists: An Ancient Controversy on the Use of
Calculators, Barbara E. Reynolds, 24:3, 1993, 218-223
An Early Iterative Method for the Determination of Sine of One Degree, Farhad Riahi, 26:1, 1995, 16-21, 0.6
Did Plutarch Get Archimedes' Wishes Right?, Lester H. Lange, 26:3, 1995, 199-204, 5.2.7


2.2		History of mathematics after 1400 

The History of the Calculus, Carl B. Boyer, 1:1, 1970, 60-86
Kepler's Explanation of the Timaeus Associations, Howard Eves, 1:2, 1970, 31,
C, 0.3
Mathematics of the Yoruba People and of Their Neighbors in Southern Nigeria,
Claudia Zaslavsky, 1:2, 1970, 76-79
Terminology: logarithm, Howard Eves, 2:2, 1971, 27, C
Mathematician, Violinist, FencerBolyai, Howard Eves, 3:1, 1972, 41, C
How Gauss was Won to Mathematics, Howard Eves, 3:1, 1972, 65, C
Eighteenth Century British Mathematics, Phillip E. Johnson, 7:2, 1976, 22-27
A Brief History of Logarithms, R.C.Pierce, Jr., 8:1, 1977, 22-26
Women Mathematicians, Debra Charpentier, 8:2, 1977, 73-79
Martin Gardner: Defending the Honor of the Human Mind, Irving Joshua Matrix,
10:4, 1979, 227-244
The Pentagram and the Discovery of an Irrational Number, James R. Choike, 11:5,
1980, 312-316, 0.3
On the History and Solution of the Four-Color Map Problem, John Mitchem, 12:2,
1981, 108-119, 3.1
An Informal History of Formal Proofs: From Vigor to Rigor?, Klaus Galda, 12:2,
1981, 126-140
The Universal Domination of Geometry, J. Dieudonne, 12:4, 1981, 227-231
Structure vs. Substance: The Fall and Rise of Geometry, Robert Osserman, 12:4,
1981, 239-246
A Profile of Ronald L. Graham, Gina Bari Kolata, 12:5, 1981, 290-301
A Machine as Smart as God, Rudy Rucker, 13:2, 1982, 115-121, 9.1
Paul Halmos: Maverick Mathologist, Donald J. Albers, 13:4, 1982, 226-242
John Horton Conway: Mathematical Magus, Richard K. Guy, 13:5, 1982, 290-299
The Thread, Philip J. Davis, 14:2, 1983, 98-104
Solomon Lefschetz: A Reminescence, Albert W. Tucker, 14:3, 1983, 225-227
A Glimpse at the Polya Picture Album, G.L.Alexanderson, 14:4, 1983, 274-294
Shiing-shen Chern: A Man and His Times, Willian G. Chinn and John Lewis, 14:5,
1983, 370-376
A Historical Sketch of Olympiads: USA and International, Nura D. Turner, 16:5,
1985, 330-335
The International Mathematical Olympiad Training Session, Cecil Rousseau and
Gregg Patruno, 16:5, 1985, 362-365, 0.3, 9.3
The Autobiography of Julia Robinson, Constance Reid, 17:1, 1986, 2-21
Teaching Elementary Probability through its History, Sharon Kunoff and Sylvia
Pines, 17:3, 1986, 210-219, 7.2
The Bernoullis and the Harmonic Series, William Dunham, 18:1, 1987, 18-23,
5.4.2
Charlotte Angas Scott 1858-1931, Patricia C. Kenschaft, 18:2, 1987, 98-110
Isaac Newton: Man, Myth, and Mathematics, V. Frederick Rickey, 18:5, 1987,
362-389
Evolution of the Function Concept: A Brief Survey, Israel Kleiner, 20:4, 1989,
282-300, 9.5
FFF #12. The Authority of the Written Word, Ed Barbeau, 20:5, 1989, 404, F
The Function sin x / x, William B. Gearhart and Harris S. Shultz, 21:2, 1990,
90-99, 5.1.2, 5.1.5
The Birth of the Eotvos Competition, Agnes Arvai Wieschenberg, 21:4, 1990,
286-293, 9.3
Two Surprising Theorems on Cavalieri Congruence, Howard Eves, 22:2, 1991,
118-124, 0.3
Reading Bombelli's x-purgated Algebra, Abraham Arcavi and Maxim Bruckheimer,
22:3, 1991, 212-219, 0.7
Euler and the Fundamental Theorem of Algebra, William Dunham, 22:4, 1991,
282-293, 0.7
Misconceptions about the Golden Ratio, George Markowsky, 23:1, 1992, 2, 0.3
The Algorists vs. the Abacists: An Ancient Controversy on the Use of
Calculators, Barbara E. Reynolds, 24:3, 1993, 218-223
A "Very Pleasant Theorem", Roger Herz-Fischler, 24:4, 1993, 318-324, 0.3
Euler and Differentials, Anthony P. Ferzola, 25:2, 1994, 102-111, 5.1.3
Isaac Newton: Credit Where Credit Won't Do, Robert Weinstock, 25:3, 1994, 179-192, 0.5, 5.1.3, 5.4.3, 5.6.1
Newton's Orbit Problem: A Historian's Response, Curtis Wilson, 25:3, 1994, 193-200, 0.5, 6.4
In Defense of Newton: His Biographer Replies, Richard S. Westfall, 25:3, 1994, 201-205, 5.4.3
In Defense of Newton: A Physicist's View, A. P. French, 25:3, 1994, 206-209, 0.5, 5.6.1
Robert Weinstock Replies, Robert Weinstock, 25:3, 1994, 209-211
Newton's Principia and Inverse-Square Orbits, N. Nauenberg, 25:3, 1994, 212-221, 0.5, 6.4, 6.5
Robert Weinstock's Response to Nauenberg, Robert Weinstock, 25:3, 1994, 221-222, 0.5
Leibniz and the Spell of the Continuous, Hardy Grant, 25:4, 1994, 291-294, 9.5
An Invitation to Integration in Finite Terms, Elena Anne Marchisotto and Gholam-Ail Zakeri, 25:4, 1994, 295-308, 5.2.4, 5.2.5, 5.2.9
Functions of a Curve: Leibniz's Original Notion of Functions and Its Meaning for the Parabola, David Dennis and Jere Confrey, 26:2, 1995, 124-131, 0.3, 0.5


2.3     	Interviews

George Polya, Interviewed on His Ninetieth Birthday, G.L.Alexanderson, 10:1,
1979, 13-19
An Interview with Morris Kline: Part 1, G.L.Alexanderson, 10:3, 1979, 172-178
A Conversation with Martin Gardner, Anthony Barcellos, 10:4, 1979, 233-244
An Interview with Morris Kline: Part 2, G.L.Alexanderson, 10:4, 1979, 259-264
An Interview with H.S.M.Coxeter, Dave Logothetti, 11:1, 1980, 2-19
An Interview with Constance Reid, G.L.Alexanderson, 11:4, 1980, 226-238
An Interview with Stan Ulam, Anthony Barcellos, 12:3, 1981, 182-189
An Interview with Paul Erdos, G.L.Alexanderson, 12:4, 1981, 249-259
A Conversation with Don Knuth: Part I, Donald J. Albers and Lynn Arthur Steen,
13:1, 1982, 2-18
A Conversation with Don Knuth, Part 2, Donald J. Albers and Lynn Arthur Steen,
13:2, 1982, 128-141
John G. Kemeny: Computer Pioneer, Lynn Arthur Steen, 14:1, 1983, 18-35
A Conversation with Garrett Birkhoff, G.L.Alexanderson and Carroll Wilde, 14:2,
1983, 126-145
An Interview with Albert W. Tucker, Stephen B. Maurer, 14:3, 1983, 210-214
An Interview with Herbert Robbins, Warren Page, 15:1, 1984, 2-24
A Conversation with Henry Pollak, Donald J. Albers and Michael J. Thibodeaux,
15:3, 1984, 194-219
An Interview with the 1985 USA Team to the International Mathematical Olympiad,
Warren Page, 16:5, 1985, 336-360
An Interview with George B. Dantzig: The Father of Linear Programming, Donald
J. Albers and Constance Reid, 17:4, 1986, 292-304, 9.6
An Interview with Lipman Bers, Donald J. Albers and Constance Reid, 18:4, 1987,
266-290
An Interview with Mary Ellen Rudin, Donald J. Albers and Constance Reid, 19:2,
1988, 114-137
A Conversation with Saunders Mac Lane, Gerald L. Alexanderson, 20:1, 1989, 2-26
A Conversation with Robin Wilson, D.J.Albers and G.L.Alexanderson, 21:3, 1990,
178-195
Interview with Irving Kaplansky, Donald J. Albers, 22:2, 1991, 98-117
A Conversation with Ivan Niven, Donald J. Albers and G.L.Alexanderson, 22:5,
1991, 370-402
A Conversation with Leon Bankoff, G.L.Alexanderson, 23:2, 1992, 98-117
A Conversation with Richard K. Guy, Donald J. Albers and Gerald L.
Alexanderson, 24:2, 1993, 122-148
Freeman Dyson: Mathematician, Physicist, and Writer, Donald J. Albers, 25:1,
1994, 2-21
Still Questioning Authority: An Interview with Jean Taylor, Don Albers, 27:4, 1996, 250-266
An Interview with Tom Apostol, Donald J. Albers, 28:4, 1997, 250-270
An Interview with Lars V. Ahlfors, Donald J. Albers, 29:2, 1998, 82-92
In Love with Geometry, Dan Pedoe, 29:3, 1998, 170-188



