TAILIEUCHUNG - THE AMERICAN MATHEMATICAL MONTHLY VOLUME 119, NO. 1

Rediscovering Mathematics is an eclectic collection of mathematical topics and puzzles aimed at talented youngsters and inquisitive adults who want to expand their view of mathematics. By focusing on problem solving, and discouraging rote memorization, the book shows how to learn and teach mathematics through investigation, experimentation, and discovery. Rediscovering Mathematics is also an excellent text for training math teachers at all levels | THE AMERICAN MATHEMATICAL MONTHLY . m VOLUME 119 NO. 1 JANUARY 2012 A Letter from the Editor 3 Scott Chapman Invariant Histograms 4 Daniel Brinkman and Peter J. Olver Zariski Decomposition A New Old Chapter of Linear Algebra 25 Thomas Bauer Mirel Caibar and Gary Kennedy Another Way to Sum a Series Generating Functions Euler 42 and the Dilog Function Dan Kalman and Mark McKinzie NOTES A Class of Periodic Continued Radicals 52 Costas J. Efthimiou A Geometric Interpretation of Pascal s Formula for 58 Sums of Powers of Integers Parames Laosinchai and Bhinyo Panijpan Covering Numbers in Linear Algebra 65 Pete L. Clark PROBLEMS AND SOLUTIONS 68 REVIEWS An Introduction to the Mathematics of Money. By David 76 Lovelock Marilou Mendel and A. Larry Wright Alan Durfee An Official Publication of the Mathematical Association of America New title from the MAA Rediscovering Mathematics You Do the Math Shai Simonson Rediscovering Mathematics i s an eclectic collection of mathematical topics and puzzles aimed at talented youngsters and inquisitive adults who want to expand their view of mathematics. By focusing on problem solving and discouraging rote memorization the book shows how to learn and teach mathematics through investigation experimentation and discovery. Rediscovering Mathematics is also an excellent text for training math teachers at all levels. Topics range in difficulty and cover a wide range of historical periods with some examples demonstrating how to uncover mathematics in everyday life including number theory and its application to secure communication over the Internet the algebraic and combinatorial work of a medieval mathematician Rabbi and applications of probability to sports casinos and everyday life. Rediscovering Mathematics provides a fresh view of mathematics for those who already like the subject and offers a second chance for those who think they don t. To order call 1-800-331-1622 or visit us online at MAA MATHEMATICAL ASSOCIATION OF .

• Toán học
• Invariant Histograms
• Linear Algebra
• Covering Numbers
• Class of Periodic
• Continued Radicals
• Generating Functions