The final issue of volume 46 completes The College Mathematics Journal's series of lead articles from Pólya Award and other MAA writing award winners. In this issue, read about a student who caught Bud Brown teaching the same theorem in two classes and join in her understanding of the connection between the contexts. There are two other pages inspired by the MAA's centennial celebration. Brian Beasley and David Stone consider the history of posing mathematical problems from Johann Bernoulli up through the vibrant Problems and Solutions sections of the MAA journals, considering how these popular sections contribute to research and teaching. The review section this time consists of excerpts from 18 interviews posted on the MAA's centennial website; enjoy finding out more about some of the individuals who help make the MAA so lively and effective. -Brian Hopkins
Vol 46 No 5, pp 324-400
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ARTICLES
Saints and Scoundrels and Two Theorems That Are Really the Same
Ezra Brown
The Chinese remainder theorem and the polynomial interpolation theorem are foundational theorems of number theory and numerical analysis, respectively. These two theorems are special cases of a construct in a more general setting and we describe a scenario—namely, two back-to-back classes—in which students can discover this fact. We end by describing that general setting, in which the key idea is an ability to write 1 in a special way.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.326
Proof Without Words: Centered Triangular Numbers
Roger B. Nelsen
We wordlessly prove a theorem relating centered triangular numbers to the ordinary triangular numbers.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.335
Journal Problems Sections: Modern Challenges and Teaching Tools
Brian D. Beasley and David R. Stone
As the Mathematical Association of America enters its second century, this article cites some historical mathematical challenges, relating this unique disciplinary practice to the problems sections in today's journals. It presents some results of a survey conducted with the editors of problems sections in various journals and with several mathematicians active throughout their careers as posers and solvers of problems. For example, it includes their views on the general role of problem solving in the mathematical enterprise, their experience with specific applications in both teaching and research, and a sample of their all-time favorite problems.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.336
Proof Without Words: Bounding the Euler–Mascheroni Constant
Meiyue Shao
We show bounds for the Euler–Mascheroni constant using the trapezoidal and midpoint approximations for integrals.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.347
A Sufficient Condition for Subgroups with Prime Indices to Be Normal
Cosmin Pohoata and Richard Stong
We extend two group theory exercises to determine a necessary condition for a prime index finite subgroup to be normal.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.348
Predicting Wins and Losses: A Volleyball Case Study
Elizabeth Knapper and Hope McIlwain
For a sports fan, predicting whether a favored team will win or lose can be an enticing past time. Using the mathematical ranking method known as the Massey method, we use data from volleyball matches to rate and rank teams. We then use our rankings to predict the outcome of future matches. As an example, we apply these methods to the 2013 women's indoor volleyball season of the Atlantic Sun Conference.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.352
Explicit Form of the Faulhaber Polynomials
José Luis Cereceda
Hersh recently showed that the Faulhaber polynomials, related to sums of consecutive powers, can be expressed as even or odd polynomials in the variable offset by one-half. In this article, we use generating functions to give explicit formulas for all terms in these polynomials.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.359
Classroom Capsules
A Short Proof of Symmetric Inequalities
Kambiz Razminia
We present a general simple approach for proving symmetric inequalities and apply it to several examples.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.364
A Note on the Fundamental Theorem of Calculus
Zengxiang Tong
We redeem some “bad” choices for antiderivatives in applications of the fundamental theorem of calculus and suggest a revision for its statement.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.367
Problems and Solutions
Problems and Solutions: 369-376
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.369
Book Review
Excerpts From MAA Interviews
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.377
Media Highlights
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.385
George Pólya Awards for 2015
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.46.5.393