3 	Discrete Mathematics
 
3.1 		Graph theory

Shapes of the Future, Victor Klee, 2:2, 1971, 14-27, 0.3
Topological Regular Solids, Stewart S. Cairns, 4:1, 1973, 74-76, C
Partitions of the Plane, Nathan Hoffman, 5:2, 1974, 71-73, C, 0.3
MathematicsIs It Any of Your Business?, Ralph Mansfield, 6:3, 1975, 20-26, 1.2,
9.1
The Game of Sprouts, Gordon D. Prichett, 7:4, 1976, 21-25, 9.2
Binary Grids and a Related Counting Problem, Nathan Hoffman, 9:4, 1978,
267-272, 6.3
The Pigeonhole Principle, Kenneth R. Rebman, 10:1, 1979, 3-13, 9.3
Who Stole the Apples and The Sticks?, Ross Honsberger, 10:1, 1979, 30-32, 3.3
The Challenge of Classifying Polyhedra, Jean J. Pedersen, 11:3, 1980, 162-173
(also 18:5, 1987, 410)
An Application of Turan's Theorem, Ross Honsberger, 11:3, 1980, 196-200
On the History and Solution of the Four-Color Map Problem, John Mitchem, 12:2,
1981, 108-119. 2.2
Chain Letters: A Poor Investment Unless..., David J. Thuente, 13:1, 1982,
28-35, 7.2
Semi-Regular Lattice Polygons, Ross Honsberger, 13:1, 1982, 36-44, 9.3
Computer-Generated Knight Tours, Michael Gilpin, 13:4, 1982, 252-259, 3.3, 9.2
Labeling of Graphs, J.L.Brenner, 14:1, 1983, 36-41
Connect-It Games, Frank Harry and Robert W. Robinson, 15:5, 1984, 411-419, 9.2
Realization of Parity Visits in Walking a Graph, Robert C. Bugham and Ronald D.
Dutton and Phyllis Z. Chinn and Frank Harary, 16:4, 1985, 280-282, C
A Discrete Look at 1 + 2 + ... + n, Loren C. Larson, 16:5, 1985, 369-382, 0.2,
0.9, 3.2, 5.4.2, 6.3
Trees and Tennis Rankings, Curtis Cooper, 17:1, 1986, 76-78, C, 3.2
Coloring Points in the Unit Square, Charles H. Jepsen, 17:3, 1986, 231-237,
5.1.4
Combinatorics by Coin Flipping, Joel Spencer, 17:5, 1986, 407-412, 3.2, 7.2
Facility Location Problems, Fred Buckley, 18:1, 1987, 24-32, 9.10
One Factorization of Graphs: Tournament Applications, W.D.Wallis, 18:2, 1987,
116-123
How to Define an Irregular Graph, Gery Chartrand and Paul Erdos and Ortrud B.
Oellermann, 19:1, 1988, 36-42
Constructing a Map from a Table of Intercity Distances, Richard J. Pulskamp,
19:2, 1988, 154-163, 4.5, 9.10
Are Graphs Finally Surfacing?, Lowell W. Beineke, 20:3, 1989, 206-225
The Number of Paths in a Rooted Binary Tree of Infinite Height, Roger H. Marty,
21:4, 1990, 305-307, C
Using Euler's Formula to Solve Plane Separation Problems, Thomas L. Moore,
22:2, 1991, 125-130, 3.2
Graceful Graphs and Sparsely Marked Rulers: Student Research Projects, L.R.King
and Harold B. Reiter, 22:3, 1991, 232-234
Optimal Locations, Bennett Eisenberg and Samir Khabbaz, 23:4, 1992, 282-289,
0.4, 9.9
Graphs, Matrices, and Subspaces, Gilbert Strang, 24:1, 1993, 20-28, 4.1, 4.3
The Linear Transformation Associated with a Graph: Student Research Project,
Irl C. Bivens, 24:1, 1993, 76-78, 4.3, 9.1
Using PROLOG in Discrete Mathematics, Antonio M. Lopez, Jr., 24:4, 1993,
357-365, 3.4, 9.1
Independent Sets and the Golden Ratio, William Staton and Clifton Wingard, 26:4, 1995, 292-296
A Combinatorial Queueing Model, Shahar Boneh and David C. Ogden, 26:5, 1995, 346-357, 3.2
Redundancy and Reliability of Communication Networks, Ralph P. Grimaldi and Douglas R. Shier, 27:1, 1996, 59-67
The "Join the Club" Interpretation of Some Graph Algorithms, Harold Reiter and Isaac Sonin, 27:1, 1996, 54-58, C
Some Graphs Whose Vertices Pair Off by Degree: Part I, Irl Bivens and Stephen L. Davis, 27:2, 1996, 127-135
Some Graphs Whose Vertices Pair Off by Degree: Part II, Irl Bivens and Stephen L. Davis, 27:3, 1996, 213-219
Colored Polygon Triangulations, Duane W. DeTemple, 29:1, 1998, 43-47, C
Modeling Trees with a Stochastic Matrix, Anne M. Burns, 29:3, 1998, 230-236, 8.3
An Algorithm for Drawing the n-Cube, Van Bain, 29:4, 1998, 320-322, C


3.2 		Combinatorics

Factoring Functions, J.C.Bodenrader, 2:1, 1971, 23-26, 0.6, 5.1.2, 9.1
Pascal's Triangle, Karl J. Smith, 4:1, 1973, 1-13, 0.6, 9.2
Checkerboards and Sugar Cubes: Geometric Counting Patterns, David R. Duncan and
Bonnie H. Litwiller, 4:2, 1973, 41-47
A Study of the Coefficients J[n, i], David L. Jones, 5:4, 1974, 12-15
A Computer Solution to "Instant Insanity", Larry Collister, 6:2, 1975, 36-41
Stories in Combinatorial Geometry, Ross Honsberger, 10:5, 1979, 344-347, 0.5
A Combinatorial Proof of Euler's Formula, Iain T. Adamson, 11:4, 1980, 272-273,
C, 9.3
An Application from Combinatorics to Dice-Sum Frequencies, David L. Pugh, 11:5,
1980, 331-333, C, 7.1
An Alternative Proof to Dirac's Theorem, Penelope Barlow, 12:1, 1981, 57-58, C
On Dice-Sum Frequencies, V.N.Murty, 12:3, 1981, 209-211, C, 7.2
Point-and-Line Proof for the Sum of Cubes, Barbara Turner, 12:4, 1981, 270-271,
C
Paths and Pascal Numbers, John F. Lucas, 14:4, 1983, 329-341, 9.2
A Sequel to "Another Way of Looking at n!", William Moser, 15:2, 1984, 142-143,
C, 5.2.7, 5.7.2
Pascal's Triangle, Difference Tables and Arithmetic Sequences of Order N,
Calvin Long, 15:4, 1984, 290-298, 5.4.1, 6.3, 9.2
On the Probability that the Better Team Wins the World Series, James L. Kepner,
16:4, 1985, 250-256, 7.2
A Discrete Look at 1 + 2 + ... + n, Loren C. Larson, 16:5, 1985, 369-382, 0.2,
0.9, 5.4.2, 3.1, 6.3
Trees and Tennis Rankings, Curtis Cooper, 17:1, 1986, 76-78, C, 3.1
The Pascal Polytope: An Extension of Pascal's Triangle to N Dimensions, John F.
Putz, 17:2, 1986, 144-155, 5.4.1, 6.3, 9.2
Combinatorics by Coin Flipping, Joel Spencer, 17:5, 1986, 407-412, 3.1, 7.2
A Division Game: How Far Can You Stretch Mathematical Induction?, William H.
Ruckle, 18:3, 1987, 212-218, 0.9, 9.9
Pascal Triangles and Combinations Where Repetitions Are Allowed, Kendell Hyde,
19:1, 1988, 60-62, C, 9.2
Rencontres Reencountered, Karl David, 19:2, 1988, 138-148, 9.4
How Many Bridge Actions?, Douglas S. Jungreis and Erich Friedman, 19:2, 1988,
171-172, C, 7.1
Ties at Rotation, Howard Lewis Penn, 19:3, 1988, 230-239, 9.10
Musical Notes, Angela B. Shiflet, 19:4, 1988, 345-347, C, 7.2, 9.2
A Chessboard Coloring Problem, May Beresin and Eugene Levine and John Winn,
20:2, 1989, 106-114
On-Line Partitioning of Partially Ordered Sets, William T. Trotter, 20:2, 1989,
124-131
It's Magic! Multiplication Theorems for Magic Squares, Daniel Widdis and R.
Bruce Richter, 20:4, 1989, 301-306, 9.2, 9.3
The Eternal Trianglea History of a Counting Problem, Mogens Esrom Larsen, 20:5,
1989, 370-384, 6.3
Herbert and the Hungarian Mathematician: Avoiding Certain Subsequence Sums,
Dean S. Clark and James T. Lewis, 21:2, 1990, 100-104
Using Euler's Formula to Solve Plane Separation Problems, Thomas L. Moore,
22:2, 1991, 125-130, 3.1
Counting It Twice, Doris Schattschneider, 22:3, 1991, 203-211
Clapping MusicA Combinatorial Problem, Joel K. Haack, 22:3, 1991, 224-227, C
FFF #46. A Straightforward Cancellation, Ed Barbeau, 22:5, 1991, 403-404, F,
0.2
Rubberbanding and Holding Out, James C. Kirby, 23:2, 1992, 148-149, C
Square-Free Sets on Square Grids: Student Research Project, Stephen L. Davis,
23:3, 1992, 214-224
Software Review: EDUCOM Higher Education Software Awards for 1991:
Combinatorica@, Bruce E. Sagan, 23:4, 1992, 334-339, 3.4
Some Applications of Elementary Linear Algebra in Combinatorics, Richard A.
Brualdi and Jennifer J. Q. Massey, 24:1, 1993, 10-19, 4.7
Permutation Puzzles: Student Research Project, John H. Wilson, 24:2, 1993,
163-165, 9.2
The Doors: Student Research Project, L.R.King and Benjamin G. Klein and Irl C.
Bivens, 24:3, 1993, 245-246
Remarks Concerning "Square-Free Sets on Square Grids": Student Research
Project, H.L.Abbott, 24:4, 1993, 353-355
Lottery Drawings Often Have Consecutive Numbers, David M. Berman, 25:1, 1994,
45-47, C
Investigation of a Recurrence Relation: Student Research Project, Dmitri Thoro and Linda Valdes, 25:4, 1994, 322-324, 6.3, 9.3
Eulerian Polynomials and Faulhaber's Result on Sums of Powers of Integers, H. K. Krishnapriyan, 26:2, 1995, 118-123
Pizza Combinatorics, Griffin Weber and Glenn Weber, 26:2, 1995, 141-143, C
Sums of Selected Binomial Coefficients, David R. Guichard, 26:3, 1995, 209-213
A Combinatorial Queueing Model, Shahar Boneh and David C. Ogden, 26:5, 1995, 346-357, 3.1
Pascal's Triangle Gets Its Genes from Stirling Numbers of the First Kind, Tommy Wright, 26:5, 1995, 368-371
A Master Key for Ten Locks, Stephen R. Cavior, 27:1, 1996, 33-36
Generalizations of a Mathematical Olympiad Problem, Joe Klerlein and Scott Sportsman, 27:4, 1996, 296-297, 9.3
Multiple Derivatives of Compositions: Investigating Some Special Cases, Irl C. Bivens, 28:4, 1997, 299-300, 5.7.1
FFF #127. Arranging a Collection of Objects, Montie Monzingo, 29:2, 1998, 134, F
Nothing Counts for Something, Norton Starr, 29:4, 1998, 308-309, C


3.3		Other topics in discrete mathematics (also see 6.3)

Who Stole the Apples and The Sticks?, Ross Honsberger, 10:1, 1979, 30-32, 3.1
Computer-Generated Knight Tours, Michael Gilpin, 13:4, 1982, 252-259, 3.1, 9.2
Drawing the Line Segment Connecting Two Points, Harley Flanders, 18:1, 1987,
53-57, 0.4, 8.1
Card Shuffling in Discrete Mathematics, Steve M. Cohen and Paul R. Coe, 26:3, 1995, 224-227, C, 9.4
Exploring Fibonacci Numbers Mod M, Jack Ryder, 27:2, 1996, 122-124, C, 9.3
A Better Draft: Fair Division of the Talent Pool, Bryan Dawson, 28:2, 1997, 82-88
Putting the Pieces Together: Understanding Robinson's Nonperiodic Tilings, Aimee Johnson and Kathleen Madden, 28:3, 1997, 172-181, 0.3
Weighing Coins: Divide and Conquer to Detect a Counterfeit, Mario Martelli and Gerald Gannon, 28:5, 1997, 365-367, 0.9
A Discrete Intermediate Value Theorem, Richard Johnsonbaugh, 29:1, 1998, 42, C, 0.9
FFF #134. Hockey Ranking, Dave Trautman, 29:5, 1998, 406-407, F


3.4		Software for discrete mathematics

A Mathematics Software Database, R.S.Cunningham and David A. Smith, 17:3, 1986,
255-266, 0.10, 4.8, 5.8, 6.7, 7.4, 9.11
A Mathematics Software Database Update, R.S.Cunningham and David A. Smith,
18:3, 1987, 242-247, 0.10, 4.8, 5.8, 6.7, 7.4, 9.11
The Compleat Mathematics Software Database, R.S.Cunningham and David A. Smith,
19:3, 1988, 268-289, 0.10, 4.8, 5.8, 6.7, 7.4, 9.11
EDUCOM Higher Education Software Awards for 1991: Combinatorica@, Bruce E.
Sagan, 23:4, 1992, 334-339, 3.2
Using PROLOG in Discrete Mathematics, Antonio M. Lopez, Jr., 24:4, 1993,
357-365, 3.1, 9.1




