Algebra and Number Theory

• Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability, by Peter Pesic. Reviewed by David Graves.
  
• Abstract Algebra, Third Edition, by David S. Dummit and Richard M. Foote. Briefly noted.
  
• Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, by David Joyner. Reviewed by Donald L. Vestal
  
• Algebra, volumes I and II, by B. L. van der Waerden. Briefly noted
  
• Algebra and Geometry, by Alan F. Beardon. Reviewed by Stephen Ahearn
  
• Algebra from A to Z, Vols 1-5, by A.W. Goodman. Briefly noted.
  
• Algebra in Ancient and Modern Times, by V. S. Varadarajan. Reviewed by Ed Sandifer
  
• Algebraic Numbers and Algebraic Functions, by Emil Artin. Reviewed by Fernando Q. Gouvêa
  
• Algebraic Projective Geometry, by J. G. Semple and G. T. Kneebone. Briefly noted.
  
• Analytic Number Theory: An Introductory Course, by Paul T. Bateman and Harold G. Diamond. Briefly noted.
  
• Arabesques and Geometry, by A. F. Costa and B. Gomez (Springer VideoMATH). Reviewed by Mark McKibben
  
• Arithmetic for Teachers: With Applications and Topics from Geometry, by Gary R. Jensen. Reviewed by William P. Berlinghoff
  
• Basic Linear Algebra, by T. S. Blyth and E. F. Robertson. Reviewed by Maria G. Fung
  
• The Beginnings and Evolution of Algebra, by Isabella Bashmakova and Galina Smirnova. Reviewed by G. L. Alexanderson
  
• A Brief Guide to Algebraic Number Theory, by H. P. F. Swinnerton-Dyer. Briefly noted.
  
• Categories and Modules: With K-theory in View, by A. J. Berrick and M. E. Keating. Briefly noted.
  
• Codebreakers: Arne Beurling and the Swedish Crypto Program During World War II, by Bengt Beckman. Reviewed by Donald L. Vestal
  
• Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, by W. Magnus, A. Karrass, and D. Solitar. Reviewed by Joseph Rotman
  
• Computational Excursions in Analysis and Number Theory, by Peter Borwein. Reviewed by Charles Ashbacher
  
• A Course in Computational Number Theory, by David Bressoud and Stan Wagon. Reviewed by David P. Roberts
  
• Cryptography: An Introduction, edited by V. V. Yaschenko. Briefly noted
  
• Cryptological Mathematics, by Robert Edward Lewand. Reviewed by Thomas R. Berger
  
• The Development of Prime Number Theory, by W. Narkiewicz. Briefly noted.
  
• Discourses on Algebra, by Igor R. Shafarevich. Reviewed by Mihaela Poplicher
  
• Discovering Number Theory, by Jeff Holt and John Jones. Reviewed by Donald L. Vestal
  
• Diophantus and Diophantine Equations, by Isabella Grigoryevna Bashmakova. Reviewed by David Graves
  
• Elementary Algebraic Geometry, by Klaus Hulek. Reviewed by José Felipe Voloch
  
• Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis, by Felix Klein. Briefly noted
  
• Elementary Mathematics from an Advanced Standpoint: Geometry, by Felix Klein. Briefly noted
  
• Elementary Number Theory and its Applications, 5th Edition, by Kenneth H. Rosen. Reviewed by David P. Roberts
  
• Elementary Number Theory, Group Theory and Ramanujan Graphs, by Giuliana Davidoff, Peter Sarnak. and Alain Valette. Briefly noted
  
• Elementary Number Theory in Nine Chapters, by James J. Tattersall. Briefly noted.
  
• The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry, by Mario Livio. Reviewed by Darren Glass
  
• Equations and Inequalities: Elementary Probems and Theorems in Algebra and Number Theory, by Jiri Herman, Radan Kucera, and Jaromir Simsa. Reviewed by Donald L. Vestal
  
• Ergodic Theory of Numbers, by Karma Dajani and Cor Kraaikamp. Reviewed by Jim Walsh
  
• Essays in Constructive Mathematics, by Harold M. Edwards. Reviewed by Bonnie Shulman
  
• Exploring the Number Jungle: A Journey into Diophantine Analysis, by Edward B. Burger. Reviewed by Fernando Q. Gouvêa
  
• Fearless Symmetry: Exposing the Hidden Patterns of Numbers, by Avner Ash and Robert Gross. Reviewed by Darren Glass
  
• The Fermat Diary, by C. J. Mozzochi. Reviewed by Robert A. McGuigan
  
• Fermat's Last Theorem for Amateurs, by Paulo Ribenboim. Reviewed by David Graves
  
• Field Theory and its Classical Problems, by Charles Robert Hadlock. Briefly noted.
  