4 	Linear Algebra
 
4.1 		Matrices, systems of linear equations, and matrix algebra

Mathematics, A Solitary Game, Olof Hanner, 1:2, 1970, 5-16, 0.2
On One-Sided Inverses of Matrices, Elmar Zemgalis, 2:1, 1971, 45-48
On Transformations and Matrices, Marc Swadener, 4:3, 1973, 44-51, 4.4
Computer-Generated Problem Sets: Simultaneous Equations and Matrices, Samuel W.
Spero and Mary Koehler, 8:3, 1977, 182-187
Binomial Matrices, Jay E. Strum, 8:5, 1977, 260-266
Integer Matrices Whose Inverses Contain Only Integers, Robert Hanson, 13:1,
1982, 18-21
Mathematics in Archaeology, Gareth Williams, 13:1, 1982, 56-58, C
The Mathematics of Tucker: A Sampler, Albert W. Tucker, 14:3, 1983, 228-232
Basic Null Space Calculations, Dan Kalman, 15:1, 1984, 42-47
The Electronic Spreadsheet and Mathematical Algorithms, Deane E. Arganbright,
15:2, 1984, 148-157, 5.4.1, 7.3, 9.6
Visual Thinking about Rotations and Reflections, Tom Brieske, 15:5, 1984,
406-410, 4.4
Classifying Row-reduced Echelon Matrices, Stewart Venit and Wayne Bishop, 17:2,
1986, 169-170, C
Self-Inverse Integer Matrices, Robert Hanson, 16:3, 1985, 190-198
Using Minitab in Linear Algebra, Raymond N. Greenwell, 16:3, 1985, 216-218
Harvesting a Grizzly Bear Population, Michael Caulfield and John Kent and
Daniel McCaffrey, 17:1, 1986, 34-46, 4.6, 9.10
Teaching Mathematics Using APL, Edward J. LeCuyer, Jr., 17:4, 1986, 344-357
On Polynomial Matrix Equations, Harley Flanders, 17:5, 1986, 388-391, 4.5
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 0.2,
5.1.2, 5.1.5, 5.2.3, 5.2.4, 5.2.5
Why Should We Pivot in Gaussian Elimination?, Edward Rozema, 19:1, 1988, 63-72,
4.6
Notational Collisions, J. Hillel, 20:5, 1989, 418-422, C, 1.2
Minimum Dimension for a Square Matrix of Order n, Robert Hanson, 21:1, 1990,
28-34, 9.4
A Tool for Teaching Linar Programming within MATLAB, David R. Hill, 21:1, 1990,
55-56, C, 9.9
Software Review: Linear Algebra Software for the IBM PC, David P. Kraines and
Vivian Y. Kraines, 21:1, 1990, 57-64, 4.8
FFF #16. Nonsquare Invertible Matrices, Ed Barbeau, 21:2, 1990, 127, F (also
22:3, 1991, 223 and 23:3, 1992, 204)
A Zero-Row Reduction Algorithm for Obtaining the gcd of Polynomials, Sidney H.
Kung and Yap S. Chua, 21:2, 1990, 138-141, 0.7, 9.4
Elementary Row Operations and LU Decomposition, David P. Kraines and Vivian Y.
Kraines and David A. Smith, 21:5, 1990, 418-419, C
Rotations in Space and Orthogonal Matrices, David P. Kraines, 22:3, 1991,
245-247, C, 4.3, 4.4, 4.5
Number Theory and Linear Algebra: Exact Solutions of Integer Systems, George
Mackiw, 23:1, 1992, 52-58, 9.3
Gems of Exposition in Elementary Linear Algebra, David Carlson and Charles R.
Johnson and David Lay and A. Duane Porter, 23:4, 1992, 299-303, 1.2, 4.5, 4.7
A Random Ladder Game: Permutations, Eigenvalues, and Convergence of Markov
Chains, Lester H. Lange and James W. Miller, 23:5, 1992, 373-385, 4.5, 9.10
Graphs, Matrices, and Subspaces, Gilbert Strang, 24:1, 1993, 20-28, 3.1, 4.3
Teaching Linear Algebra: Must the Fog Always Roll In?, David Carlson, 24:1,
1993, 29-40, 1.2
The Linear Algebra Curriculum Study Group Recommendations for the First Course
in Linear Algebra, David Carlson and Charles R. Johnson and David C. Lay and A.
Duane Porter, 24:1, 1993, 41-46, 1.2, 4.2, 4.3, 4.5
Linear Algebra and Affine Planar Transformations, Gerald J. Porter, 24:1, 1993,
47-51, 0.4, 4.4
FFF. Matrices and the TI-81 Graphics Calculator, Constance J. Gardner, 24:1,
1993, 64, F, 0.2
Gaussian Elimination in Integer Arithmetic: An Application of the L-U
Factorization, Thomas Hern, 24:1, 1993, 67-71, C
Iterative Methods in Introductory Linear Algebra, Donald R. LaTorre, 24:1,
1993, 79-88, 4.5, 9.6
Software Review: Spreadsheets in Linear Algebra, Deane Arganbright, 24:1, 1993,
89-94, 4.8
How Does the NFL Rate the Passing Ability of Quarterbacks?, Roger W. Johnson,
24:5, 1993, 451-453, C
Using Computer Algebra Systems to Teach Linear Algebra (software review),
Maurino P. Bautista, 24:5, 1993, 462-471, 4.5, 4.8
Round-off, Batting Averages, and Ill-Conditioning, Edward Rozema, 25:4, 1994, 314-317, C, 4.6
Matrix Patterns and Undertermined Coefficients, Herman Gollwitzer, 25:5, 1994, 444-448, C, 6.2
For matrices: AB transpose equals B transpose times A transpose (proof by picture), James G. Simmonds, 26:3, 1995, 250, C
Linear Algebra on the Gridiron, Daniel C. Isaksen, 26:5, 1995, 358-360
Using the College Mathematics Journal Topic Index in Undergraduate Courses, Donald E. Hooley, 28:2, 1997, 106-109, 4.2, 5.1.4, 5.7.1
FFF #114. An Inversion Conundrum, Barry D. Ganapol, 28:2, 1997, 120, F
A Diagonal Perspective on Matrices, Eugene C. Boman and Margaret A. Misconish, 29:1, 1998, 37-38, C


4.2 		Determinants (also see 5.5)

On the Evaluation of Determinants by Chio's Method, L.E.Fuller and J.D.Logan,
6:1, 1975, 8-10
A Geometrical Proof of Cramer's Rule, R.R.Baldino, 9:2, 1978, 106-107, C
Determinants: A Short Program, Alban J. Roques, 10:5, 1979, 340-343
Predetermined Determinants, David C. Buchtal, 16:4, 1985, 277-279, C
The Surveyor's Area Formula, Bart Braden, 17:4, 1986, 326-337, 5.2.6, 5.2.8
Computing Determinants, Clyde Dubbs and David Siegel, 18:1, 1987, 48-50, C
Cramer's Rule via Selective Annihilation, Dan Kalman, 18:2, 1987, 136-137, C,
4.3
Convex Coordinates, Probabilities, and the Superposition of States, J.N.Boyd
and P.N.Raychowdhury, 18:3, 1987, 186-194, 9.7
A Nonstandard Approach to Cramer's Rule, Sidney H. Kung, 19:1, 1988, 59-60, C
An Alternative Proof of Cramer's Rule, Stephen H. Friedberg, 19:2, 1988, 171, C
Apropos Predetermined Determinants, Antal E. Fekete, 19:3, 1988, 254-257, C
Evaluating "Uniformly Filled" Determinants, Simon M. Goberstein, 19:4, 1988,
343-345, C
Determinants of Sums, Marvin Marcus, 21:2, 1990, 130-134, C
On 'Uniformly Filled' Determinants, Carsten Thomassen and Herbert S. Wilf,
21:2, 1990, 135-137, C
Determinantal Loci, Marvin Marcus, 23:1, 1992, 44-47, C
FFF #55. Even and Odd Permutations, Ed Barbeau, 23:3, 1992, 204, F, 9.4 (also
23:4, 1992, 305 and 24:4, 1993, 346)
The Linear Algebra Curriculum Study Group Recommendations for the First Course
in Linear Algebra, David Carlson and Charles R. Johnson and David C. Lay and A.
Duane Porter, 24:1, 1993, 41-46, 1.2, 4.1, 4.3, 4.5
Roots of Cubics via Determinants, Robert Y. Suen, 25:2, 1994, 115-117, 0.7
Using the College Mathematics Journal Topic Index in Undergraduate Courses, Donald E. Hooley, 28:2, 1997, 106-109, 4.1, 5.1.4, 5.7.1
Cramer's Rule (proof by picture), The Mathematica Initiative, 28:2, 1997, 118, C
Finding a Determinant and Inverse Matrix by Bordering, Yong-Zhuo Chen and Richard F. Melka, 29:1, 1998, 38-39, C


4.3 		Vector spaces and inner product spaces (also see 5.5)

Vectors Point Toward Pisa, Richard A. Dean, 2:2, 1971, 28-39, 6.3
Orthogonal Basis: A Computational Alternative, Lehi T. Smith, 11:4, 1980, 274,
C
Cramer's Rule via Selective Annihilation, Dan Kalman, 18:2, 1987, 136-137, C,
4.2
FFF #35. Yet Another Proof that 0=1, Ed Barbeau, Editor, 22:2, 1991, 131, F
Rotations in Space and Orthogonal Matrices, David P. Kraines, 22:3, 1991,
245-247, C, 4.1, 4.5
Graphs, Matrices, and Subspaces, Gilbert Strang, 24:1, 1993, 20-28, 4.1, 3.1
The Linear Algebra Curriculum Study Group Recommendations for the First Course
in Linear Algebra, David Carlson and Charles R. Johnson and David C. Lay and A.
Duane Porter, 24:1, 1993, 41-46, 1.2, 4.1, 4.2, 4.5
Arithmetic Matrices and the Amazing Nine-Card Monte, Dean Clark and Dilip K.
Datta, 24:1, 1993, 52-56
Subspaces and Echelon Forms, David C. Lay, 24:1, 1993, 57-62
A Geometric Interpretation of the Columns of the (Pseudo)Inverse of A, Melvin
J. Maron and Ghansham M. Manwani, 24:1, 1993, 73-75, C
A Class of Pleasing Periodic Designs, Federico Fernandez, 29:1, 1998, 18-26, 9.3, 9.4
When Is "Rank" Additive?, David Callan, 29:2, 1998, 145-147, C
Generating Exotic-Looking Vector Spaces, Michael A. Carchidi, 29:4, 1998, 304-308, C
A Picture is Worth a Thousand Words, J. B. Thoo, 29:5, 1998, 408-411, C



4.4		Linear transformations

On Transformations and Matrices, Marc Swadener, 4:3, 1973, 44-51, 4.1
Visual Thinking about Rotations and Reflections, Tom Brieske, 15:5, 1984,
406-410, 4.1
The Matrix of a Rotation, Roger C. Alperin, 20:3, 1989, 230, C, 8.3
Rotations in Space and Orthogonal Matrices, David P. Kraines, 22:3, 1991,
245-247, C, 4.1, 4.3, 4.5
Linear Algebra and Affine Planar Transformations, Gerald J. Porter, 24:1, 1993,
47-51, 0.4, 4.1
Rotation Matrices in the Plane without Trigonometry, Arnold J. Insel, 24:1,
1993, 71-73, C
The Linear Transformation Associated with a Graph: Student Research Project,
Irl C. Bivens, 24:1, 1993, 76-78, 3.1, 9.1
Fractals in Linear Algebra, James A. Walsh, 27:4, 1996, 298-304, 6.3

4.5 		Eigenvalues and eigenvectors

Linear Algebra: A Potent Tool, Anneli Lax, 7:2, 1976, 3-15
On Polynomial Matrix Equations, Harley Flanders, 17:5, 1986, 388-391, 4.1
Constructing a Map from a Table of Intercity Distances, Richard J. Pulskamp,
19:2, 1988, 154-163, 3.1, 9.10
FFF #24. The Cayley-Hamilton Theorem, Ed Barbeau, 21:4, 1990, 303, F (also
22:3, 1991, 222-223 and 22:5, 1991, 405-406)
Rotations in Space and Orthogonal Matrices, David P. Kraines, 22:3, 1991,
245-247, C, 4.1, 4.3
Eigenvectors and Jordan Bases Using Symbolic Programs, Robert J. Hill and
Robert D. Bechtel, 23:1, 1992, 59-63, C
Systems of Linear Differential Equations by Laplace Transform, H. Guggenheimer,
23:3, 1992, 196-202, 6.2
Gems of Exposition in Elementary Linear Algebra, David Carlson and Charles R.
Johnson and David Lay and A. Duane Porter, 23:4, 1992, 299-303, 1.2, 4.1, 4.7
A Random Ladder Game: Permutations, Eigenvalues, and Convergence of Markov
Chains, Lester H. Lange and James W. Miller, 23:5, 1992, 373-385, 4.1, 9.10
The Linear Algebra Curriculum Study Group Recommendations for the First Course
in Linear Algebra, David Carlson and Charles R. Johnson and David C. Lay and A.
Duane Porter, 24:1, 193, 41-46, 1.2, 4.1, 4.2, 4.3
Iterative Methods in Introductory Linear Algebra, Donald R. LaTorre, 24:1,
1993, 79-88, 4.1, 9.6
Using Computer Algebra Systems to Teach Linear Algebra (software review),
Maurino P. Bautista, 24:5, 1993, 462-471, 4.1, 4.8
Approaches to the Formula for the nth Fibonacci Number, Russell Jay Hendel,
25:2, 1994, 139-142, C, 0.2, 5.4.2, 9.3, 9.5
Computing Jordan Canonical Forms, Patrick Costello, 25:3, 1994, 231-234, C, 4.7, 4.8
A Simple Estimate of the Condition Number of a Linear System, Heinrich W. Guggenheimer, Alan S. Edelman, and Charles R. Johnson, 26:1, 1995, 2-5, 4.6
The Matrix Exponential Function and Systems of Differential Equations Using Derive@, Robert J. Hill and Mark S. Mazur, 26:2, 1995, 146-151, 6.2
Eigenpictures: Picturing the Eigenvector Problem, Steven Schonefeld, 26:4, 1995, 316-319, C
Complex Eigenvalues and Rotations: Are Your Students Going in Circles?, James Duemmel, 27:5, 1996, 378-381, C
Eigenpictures and Singular Values of a Matrix, Peter Zizler and Holly Fraser, 28:1, 1997, 59-62, C, 5.7.3
Take a Walk on the Boardwalk, Stephen D. Abbott and Matt Richey, 28:3, 1997, 162-171, 9.10
Clock Hands Pictures for 2x2 Real Matrices, Charles R. Johnson and Brenda K. Kroschel, 29:2, 1998, 148-150, C
FFF.  How Large Is the Set of Degenerate Real Symmetric Matrices?, Peter D. Lax, 29:3, 1998, 219-220, F


4.6 		Numerical methods of linear algebra

A Machine-Oriented Technique for the Complete Solution of Linear Systems, Eric
J. Nelson, 8:3, 1977, 161-164
Harvesting a Grizzly Bear Population, Michael Caulfield and John Kent and
Daniel McCaffery, 17:1, 1986, 34-46, 4.1, 9.10
Why Should We Pivot in Gaussian Elimination?, Edward Rozema, 19:1, 1988, 63-72,
4.1
Connecting the Dots Parametrically: An Alternative to Cubic Splines, Wilbur J.
Hildebrand, 21:3, 1990, 208-215, 5.6.1, 9.6
Round-off, Batting Averages, and Ill-Conditioning, Edward Rozema, 25:4, 1994, 314-317, C, 4.1
A Simple Estimate of the Condition Number of a Linear System, Heinrich W. Guggenheimer, Alan S. Edelman, and Charles R. Johnson, 26:1, 1995, 2-5, 4.5
A Singularly Valuable Decomposition: The SVD of a Matrix, Dan Kalman, 27:1, 1996, 2-23
Of Memories, Neurons, and Rank-One Corrections, Kevin G. Kirby, 28:1, 1997, 2-19, 8.4
The Generalized Spectral Decomposition of a Linear Operator, Garret Sobczyk, 28:1, 1997, 27-38, 9.4
Gaussian Elimination and Dynamical Systems, Kathie Yerion, 28:2, 1997, 89-97, 9.6
A Fresh Approach to the Singular Value Decomposition, Colm Mulcahy and John Rossi, 29:3, 1998, 199-207


4.7		Other topics in linear algebra

Gems of Exposition in Elementary Linear Algebra, David Carlson and Charles R.
Johnson and David Lay and A. Duane Porter, 23:4, 1992, 299-303, 1.2, 4.1, 4.5
Some Applications of Elementary Linear Algebra in Combinatorics, Richard A.
Brualdi and Jennifer J. Q. Massey, 24:1, 1993, 10-19, 3.2
Problem Collection for Linear Algebra, Ed Barbeau, 24:1, 1993, 64-66, F
Computing Jordan Canonical Forms, Patrick Costello, 25:3, 1994, 231-234, C, 4.5, 4.8

4.8		Software for linear algebra
 
A Mathematics Software Database, R.S.Cunningham and David A. Smith, 17:3, 1986,
255-266, 0.10, 3.4, 5.8, 6.7, 7.4, 9.11
A Mathematics Software Database Update, R.S.Cunningham and David A. Smith,
18:3, 1987, 242-247, 0.10, 3.4, 5.8, 6.7, 7.4, 9.11
The Compleat Mathematics Software Database, R.S.Cunningham and David A. Smith,
19:3, 1988, 268-289, 0.10, 3.4, 5.8, 6.7, 7.4, 9.11
Linear Algebra Software for the IBM PC, David P. Kraines and Vivian Y. Kraines,
21:1, 1990, 57-64, 4.1
Mathematics by Machine with Mathematica@, Alan Hoenig, 21:2, 1990, 146-149
Derive@, A Mathematical Assistant, Jeanette R. Palmiter, 23:2, 1992, 158-161
Spreadsheets in Linear Algebra, Deane Arganbright, 24:1, 1993, 89-94, 4.1
Theorist@, Francis Gulick, 24:2, 1993, 178-182
Using Computer Algebra Systems to Teach Linear Algebra (software review),
Maurino P. Bautista, 24:5, 1993, 462-471, 4.1, 4.5
Computing Jordan Canonical Forms, Patrick Costello, 25:3, 1994, 231-234, C, 4.5, 4.7
Software Review: f(g) Scholar, David C. Arney and Daniel J. Arney, 26:5, 1995, 401-403, 0.10, 5.8


5	Calculus
 
5.1 		Limits and differentiation

5.1.1		Limits (including l'Hopital's rule)

Delta as a Function of Epsilon,  A Suggestion for the Calculus Teacher,  John
W. LeDuc,  4:3,  1973,  85-86,  C
A Note on Epsilons and Deltas, Peter A. Lindstrom, 5:3, 1974, 12-14
Another Note on Epsilons and Deltas, Larry F. Bennett, 7:3, 1976, 18
Comparing a^b and b^a Using Elementary Calculus, John T. Varner III, 7:4, 1976,
46, C, 5.1.2
An Interesting Approach to Delta, Epsilon Proofs, Allen R. Angel, 8:5, 1977,
278-280
Note on l'Hopital's Rule for the Indeterminate Form infinity over infinity,
James E. Carpenter, 9:2, 1978, 73-74
A Neglected Approach to the Logarithm, Bruce S. Babcock and John W. Dawson,
Jr., 9:3, 1978, 136-140, 5.3.2
Stirling's Formula Improved, Jerry B. Keiper, 10:1, 1979, 38-39, C
L'Hopital's Rule and the Continuity of the Derivative, J. P. King, 10:3, 1979,
197-198, C
Calculator-Demonstrated Math Instruction, George McCarty, 11:1, 1980, 42-48,
5.2.2, 5.4.2, 9.6
Calculators to Motivate Infinite Composition of Functions, E.D.McCune and
R.G.Dean and W.D.Clark, 11:3, 1980, 189-195
Delta, Epsilon, and Polynomials, Andre L. Yandl, 11:4, 1980, 263-266
Fixed Point IterationAn Interesting Way to Begin a Calculus Course, Thomas
Butts, 12:1, 1981, 2-7, 1.2, 9.6
Probability Solution to a Limit Problem, Homer W. Austin, 13:4, 1982, 272, C,
7.2
The Epsilon-Delta Connection, Larry King, 14:1, 1983, 42-47
Some Subtleties in l'Hopital's Rule, Robert J. Bumcrot, 15:1, 1984, 51-52, C
Alternate Approach to Two Familiar Results, Norman Schaumberger, 15:5, 1984,
422-423, C, 5.1.2
Bernoulli's Inequality and the Number e, Joseph Wiener, 16:5, 1985, 399-400, C
Using Riemann Sums in Evaluating a Familiar Limit, Frank Burk, 17:2, 1986,
170-171, C, 5.2.1, 5.3.2
Interactive Graphics for Multivariable Calculus, Michael E. Frantz, 17:2, 1986,
172-181, 5.1.4, 5.7.1, 1.2
Picturing Infinite Values, Robert A. Cicenia, 17:4, 1986, 322-325
An Unexpected Appearance of the Golden Ratio, George Manuel and Amalia
Santiago, 19:2, 1988, 168-170, C, 0.4
A Discrete l'Hopital's Rule, Xun-Cheng Huang, 19:4, 1988, 321-329, 9.5
A Generalization of the limit of [(n!)^(1/n)]/n = e^(-1), Norman Schaumberger,
20:5, 1989, 416-418, C, 9.5
A Recursively Computed Limit, Stephan C. Carlson and Jerry M. Metzger, 21:3,
1990, 222-224, C
A Geometric Proof of the limit as d approaches 0 from the positive side of -d
ln d equals 0, John H. Mathews, 23:3, 1992, 209-210, C
A Circular Argument, Fred Richman, 24:2, 1993, 160-162, C
Does a Parabola Have an Asymptote?, David Bange and Linda Host, 24:4, 1993,
331-342, 5.1.5, 5.6.1
Maclaurin Expansion of Arctan x via L'Hopital's Rule, Russell Euler, 24:4,
1993, 347-350, C, 5.4.3
FFF #69. Calculation of a Limit, Cherie D'Mello, 25:1, 1994, 36, F
Some Extensions of a Ubiquitous Geometric Limit Problem, David N. Adler, 27:4, 1996, 290-291, C
FFF. Two Limit Fallacies, Ed Barbeau, editor, 28:1, 1997, 44-46, F

Introduction to Limits, or Why Can't We Just Trust the Table?, Allen J. Schwenk, 28:1, 1997, 51, C
Geometric Evaluation of a Limit (proof by picture), Guanshen Ren, 28:3, 1997, 186, C
Order Relations and a Proof of l'Hopital's Rule, Leonard Gillman, 28:4, 1997, 288-292, C
Proof of a Common Limit (x / ex) (proof without words), Alan H. Stein and Dennis McGavran, 29:2, 1998, 147, C