• A First Course in Abstract Algebra: Rings, Groups, and Fields, by Marlow Anderson and Todd Feil. Briefly noted
  
• The Fourier-Analytic Proof of Quadratic Reciprocity, by Michael C. Berg. Briefly noted.
  
• Function Field Arithmetic, by Dinesh Thakur. Briefly noted
  
• Further Linear Algebra, by T.S. Blyth and E.F. Robertson. Reviewed by Morteza Seddighin
  
• Galois Theory of p-Extensions, by Helmut Koch. Briefly noted
  
• Gamma: Exploring Euler's Constant, by Julian Havil. Reviewed by Jeremy Gray
  
• The Geometry of Numbers, by C. D. Olds, Anneli Lax, and Giuliana Davidoff. Reviewed by Henry Cohn
  
• The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry, by David Eisenbud. Reviewed by David P. Roberts
  
• Grothendieck-Serre Correspondence: Bilingual Edition. Briefly noted
  
• Group Representation Theory for Physicists, by Jin-Quan Chen, Jialun Ping, and Fan Wong. Briefly noted.
  
• Handbook of Elliptic and Hyperelliptic Curve Cryptography, by Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, and Frederik Vercauteren. Reviewed by Fernando Q. Gouvêa
  
• Identification Numbers and Check Digit Schemes, by Joseph Kirtland. Reviewed by Doug Ensley.
  
• In Code: A Mathematical Journey, by Sarah Flannery with David Flannery. Reviewed by Marvin Schaefer
  
• Innovations in Teaching Abstract Algebra, ed. by Allen C. Hibbard and Ellen J. Maycock. Reviewed by Andrew B. Perry
  
• An Introduction to Number Theory, by Graham Everest and Thomas Ward. Reviewed by Rob Benedetto
  
• Invitation to the Mathematics of Fermat-Wiles, by Yves Hellegouarch. Reviewed by Donald L. Vestal
  
• Irrational Numbers, by Ivan Niven. Briefly noted
  
• Lattices and Ordered Algebraic Structures, by T.S. Blyth. Briefly noted
  
• Lectures in Number Theory, by P. G. L. Dirichlet, with supplements by Richard Dedekind. Briefly noted.
  
• Lectures on the Icosahedron, by Felix Klein. Briefly noted
  
• The Legacy of Niels Henrik Abel, ed. by Olav Arnfinn Laudal and Ragni Piene. Briefly noted
  
• Linear Algebra: Examples and Applications, by Alain M. Robert. Reviewed by Luiz Henrique de Figueiredo
  
• Linear Algebra Gems, ed. by David Carlson, Charles R. Johnson, David C. Lay, and A. Duane Porter. Reviewed by Michele Intermont
  
• Logic as Algebra, by Paul Halmos and Steven Givant. Reviewed by Mark Johnson
  
• Making Transcendence Transparent: An Intuitive Approach to Classical Transcendental Number Theory, by Edward B. Burger and Robert Tubbs. Reviewed by Álvaro Lozano Robledo
  
• Math Talks for Undergraduates, by Serge Lang. Reviewed by Richard K. Guy
  
• Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry, by Branislav Kisacanin. Reviewed by Carl D. Mueller
  
• Matrix Analysis and Applied Linear Algebra, by Carl D. Meyer. Reviewed by Joel Foisy
  
• Matrix Groups for Undergraduates, by Kristopher Tapp. Reviewed by David P. Roberts
  
• Matrix Groups: An Introduction to Lie Group Theory, by Andrew Baker. Reviewed by David P. Roberts
  
• Modular Forms and Galois Cohomology, by Haruzo Hida. Briefly noted.
  
• Multiplicities and Chern Classes in Local Algebra, by Paul C. Roberts. Briefly noted.
  