5.1.2 	The derivative and mean value theorems

Factoring Functions, J. C. Bodenrader, 2:1, 1971, 23-26, 0.6, 3.2, 9.1
How Steep Is a Hill?, Robert L. Page, 3:1, 1972, 66-67, C
A Note on Derivatives of Polynomials, Aron Pinker, 3:2, 1972, 77-78, C
Generalizing Rolle's Theorem in Elementary Calculus, Rodney D. Gentry, 4:3,
1973, 11-17
Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.4, 5.2.2,
5.2.3, 5.2.5, 5.2.3, 5.7.2, 5.2.10, 5.4.2, 5.6.1
Continuous Deformation of a Polynomial into Its Derivatives, Roland E. Larson,
5:2, 1974, 68-69, C, 0.7
When Does (fg )'=f'g'?, Lewis G. Maharam and Edward P. Shaughnessy, 7:1, 1976,
38-39, C
Comparing a^b and b^a Using Elementary Calculus, John T. Varner III, 7:4, 1976,
46, C, 5.1.1
An Elementary Result on Derivatives, David A. Birnbaum and Northrup Fowler III,
8:1, 1977, 10-11
Some Elementary Results Related to the Mean Value Theorem, Roy E. Myers, 8:1,
1977, 51-53, C
Differentiating Area and Volume, Jay I. Miller, 9:1, 1978, 47-49, C
Some Functional Equations for the Calculus Student, Stephen J. Milles and Henry
J. Schultz, 9:4, 1978, 205-209
Differentiation and Synthetic Division, Dan Kalman, 10:1, 1979, 37, C
Travelers' Surprises, R. P. Boas, 10:2, 1979, 82-88
Another Application of the Mean Value Theorem, Norman Schaumberger, 10:2, 1979,
114-115, C
An Alternate Approach to the Derivative of the Trigonometric Functions, Norman
Schaumberger, 10:4, 1979, 276-277, C
Derivatives Without Limits, Harry Sedinger, 11:1, 1980, 54-55, C, 5.1.3
Wavefronts, Box Diagrams,  and the Product Rule: A Discovery Approach, John W.
Dawson, Jr., 11:2, 1980, 102-106, 7.2
A Geometric Proof of Cauchy's Generalized Law of the Mean, Mary Powderly, 11:5,
1980, 329-330, C
A Mean Generating Function, Jack C. Slay and J.L.Solomon, 12:1, 1981, 27-29,
7.3
Who Needs Those Mean-Value Theorems, Anyway?, Ralph Boas, 12:3, 1981, 178-191
The Sums of Zeros of Polynomial Derivatives, Michael W. Ecker, 13:5, 1982,
328-329, C
Exactly n-Times Differentiable Functions, Robert Bumcrot, 14:3, 1983, 258-259,
C
The Derivatives of Sin x and Cos x, Norman Schaumberger, 15:2, 1984, 143-145, C
Another Look at x^(1/x), Norman Schaumberger, 15:3, 1984, 249-250, C, 5.4.1
Alternate Approaches to Two Familiar Results, Norman Schaumberger, 15:5, 1984,
422-423, C, 5.1.1
A Self-Contained Derivation of the Formula of the Derivative with Respect to x
of x^r for Rational r, Peter A. Lindstrom, 16:2, 1985, 131-132, C
Average Values and Linear Functions, David E. Dobbs, 16:2, 1985, 132-135, 5.2.1
Testing Understanding and Understanding Testing, Jean Pedersen and Peter Ross,
16:3, 1985, 178-185, 0.2, 1.2, 5.2.2
More Applications of the Mean Value Teorem, Norman Schaumberger, 16:5, 1985,
397-398, C
Rolle over LagrangeAnother Shot at the Mean Value Theorem, Robert S. Smith,
17:5, 1986, 403-406
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 0.4,
4.1, 5.1.5, 5.2.3, 5.2.4, 5.2.5
The Derivatives of the Sine and Cosine Functions, Barry A. Cipra, 18:2, 1987,
139-140, C, 5.2.1
A General Form of the Arithmetic-Geometric Mean Inequality via the Mean Value
Theorem, Norman Schaumberger, 19:2, 1988, 172-173, C, 9.5
A Direct Proof of the Integral Formula for Arctangent, Arnold J. Insel, 20:3,
1989, 235-237, C, 5.2.6, 5.2.3
Automatic Differentiation and APL, Richard D. Neidinger, 20:3, 1989, 238-251,
5.1.3
The Power Rule and the Binomial Formula, Stephen H. Friedberg, 20:4, 1989, 322,
C, 5.4.2
A Simple Auxiliary Function for the Mean Value Theorem, Herb Silverman, 20:4,
1989, 323, C
The Function sin x / x, William B. Gearhart and Harris S. Shultz, 21:2, 1990,
90-99, 2.2, 5.1.5
FFF #26. Differentiating the Square of x, Ed Barbeau, 21:4, 1990, 304, F
The Derivative of x^n = nx^(n-1): Six Proofs, Russell Jay Hendel, 21:4, 1990,
312-313, C
FFF #37. 3 Equals 2, Ed Barbeau, 22:2, 1991, 132, F
The Differentiability of Sin x, David A. Rose, 22:2, 1991, 139-142, C
FFF #45. All Powers of x are Constant, Ed Barbeau, 22:5, 1991, 403, F, 0.9
FFF #47. A Natural Way to Differentiate an Exponential, Ed Barbeau, 22:5, 1991,
404, F, 5.1.3 (also 23:3, 1992, 206 and 24:3, 1993, 231)
Summation by Parts, Gregory Fredricks and Roger B. Nelsen, 23:1, 1992, 39-42,
C, 5.4.1, 5.4.2, 9.3
FFF #56. Yet Another Proof that 3 Equals 2, Ed Barbeau, 23:3, 1992, 204, F
(also 23:4, 1992, 306)
Another Proof of the Formula e equals the infinite sum of reciprocals of n!,
Norman Schaumberger, 25:1, 1994, 38-39, C, 5.3.2
Why Polynomials Have Roots, Javier Gomez-Calderon and David M. Wells, 27:2, 1996, 90-94, 5.7.1, 9.5
Newton's Method for Resolving Affected Equations, Chris Christensen, 27:5, 1996, 330-340, 0.7, 5.4.3
FFF #132. The Increment of a Product, Robert Weinstock, 29:4, 1998, 302-303, F


5.1.3 	Tangents, differentials, and differentiation

A Simple Proof of the Reflection Property for Parabolas, R. H. Cowen, 7:2,
1976, 59-60, C, 0.5
Mappings, Diagrams, Continuous Functions and Derivatives, Thomas J. Brieske,
9:2, 1978, 67-72
A Note on the Derivative of a Composite Function, V.N.Murty, 11:1, 1980, 50, C
Derivatives Without Limits, Harry Sedinger, 11:1, 1980, 54-55, C, 5.1.2
Intuition Out to Sea, William A. Leonard, 13:3, 1983, 195-196, C
Related Rates and the Speed of Light, Steven C. Althoen and John F. Weidner,
16:3, 1985, 186-189
What a Tangent Line is When it isn't a Derivative, Irl C. Bivens, 17:2, 1986,
133-143
Transitions, Jeanne L. Agnew and James R. Choike, 18:2, 1987, 124-133, 0.7,
5.6.1, 9.10
Differentials and Elementary Calculus, D.F.Bailey, 20:1, 1989, 52-53, C
Automatic Differentiation and APL, Richard D. Neidinger, 20:3, 1989, 238-251,
5.1.2
A Chaotic Search for i, Gilbert Strang, 22:1, 1991, 3-12, 6.3, 9.5
FFF #47. A Natural Way to Differentiate and Exponentiate, Ed Barbeau, 22:5,
1991, 404, F, 5.1.2 (also 23:3, 1992, 206 and 24:3, 1993, 231)
Who Needs the Sine Anyway?, Carlos C. Huerta, 23:1, 1992, 43-44, C, 5.4.2
Visualization of Limits and Limits of Visualization: Student Research Projects,
Lee H. Minor, 23:1, 1992, 48-51, 0.4, 0.5
FFF #54. A Degree of Differentiation, Ed Barbeau, 23:3, 1992, 203, F, 0.6 (also
23:4, 1992, 306 and 24:4, 1993, 345)
An Exponential Rule, G.E.Bilodeau, 24:4, 1993, 350-351, C      
A Useful Notation for Rules of Differentiation, Robert B. Gardner, 24:4, 1993,
351-352, C
FFF #70. Reading a Calculator Display, Sandra Z. Keith, 25:1, 1994, 36, F, 0.2
Euler and Differentials, Anthony P. Ferzola, 25:2, 1994, 102-111, 2.2
Isaac Newton: Credit Where Credit Won't Do, Robert Weinstock, 25:3, 1994, 179-192, 0.5, 2.2, 5.4.3, 5.6.1
The Dynamics of Newton's Method for Cubic Polynomials, James A. Walsh, 26:1, 1995, 22-28, 6.3
The Spider's Spacewalk Derivation of sin' and cos', Tim Hesterberg, 26:2, 1995, 144-145, C
The Falling Ladder Paradox, Paul Scholten and Andrew Simoson, 27:1, 1996, 49-54, C, 6.2
Bond Duration: An Application of Calculus, John C. Hegarty, 27:1, 1996, 47-49, C
FFF #110. The Speeder's Delight, Carl E. Crockett, 27:5, 1996, 370-371, F
Area and Perimeter, Volume and Surface Area, Jingcheng Tong, 28:1, 1997, 57, C, 0.4
A Continuous Version of Newton's Method, Steven M. Hetzler, 28:5, 1997, 348-351, 6.3


5.1.4	Maxima and minima 

Using Polyhedrons to Define Maximum Volumes, D. L. Carleton, 3:1, 1972, 30-32
Some Socially Relevant Applications of Elementary Calculus, Colin Clark, 4:2,
1973, 1-15, 6.1
An Interpolation Question Resolved by Calculus, Martin D. Landau and William R.
Jones, 4:1, 1973, 36-39
Four Theorems About Montana, H. E. Reinhardt, 4:1, 1973, 76-78, C
Construction of an Exercise Involving Minimum Time, Robert Owen Armstrong, 5:2,
1974, 12-14
Maximize x(a-x), L. H. Lange, 5:1, 1974, 22-24, 0.2
A Set of Trigonometric Inequalities with Applications to Maxima and Minima,
Norman Schaumberger, 5:3, 1974, 26-30, 0.6
Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.2, 5.2.2,
5.2.3, 5.2.5, 5.2.10, 5.4.2, 5.6.1, 5.7.2
What Is an Application of Mathematics?, Clifford Sloyer, 7:3, 1976, 19-26, 9.10
A Calculus Proof of the Arithmetic-Geometric Mean Inequality, Norman
Schaumberger, 9:1, 1978, 16-17
On the "Rule of 72", Warren B. Gordon and Harold D. Shane, 10:2, 1979, 117-118,
C
An interesting way to test students' understanding of the first derivative
test, Dick A. Wood, 10:2, 1979, 118, C
How Good is the "Rule of 72"?, Alan Kroopnick, 10:4, 1979, 279-280, C
Another way to test understanding of the first derivative test, Thomas M.
Greene, 10:4, 1979, 282-283, C
Must a "Dud" Necessarily Be an Inflection Point?, Michail W. Ecker, 12:5, 1981,
332-333, C
A Bifurcation Problem in First Semester Calculus, W. L. Perry, 14:1, 1983,
57-60, C
When Does a Square Give Maximum Area?, Ray C. Shiflett and Harris S. Shultz,
14:3, 1983, 194-196
Some Maximal Rectangles and the Realities of Applied Mathematics, Michael R.
Latina, 14:3, 1983, 248-252
To Build a Better Box, Kay Dundas, 15:1, 1984, 30-36
The Maximum and Minimum of Two Numbers Using the Quadratic Formula, Dan Kalman,
15:4, 1984, 329-330, C, 9.5
The Problem of Managing a Strategic Reserve, David Cole, Loren Haarsma and Jack
Snoeyink, 17:1, 1986, 48-60, 6.1, 9.10
A Note on Differentiation, Russell Euler, 17:2, 1986, 166-167, C
Interactive Graphics for Multivariable Calculus, Michael E. Frantz, 17:2, 1986,
172-181, 1.2, 5.1.1, 5.7.1
Coloring Points in the Unit Square, Charles H. Jepsen, 17:3, 1986, 231-237, 3.1
Computer Algebra Systems in Undergraduate Mathematics, Don Small and John
Hosack and Kenneth Lane, 17:5, 1986, 423-433, 1.2, 5.1.5, 5.2.2, 5.4.2
A Surprising Max-Min Result, Herbert Bailey, 18:3, 1987, 225-229, C
Fibonacci Numbers and Computer Algorithms, John Atkins and Robert Geist, 18:4,
1987, 328-336, 6.3, 8.1
On Partitioning a Real Number, William Staton, 19:1, 1988, 53-54, C, 9.3
Behold! Two Extremum Problems (and the Arithmetic-Geometric Mean Inequality),
Paolo Montuchi and Warren Page, 19:4, 1988, 347, C, 0.4
Hanging a Bird Feeder: Food for Thought, John W. Dawson, Jr., 21:2, 1990,
129-130, C
Using a Computer Algebra System to Solve for Maxima and Minima, Robert Lopez
and John Mathews, 21:5, 1990, 410-414
Extrema and Saddle Points, David P. Kraines and Vivian Y. Kraines and David A.
Smith, 21:5, 1990, 416-418, C, 5.7.1
FFF #34. The Shortest Distance from a Point to a Parablola, Ed Barbeau, 22:2,
1991, 131, F (also 23:1, 1992, 38)
The Isoperimetric Quotient: Another Look at an Old Favorite, G.D.Chakerian,
22:4, 1991, 313-315, C
Using Computer Graphics to Help Analyze Complicated Functions, Paul B. Massell,
22:4, 1991, 327-331, 5.1.5
Individualized Computer Investigations for Calculus, Sheldon P. Gordon, 23:5,
1992, 426-428, C, 5.1.5, 0.7
The Best Shape for a Tin Can, P.L.Roe, 24:3, 1993, 233-236, C, 9.10
The Curious 1/3, James E. Duemmel, 24:3, 1993, 236-237, C
What is the Biggest Rectangle You Can Put Inside a Given Triangle?, Lester H.
Lange, 24:3, 1993, 237-240, C
Old Calculus Chestnuts: Roast, or Light a Fire?, Margaret Cibes, 24:3, 1993,
241-243, C, 1.2
An Optimization Oddity, R. H. Eddy and R. Fritsch, 25:3, 1994, 227-229, C, 9.5
A Visual Proof of Eddy and Fritsch's Minimal Area Property, Robert Pare, 26:1, 1995, 43-44, C, 5.7.2
The Chair, the Area Rug, and the Astroid, Mark Schwartz, 26:3, 1995, 229-231, C, 5.6.1
The Rental Car Problem, Gary D. White and Kirby Smith, 27:5, 1996, 374-378, C, 5.2.1
Halley's Gunnery Rule, C. W. Groetsch, 28:1, 1997, 47-50, C
Using the College Mathematics Journal Topic Index in Undergraduate Courses, Donald E. Hooley, 28:2, 1997, 106-109, 4.1, 4.2, 5.7.1
The Pen and the Barn, Peter Schumer, 28:3, 1997, 205-206, C
FFF #123. A Foot by Any Other Name, David Protas, 29:1, 1998, 34, F
Two Historical Applications of Calculus, Alexander J. Hahn, 29:2, 1998, 93-103, 5.2.9
Minimal Pyramids, Michael Scott McClendon, 29:3, 1998, 224-226, C

       	
5.1.5	Graphs of functions

The Quadratic Polynomial and Its Zeroes, C.A.Long, 3:1, 1972, 23-29, 0.7, 9.5
Graphing a Cubic Using Calculus and a Computer, Roland E. Larsen, 6:1, 1975,
32-40, 0.7
Darboux's Theorem and Points of Inflection, Michael Olinick and Bruce B.
Peterson, 7:3, 1976, 5-9
A Flexible Model for Peak, Ridge, and Pass, Cliff Long, 7:3, 1976, 16-17
Discovering a Calculus Theorem, John Taylor Varner III, 8:5, 1977, 304, C
Income Tax Averaging and Convexity, Michael Henry and G. E. Trapp, Jr., 15:3,
1984, 253-255, C, 0.8, 5.7.1, 9.5
Geometrically Asymptotic Curves, Dan Kalman, 16:3, 1985, 199-206, 9.5
Routine Problems, Sherman Stein, 16:5, 1985, 383-385, 0.2, 1.2
Does "hold water" Hold Water?, Ralph P. Boas, 17:4, 1986, 341, C
Computer Algebra Systems in Undergraduate Mathematics, Don Small and John
Hosack and Kenneth Lane, 17:5, 1986, 423-433, 1.2, 5.1.4, 5.2.2, 5.4.2
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 0.2,
4.1, 5.1.2, 5.2.3, 5.2.4, 5.2.5
Problem Solving Using Microcomputers, Franklin Demana and Bert Waits, 18:3,
1987, 236-241
Pitfalls in Graphical Computation, or Why a Single Graph Isn't Enough, Franklin
Demana and Bert K. Waits, 19:2, 1988, 177-183, 0.6
Parameter-generated Loci of Critical Points of Polynomials, F. Alexander
Norman, 19:3, 1988, 223-229, 0.7, 9.5
Teaching with CAL: A Mathematics Teaching and Learning Environment, James E.
White, 19:5, 1988, 424-443, 1.2
Graphing the Complex Zeros of Polynomials Using Modulus Surfaces, Clff Long and
Thomas Hern, 20:2, 1989, 98-105, 0.7, 9.5
The Curious Fate of an Applied Problem, Alan H. Schoenfeld, 20:2, 1989,
115-123, 8.3, 9.5
Graphing with the HP-28S, John Selden and Annie Selden, 20:5, 1989, 423-432,
1.2
Calculus Quiz, David P. Kraines and Vivian Y. Kraines and David A. Smith, 20:5,
1989, 437-438, C, 1.2
(Sin x)^2: A Sheep in Wolf's Clothing, Mark E. Saul, 21:1, 1990, 43-44, C, 0.6
Quick Function Evaluation, Daniel S. Yates, 21:1, 1990, 51, C, 0.2
The Function sin x / x, William B. Gearhart and Harris S. Shultz, 21:2, 1990,
90-99, 2.2, 5.1.2
A Thousand Points of Light, Gilbert Strang, 21:5, 1990, 406-409
Single Equations Can Draw Pictures, Keith M. Kendig, 22:2, 1991, 134-139, C,
0.4, 0.5, 5.6.1, 5.6.2
FFF #41. The Hazards of Applying Limits without a License, Ed Barbeau, 22:3,
1991, 221, F (also 25:1, 1994, 36-37)
Positivity from Evaluation of a Single Point, Henry Mark Smith, 22:3, 1991,
230-231, C, 0.2
Using Computer Graphics to Help Analyze Complicated Functions, Paul B. Massell,
22:4, 1991, 327-331, 5.1.4
Graphs of Rational Functions for Computer Assisted Calculus, Stan Byrd and
Terry Walters, 22:4, 1991, 332-334, C
Individualized Computer Investigations for Calculus, Sheldon P. Gordon, 23:5,
1992, 426, C, 0.7, 5.1.4
Does a Parabola Have an Asymptote?, David Bange and Linda Host, 24:4, 1993,
331-342, 5.1.1, 5.6.1
Computer-Aided Delusions, Richard L. Hall, 24:4, 1993, 366-369
FFF #75. The Wilting Lines, Randall K. Campbell-Wright, 25:3, 1994, 223, F (also 26:4, 1995, 304 )
Using the Sign Function to Analyze Graphs, Richard J. Pulskamp and William J. Larkin III, 25:4, 1994, 327-328, C
Can We Use the First Derivative to Determine Inflection Points?, Duane Kouba, 26:1, 1995, 31-34
Critical Points of Polynomial Families, Elias Y. Deeba, Dennis M. Rodriquez, and Ibrahim Wazir, 27:4, 1996, 291-295, C, 0.7
Dynamic Function Visualization, Mark Bridger, 27:5, 1996, 361-369, 5.8, 9.5
Bounding the Roots of Polynomials, Holly P. Hirst and Wade T. Macey, 28:4, 1997, 292-295, C, 0.7
Undersampled Sine Waves, J. C. Derderian and Enriqueta Rodriguez-Carrington, 29:3, 1998, 213-218, 0.6


5.2 		Integration 
		
5.2.1		Definition of integrals and the fundamental theorem

Evaluating the integral from a to b of x^k dx Where k Is Any Negative Integer
Other Than -1, Norman Schaumberger, 4:2, 1973, 91-93, C
Some Comments on the Exceptional Case in a Basic Integral Formula, Norman
Schaumberger, 5:3, 1974, 58, C, 5.3.2
Mean Value Type Theorems of Integral Calculus, C. W. Baker, 10:1, 1979, 35-37,
C
Using Integrals to Evaluate Voting Power, Philip D. Straffin, Jr., 10:3, 1979,
179-191, 7.2
Is Ln the Other Shoe?, Byron L. McAllister and J. Eldon Whitesitt, 12:1, 1981,
20-23, 5.3.2
Finding Bounds for Definite Integrals, W. Vance Underhill, 15:5, 1984, 426-429,
C, 5.2.2
Inverse Functions, Ralph P. Boas, 16:1, 1985, 42-47, 5.3.2, 5.4.2
Average Values and Linear Functions, David E. Dobbs, 16:2, 1985, 132-135, C,
5.1.2
Using Riemann Sums in Evaluating a Familiar Limit, Frank Burk, 17:2, 1986,
170-171, C, 5.1.1, 5.3.2
The Derivatives of the Sine and Cosine Functions, Barry A. Cipra, 18:2, 1987,
139-140, C, 5.1.2
Two Simple Recursive Formulas for Summing 1^k + 2^k + ... + n^k, Michael
Carchidi, 18:5, 1987, 406-409, C, 6.3
FFF #6. Cauchy's Negative Definite Integral, Ed Barbeau, 20:3, 1989, 226, F
(also 20:4, 1989, 318)
Riemann Integral of cos x, John H. Mathews and Haines S. Schultz, 20:3, 1989,
237, C
FFF #8. A Positive Vanishing Integral, Ed Barbeau, 20:4, 1989, 317, F (also
20:5, 1989, 404)
Sums and Differences vs. Integrals and Derivatives, Gilbert Strang, 21:1, 1990,
20-27
Teaching Riemann Sums Using Computer Symbolic Algebra Systems, John H. Mathews,
21:1, 1990, 51-55, C, 5.2.2
Using the Finite Difference Calculus to Sum Powers of Integers, Lee Zia, 22:4,
1991, 294-300, 5.4.1, 5.4.2
Physical Demonstrations in the Calculus Classroom, Tom Farmer and Fred Gass,
23:2, 1992, 146-148, C, 1.2, 6.1
How Should We Introduce Integration?, David M. Bressoud, 23:4, 1992, 296-298,
1.2
Riemann Sums and the Exponential Function, Sheldon P. Gordon, 25:1, 1994,
39-40, C, 5.3.2
The Integral of x^(1/2), etc., John H. Mathews, 25:2, 1994, 142-144, C
The Point-Slope Formula Leads to the Fundamental Theorem of Calculus, Anthony J. Macula, 26:2, 1995, 135-139, C
The Rental Car Problem, Gary D. White and Kirby Smith, 27:5, 1996, 374-378, C, 5.1.4
An Example Demonstrating the Fundamental Theorem of Calculus, Bob Palais, 29:4, 1998, 311-312, C