• The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, by Marcus du Sautoy. Reviewed by Stacy G. Langton
  
• My Numbers, My Friends: Popular Lectures on Number Theory, by Paulo Ribenboim. Reviewed by Marvin Schaefer
  
• New Visual Perspectives on Fibonacci Numbers, by Krassimir Atanassova, Vassia Atanassova, Anthony Shannon and John Turner. Briefly noted
  
• The Number π, by Pierre Eymard and Jean-Pierre Lafon. Reviewed by Henry Ricardo
  
• Number: from Ahmes to Cantor, by Midhat Gazalé. Reviewed by Marvin Schaefer
  
• Numbers, Groups & Codes, Second Edition, by J. F. Humphreys and M. Y. Prest. Reviewed by Thomas R. Berger
  
• On Quaternions and Octonions, by John Horton Conway and Derek A. Smith. Reviewed by Michael Berg
  
• Oval Track and other Permutation Puzzles, and just enough group theory to solve them, by John O. Kiltinen. Reviewed by Ruth I. Berger
  
• Pascal's Arithmetical Triangle: The story of a mathematical idea, by A. W. F. Edwards. Reviewed by Herbert E. Kasube
  
• Pi: A Source Book, Third Edition, ed. by Lennart Berggren, Jonathan Borwein, and Peter Borwein. Briefly noted
  
• Pi Unleashed, by by Jörg Arndt and Christoph Haenel. Reviewed by Carl D. Mueller
  
• Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer, by Charles W. Curtis. Reviewed by Andrew Leahy
  
• Pluckings from the Tree of Smarandache Sequences and Functions, by Charles Ashbacher. Briefly Noted.
  
• Power Play, by Ed Barbeau. Reviewed by David Graves
  
• Practical Linear Algebra: A Geometry Toolbox, by Gerald Farin and Dianne Hansford. Reviewed by Warren Johnson
  
• A Prime for the Millennium, by John B. Cosgrave. Briefly Noted.
  
• The Prime Number Theorem, by G. J. O. Jameson. Reviewed by David M. Bressoud
  
• The Prime Numbers and their Distribution, by Gérald Tenenbaum and Michel Mendès-France. Reviewed by Michael Berg
  
• Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, by John Derbyshire. Reviewed by S. W. Graham
  
• A Primer of Analytic Number Theory: From Pythagoras to Riemann, by Jeffrey Stopple. Reviewed by S. W. Graham
  
• Problems in Algebraic Number Theory, Second Editon, by Jody Esmonde and M. Ram Murty. Briefly noted.
  
• Project Origami: Activities for Exploring Mathematics, by Thomas Hull. Reviewed by Steven Frankel
  
• Pythagorean Triangles, by Wacław Sierpiński. Reviewed by Donald L. Vestal
  
• Ramsey Theory on the Integers, by Bruce M. Landman and Aaron Robertson. Reviewed by Mihaela Poplicher
  
• Reciprocity Laws : From Euler to Eisenstein, by Franz Lemmermeyer. Briefly noted.
  
• Representation Theory of Finite Reductive Groups, by Marc Cabanes and Michel Enguehard. Briefly noted
  
• Resources for Teaching Linear Algebra, edited by David Carlson et. al. Reviewed by Rebecca Berg
  
• The Riemann Hypothesis: The Greatest Unsolved Problem of Mathematics, by Karl Sabbagh. Reviewed by S. W. Graham
  
• The Riemann Zeta-Function, by Aleksandar Ivic. Briefly noted
  
• Ruler and the Round: Classic Problems in Geometric Constructions, by Nicholas D. Kazarinoff. Reviewed by P. N. Ruane
  
• Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers, by Dan Rockmore. Reviewed by S. W. Graham
  
• The Structure of Spherical Buildings, by Richard M. Weiss. Briefly noted
  
• Surveys in Number Theory: Papers from The Millennial Conference on Number Theory, ed. by M. A. Bennett, B. C. Berndt, N. Boston, H. G. Diamond, A. J. Hildebrand, and W. Philipp. Briefly noted.
  
• Symmetry and the Monster: One of the Greatest Quests of Mathematics, by Mark Ronan. Reviewed by Darren Glass
  
• A Taste of Jordan Algebras, by Kevin McCrimmon. Reviewed by Michael Berg
  
• The Theory of Finite Groups: An Introduction, by Hans Kurzweil and Bernd Stellmacher. Briefly noted
  
• Topics in Number Theory, by Paul Erdös and János Surányi. Reviewed by Donald L. Vestal