5.2.2	Numerical integration

Encouraging Mathematical Inquisitiveness, Carl L. Main, 1:1, 1970, 32-36, 5.4.2
Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.2, 5.1.4,
5.2.3, 5.2.5, 5.2.10, 5.4.2, 5.6.1, 5.7.2
An Integral Approximation Exact for Fifth-Degree Polynomials, Burt M.
Rosenbaum, 7:3, 1976, 10-14, 9.6
A Short Program for Simpson's or Gazdar's RuleIntegration on Handheld
Programmable Calculators, Abdus Sattar Gazdar, 9:3, 1978, 182-185
Calculator-Demonstrated Math Instruction, George McCarty, 11:1, 1980, 42-48,
5.1.1, 5.4.2, 9.6
Finding Bounds for Definite Integrals, W. Vance Underhill, 15:5, 1984, 426-429,
C, 5.2.1
Behold! The Midpoint Rule is Better than the Trapezoidal Rule for Concave
Functions, Frank Burk, 16:1, 1985, 56, C
Testing Understanding and Understanding Testing, Jean Pedersen and Peter Ross,
16:3, 1985, 178-185, 0.2, 1.2, 5.1.2
Numerical Integration via Integration by Parts, Frank Burk, 17:5, 1986,
418-422, C, 5.2.5
Computer Algebra Systems in Undergraduate Mathematics, Don Small and John
Hosack and Kenneth Lane, 17:5, 1986, 423-433, 1.2, 5.1.4, 5.1.5, 5.4.2
Archimedes' Quadrature and Simpson's Rule, Frank Burk, 18:3, 1987, 222-223, C
A Clamped Simpson's Rule, James A. Uetrecht, 19:1, 1988, 43-52, 9.6
Applications of Transformation to Numerical Integration, Chris W. Avery and
Frank D. Soler, 19:2, 1988, 166-168, C
Teaching Riemann Sums Using Computer Symbolic Algebra Systems, John H. Mathews,
21:1, 1990, 51-55, C, 5.2.1
Circumference of a CircleThe Hard Way, David P. Kraines and Vivian Y. Kraines
and David A. Smith, 21:2, 1990, 142-144, C, 5.2.10
Determining Sample Sizes for Monte Carlo Integration, David Neal, 24:3, 1993,
254-259, C, 7.3, 9.10
Cubic Splines from Simpson's Rule, Nishan Krikorian and Mark Ramras, 27:2, 1996, 124-126, C, 9.6	
5.2.3	Change of variable (substitution)

Some Problems of Utmost Gravity, William C. Stretton, 3:1, 1972, 72-75, C, 5.7.2
Formal Integration: Dangers and Suggestions, S. K. Stein, 5:1, 1974, 1-7, 5.2.8
Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.2, 5.1.4, 5.2.2, 5.2.5, 5.2.10, 5.4.2, 5.6.1, 5.7.2
A Simple Antidifferentiation Technique, Alan H. Schoenfeld, 9:2, 1978, 104-105, C
Another Approach to the integral of sec x dx, Norman Schaumberger, 10:3, 1979, 202, C
A Standard Integral Formula, R. S. Luthar, 12:5, 1981, 329-330, C
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 0.2, 4.1, 5.1.2, 5.1.5, 5.2.4, 5.2.5
Computing Pi, Harley Flanders, 18:3, 1987, 230-235, 5.4.2, 8.1
Lattices of Trigonometric Identities, William E. Rosenthal, 20:3, 1989, 232-234, C, 0.6
A Direct Proof of the Integral Formula for Arctangent, Arnold J. Insel, 20:3, 1989, 235-237, C, 5.1.2, 5.2.6
Four Crotchets on Elementary Integration, Leroy F. Meyers, 22:5, 1991, 410-413, C, 5.2.5, 5.3.2, 6.1
Reduction Formulas Revisited, T. N. Subramaniam and D. E. G. Malm, 22:5, 1991, 421-429, 5.2.5
Gather; Don't Strew, Bob Weinstock, 23:5, 1992, 372, C
Does What Goes Up Take the Same Time to Come Down?, P. Glaister, 24:2, 1993, 155-158, C, 9.10
FFF #101. The Disappearing Factor, James C. Kirby, 27:2, 1996, 117, F, 5.2.10
FFF #102. Why Integrate?, James C. Kirby, 27:2, 1996, 118, F
Antiderivative Formulas, Jingcheng Tong, 29:1, 1998, 32, C

	
5.2.3	Change of varible (substitution)

Some Problems of Utmost Gravity, William C. Stretton, 3:1, 1972, 72-75, C,
5.7.2
Formal Integration: Dangers and Suggestions, S.K.Stein, 5:1, 1974, 1-7, 5.2.8
Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.2, 5.1.4,
5.2.2, 5.2.5, 5.2.10, 5.4.2, 5.6.1, 5.7.2
A Simple Antidifferentiation Technique, Alan H. Schoenfeld, 9:2, 1978, 104-105,
C
Another Approach to the integral of sec x dx, Norman Schaumberger, 10:3, 1979,
202, C
A Standard Integral Formula, R.S.Luthar, 12:5, 1981, 329-330, C
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 0.2,
4.1, 5.1.2, 5.1.5, 5.2.4, 5.2.5
Computing Pi, Harley Flanders, 18:3, 1987, 230-235, 5.4.2, 8.1
Lattices of Trigonometric Identities, William E. Rosenthal, 20:3, 1989,
232-234, C, 0.6
A Direct Proof of the Integral Formula for Arctangent, Arnold J. Insel, 20:3,
1989, 235-237, C, 5.1.2, 5.2.6
Four Crotchets on Elementary Integration, Leroy F. Meyers, 22:5, 1991, 410-413,
C, 5.2.5, 5.3.2, 6.1
Reduction Formulas Revisited, T.N.Subramaniam and D.E.G.Malm, 22:5, 1991,
421-429, 5.2.5
Gather; Don't Strew, Bob Weinstock, 23:5, 1992, 372, C
Does What Goes Up Take the Same Time to Come Down?, P. Glaister, 24:2, 1993,
155-158, C, 9.10
FFF #101. The Disappearing Factor, James C. Kirby, 27:2, 1996, 117, F, 5.2.10
FFF #102. Why Integrate?, James C. Kirby, 27:2, 1996, 118, F
Antiderivative Formulas, Jingcheng Tong, 29:1, 1998, 32, C

	
5.2.4	Partial fraction decomposition

An Alternative for Partial Fractions (part of the time), J.E Nymann, 14:1,
1983, 60-61, C
Efficient Techniques for Partial Fractions, Padmini T. Joshi, 14:2, 1983,
110-118
An Algebraic Approach to Partial Fractions, Phillip Schultz, 14:4, 1983,
346-348, C
An Alternative for Certain Partial Fractions, Sylvan Burgstahler, 15:1, 1984,
57-58, C
An Algebraic Approach to Partial Fractions, Joseph Wiener, 17:1, 1986, 71-72, C
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 0.2,
4.1, 5.1.2, 5.1.5, 5.2.3, 5.2.5
A Shortcut to Partial Fractions, Xun-Cheng Huang, 22:5, 1991, 413-415, C
Differentiation via Partial Fractions: A Case Against CAS, Russell Jay Hendel,
22:5, 1991, 415-417, C
An Invitation to Integration in Finite Terms, Elena Anne Marchisotto and Gholam-Ail Zakeri, 25:4, 1994, 295-308, 2.2, 5.2.5, 5.2.9
		
5.2.5	Integration by parts

The integral of f(x) exp(ax)dx, H. L. Kung, 1:2, 1970, 106, C, 5.3.2
Integration by Undetermined Coefficients, Louise Grinstein, 2:2, 1971, 98-100,
5.3.2
Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.2, 5.1.4,
5.2.2, 5.2.3, 5.2.10, 5.4.2, 5.6.1, 5.7.2
Inter-related Concepts: An Example, Mark D. Galit and John P. Pace, 7:1, 1976,
7-10
A Discovery Approach to Integration by Parts, John Staib and Howard Anton,
10:5, 1979, 353-354, C
Integration by Parts, V.N.Murty, 11:2, 1980, 90-94
Creative Teaching by Mistakes, Andrejs Dunkels and Lars-Erik Persson, 11:5,
1980, 296-300, 6.1
Differential Operators Applied to Integration, Kong-Ming Chong, 13:2, 1982,
155-157, C, 6.2
Evaluating Integrals by Differentiation, Joseph Wiener, 14:2, 1983, 168-169, C,
5.3.1
Evaluating the integrals of sec x dx and (sec x)^3 dx, Bruce Sommer and Norman
Schaumberger, 14:3, 1983, 256-257, C, 5.3.3
A Note on Integration by Parts, Andre L. Yandl, 16:4, 1985, 282-283, C
Numerical Integration via Integration by Parts, Frank Burk, 17:5, 1986,
418-422, C, 5.2.2
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 0.2,
4.1, 5.1.2, 5.1.5, 5.2.3., 5.2.4
Pi/4 and ln 2 Recursively, Frank Burk, 18:1, 1987, 51, C, 5.4.2
FFF #17. cosh x = sinh x and 1 = 0, Ed Barbeau, 21:2, 1990, 128, F, 5.3.3
FFF #19. Dolt's Theorem: 0=1, Ed Barbeau, 21:3, 1990, 216-217, F (also 22:2,
1991, 133)
Moments on a Rose Petal, Douglass L. Grant, 21:3, 1990, 225-227, C, 5.6.1
More on Tabular Integration by Parts, Leonard Gillman, 22:5, 1991, 407-410, C
Four Crotchets on Elementary Integration, Leroy F. Meyers, 22:5, 1991, 410-413,
C, 5.2.3, 5.3.2, 6.1
Reduction Formulas Revisited, T.N.Subramaniam and D.E.G.Malm, 22:5, 1991,
421-429, 5.2.3
Integrals of Products of Sine and Cosine with Different Arguments, Sherrie J.
Nicol, 24:2, 1993, 158-160, C
An Invitation to Integration in Finite Terms, Elena Anne Marchisotto and Gholam-Ail Zakeri, 25:4, 1994, 295-308, 2.2, 5.2.4, 5.2.9
FFF #96. Derivative of Products, W. Heierman, 27:1, 1996, 45, F
Who Cares if X2 + 1 = 0 Has a Solution?, Viet Ngo and Saleem Watson, 29:2, 1998, 141-144, C, 0.7, 5.4.2, 6.2

		
5.2.6	Area

Integration by Geometric InsightA Student's Approach, Ann D. Holley, 12:4,
1981, 268-270, C, 5.3.1, 5.3.2
Area of a Parabolic Region, R. Rozen and  A. Sofo, 16:5, 1985, 400-402, C, 0.5
The Surveyor's Area Formula, Bart Braden, 17:4, 1986, 326-337, 4.2, 5.2.8
Annuities as Areas, Kurt W. Riemann, 18:1, 1987, 45-47, C
A Direct Proof of the Integral Formula for Arctangent, Arnold J. Insel, 20:3,
1989, 235-237, C, 5.1.2, 5.2.3
Exploring the Volume-Surface Area Relationship, Keith A. Struss, 21:1, 1990,
40-43, C, 5.2.7
Relations between Surface Area and Volume in Lakes, Daniel Cass and Gerald
Wildenberg, 21:5, 1990, 384, 5.2.7
FFF #99. Polar Increment of Area, Peter Jarvis and Paul Schuette, 27:2, 1996, 117, F, 5.6.1	

		
5.2.7	Volume

Some Surprising Volumes of Revolution, G.L.Alexanderson and L.F.Klosinski, 6:3,
1975, 13-15
Another Way of Looking at n!, David Hsu, 11:5, 1980, 333-334, C, 5.7.2
A Note on the Surface of a Sphere, Arthur C. Segal, 13:1, 1982, 63-64, C
The Grazing Goat in n Dimensions, Marshall Fraser, 15:2, 1984, 126-134
A Sequel to "Another Way of Looking at n!", William Moser, 15:2, 1984, 142-143,
C, 3.2, 5.7.2
Return of the Grazing Goat in n Dimensions, Mark D. Meyerson, 15:5, 1984,
430-431
Exploring the Volume - Surface Area Relationship, Keith A. Struss, 21:1, 1990,
40-43, C, 5.2.6
Relations between Surface Area and Volume in Lakes, Daniel Cass and Gerald
Wildenberg, 21:5, 1990, 384-389, 5.2.6
The Volume and Centroid of the Step Pyramid of Zoser, Anthony Lo Bello, 22:4,
1991, 318-321, C, 5.2.9
Disks, Shells, and Integrals of Inverse Functions, Eric Key, 25:2, 1994,
136-138, C
Did Plutarch Get Archimedes' Wishes Right?, Lester H. Lange, 26:3, 1995, 199-204, 2.1
Finding Volumes with the Definite Integral: A Group Project, Mary Jean Winter, 26:3, 1995, 227-228, C
The World's Biggest Taco, David D. Bleecker and Lawrence J. Wallen, 29:1, 1998, 2-12, 5.3.4, 9.5
Characterizing Power Functions by Volumes of Revolution, Bettina Richmond and Tom Richmond, 29:1, 1998, 40-41, C, 6.4


5.2.8	Arc length

Arc Length Revisited, F.A.Chimenti, 4:3, 1973, 88-89, C
Formal Integration: Dangers and Suggestions, S.K.Stein, 5:2, 1974, 1-7, 5.2.3
Some Ridge-Length Problems, John W. Dawson, Jr., 7:4, 1976, 43-45, C
Surface Area and the Cylindar Area Paradox, Frieda Zames, 8:4, 1977, 207-211
Dimple or No Dimple, Jane T. Grossman and Michael P. Grossman, 13:1, 1982,
52-55
Rectangular Aids for Polar Graphs, Alice W. Essary, 13:3, 1982, 200-205, 5.6.1
The Surveyor's Area Formula, Bart Braden, 17:4, 1986, 326-337, 4.2, 5.2.6
Mercator's Rhumb Lines: A Multivariable Application of Arc Length, John Nord and Edward Miller, 27:5, 1996, 384-387, C, 5.6.1
On Arc Length, P. D. Barry, 28:5, 1997, 338-347
A Note on the Ratio of Arc Length to Chordal Length, Paul Eenigenburg, 28:5, 1997, 391-393, C
Revisiting Arc Length, Leonard Gillman, 29:2, 1998, 137-138, C
The Buckled Rail: Three Formulations, James E. Mann Jr., 29:2, 1998, 138-141, C
Arc Length Contest, Larry Riddle, 29:4, 1998, 314-320

		
5.2.9	Other theory and applications of integration

A New Look at an Old Work Problem, Bert K. Waits and Jerry L. Silver, 4:3,
1973, 52-55
Bat and Superbat, Herbert R. Bailey, 18:4, 1987, 307-314, 6.4
The Volume and Centroid of the Step Pyramid of Zoser, Anthony Lo Bello, 22:4,
1991, 318-321, C, 5.2.7
FFF #50. The Lopsided Uniform Rod, Ed Barbeau, 23:1, 1992, 36-37, F (also 24:4,
1993, 345)
FFF. The Surface Area of a Sphere, Ed Barbeau, 23:3, 1992, 206, F
An Invitation to Integration in Finite Terms, Elena Anne Marchisotto and Gholam-Ail Zakeri, 25:4, 1994, 295-308, 2.2, 5.2.4, 5.2.5
Symmetry and Integration, Roger Nelsen, 26:1, 1995, 39-41, C
A Generalization of the Mean Value Theorem for Integrals, M. Sayrafiezadeh, 26:3, 1995, 223-224, C
A Normal Density Project, Robert K. Stump, 26:4, 1995, 310-312, C


		
5.2.10		Improper integrals

Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.2, 5.1.4,
5.2.2, 5.2.3, 5.2.5, 5.4.2, 5.6.1, 5.7.2
Circumference of a CircleThe Hard Way, David P. Kraines and Vivian Y. Kraines
and David A. Smith, 21:2, 1990, 142-144, C, 5.2.2
FFF #62. An Improper Integral, Ed Barbeau, 24:4, 1993, 343, F
Numerical Methods for Improper Integrals, Gerald Flynn, 26:4, 1995, 284-291, 9.6
FFF #101. The Disappearing Factor, James C. Kirby, 27:2, 1996, 117, F, 5.2.3
FFF #117. Blowing up the Integrand, Ronald J. Fischer, 28:3, 1997, 199, F
Two Historical Applications of Calculus, Alexander J. Hahn, 29:2, 1998, 93-103, 5.1.4


5.3		Elementary and special functions 
        	
5.3.1		Inverse trigonometric functions

Applying Complex Arithmetic, Herbert L. Holden, 12:3, 1981, 190-194, 0.6, 9.3,
9.5
Integration by Geometric InsightA Student's Approach, Ann D. Holley, 12:4,
1981, 268-270, C, 5.2.6, 5.3.2
The Derivative of Arctan x, Norman Schaumberger, 13:4, 1982, 274-276, C
Evaluating Integrals by Differentiation, Joseph Wiener, 14:2, 1983, 168-169, C,
5.2.5
The Derivatives of Arcsec x, Arctan x, and Tan x, Norman Schaumberger, 17:3,
1986, 244-246, C
Three Familiar Formulas for pi via Geometry, Norman Schaumberger, 17:4, 1986,
339, C
Behold! Sums of Arctan, Edward M. Harris, 18:2, 1987, 141, C
Trigonometric Identities through Calculus, Herb Silverman, 21:5, 1990, 403, C,
0.6
Graphs and Derivatives of the Inverse Trig Functions, Daniel A. Moran, 22:5,
1991, 417, C
Gudermann and the Simple Pendulum, John S. Robertson, 28:4, 1997, 271-276, 6.4
The Derivative of the Inverse Sine, Craig Johnson, 29:4, 1998, 313, C



5.3.2 	Exponential and logarithmic functions

The integral of f(x)exp(ax) dx, H. L. Kung, 1:2, 1970, 106, C, 5.2.5
Integration by Undetermined Coefficients, Louise Grinstein, 2:2, 1971, 98-100,
5.2.5
Which is Larger, e^pi or pi^e?, Ivan Niven, 3:2, 1972, 13-15
An Alternate Classroom Proof of the Familiar Limit for e, Norman Schaumberger,
3:2, 1972, 72-73, C
Random Sieving and the Prime Number Theorem, Karl Greger, 5:1, 1974, 41-46, 9.3
Some Comments on the Exceptional Case in a Basic Integral Formula, Norman
Schaumberger, 5:3, 1974, 58, C, 5.2.1
Two More Proofs of a Familiar Inequality, Erwin Just and Norman Schaumberger,
6:2, 1975, 45, C
A Geometric Approach to a Basic Limit, Norman Schaumberger, 7:1, 1976, 11-12
Using Inverse Functions in Integration, Robert C. Crawford, 8:2, 1977, 107-109,
C, 5.3.3
A Neglected Approach to the Logarithm, Bruce S. Babcock and John W. Dawson,
Jr., 9:3, 1978, 136-140, 5.1.1
On the General Power Function, P.S.Chee and S.T.Chin, 11:1, 1980, 51, C
Is Ln the Other Shoe?, Byron L. McAllister and J. Eldon Whitesitt, 12:1, 1981,
20-23, 5.2.1
Obtaining a Numerical Estimate for e, David H. Anderson, 12:1, 1981, 30-33
A "Proof" that 0=1, Norman Schaumberger, 12:3, 1981, 211, C
Euclid's 'Elements' -excerpts from a 1660 edition, 12:2, 1981, 117, 0.3, 5.3.3
Integration by Geometric InsightA Student's Approach, Ann D. Holley, 12:4,
1981, 268-270, C, 5.2.6, 5.3.1
Motivating e by Calculator, Arthur C. Segal, 13:4, 1982, 271, C
A Nonlogarithmic Proof That (1 +1/n )^n has limit e, Lee Badger, 13:5, 1982,
331-332, C
A Logarithm Algorithm for Four-Function Calculators, David Cusick, 14:4, 1983,
322, 0.2
A Logarithm Algorithm for a Five-Function Calculator, Donald L. Muench and
Gerald Wildenberg, 14:4, 1983, 324-326
Another Way to Introduce Natural Logarithms and e, Robert R. Christian, 14:5,
1983, 424-426
Evaluating e^x Using Limits, Sheldon P. Gordon, 15:1, 1984, 63-65, 5.4.2
Inverse Functions, Ralph P. Boas, 16:1, 1985, 42-47, 5.2.1, 5.4.2
Euler's Constant, Frank Burk, 16:4, 1985, 279, C
An Instant Proof of e^pi > pi^e, Norman Schaumberger, 16:4, 1985, 280, C
Using Riemann Sums in Evaluating a Familiar Limit, Frank Burk, 17:2, 1986,
170-171, C, 5.1.1, 5.2.1
The Change of Base Formula for Logarithms, Chris Freiling, 17:5, 1986, 413, C,
0.2
Comparing B^A and A^B for A>B, John Rosendahl and James Gilmore, 18:1, 1987,
50, C
Behold! The Graphs of f and f inverse are Reflections about the Line y=x, Ayoub
B. Ayoub, 18:1, 1987, 52, C, 0.2
A Depreciation Model for Calculus Classes, John C. Hegarty, 18:3, 1987,
219-221, C
The Relationship Between Hyperbolic and Exponential Functions, Roger B. Nelsen,
19:1, 1988, 54-56, C, 5.3.3
An Efficient Logarithm Algorithm for Calculators, James C. Kirby, 19:3, 1988,
257-260, C, 9.6
The Age of the Solar System, Winston Phrobis, 21:5, 1990, 399-400, C
The Snowplow Problem Revisited, Xiao-peng Xu, 22:2, 1991, 139, C, 6.1
FFF #44. A New Way to Obtain the Logarithm, Ed Barbeau, 22:5, 1991, 403, F
Four Crotchets on Elementary Integration, Leroy F. Meyers, 22:5, 1991, 410-413,
C, 5.2.3, 5.2.5, 6.1
FFF #49. Two Transcendental Equations, Ed Barbeau, 23:1, 1992, 36, F, 0.2
The Relationship Between Hyperbolic and Exponential FunctionsRevisited, Roger
B. Nelsen, 23:3, 1992, 207-208, C, 5.3.3
Napier's Inequality (two proofs), Roger B. Nelsen, 24:2, 1993, 165, C
FFF #58. A Rational Combination of Two Transcendentals, Ed Barbeau, 24:3, 1993,
229, F, 0.2
FFF #60. A Two-Valued Function, Ed Barbeau, 24