Biscuits of Number Theory by Arthur T Benjamin, Ezra Brown
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About this book :-
Biscuits of Number Theory written by
Arthur T Benjamin, Ezra Brown
In Biscuits of Number Theory, the editors have chosen articles that are exceptionally well-written and that can be appreciated by anyone who has taken (or is taking) a first course in number theory. This book could be used as a textbook supplement for a number theory course, especially one that requires students to write papers or do outside reading. The editors give examples of some of the possibilities.
The collection is divided into seven chapters: Arithmetic, Primes, Irrationality, Sums of Squares and Polygonal Numbers, Fibonacci Numbers, Number Theoretic Functions, and Elliptic Curves, Cubes and Fermat's Last Theorem. As with any anthology, you don't have to read the Biscuits in order. Dip into them anywhere: pick something from the Table of Contents that strikes your fancy, and have at it. If the end of an article leaves you wondering what happens next, then by all means dive in and do some research. You just might discover something new!
In this book the author has an assortment of articles and notes on number theory, each item is not too big, easily digested and makes you feel all warm and fuzzy when you are through. We hope they will whet your appetite for more. This book can be taken as the first course in number theory.
Book Detail :-
Title: Biscuits of Number Theory
Author(s): Arthur T Benjamin, Ezra Brown
Publisher: Mathematical Association of America
Series: Dolciani Mathematical Exponention
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About Author :-
Author Arthur T. Benjamin is a Professor of Mathematics at Harvey Mudd College. He graduated from Carnegie Mellon University in 1983, where he earned a B.S. in Applied Mathematics with university honors. He received his Ph.D. in Mathematical Sciences in 1989 from Johns Hopkins University, where he was supported by a National Science Foundation graduate fellowship and a Rufus P. Isaacs fellowship. Since 1989, Dr. Benjamin has been a faculty member of the Mathematics Department at Harvey Mudd College, where he has served as department chair. He has spent sabbatical visits at Caltech, Brandeis University, and University of New South Wales in Sydney, Australia.
1999, Professor Benjamin received the Southern California Section of the Mathematical Association of America (MAA) Award for Distinguished College or University Teaching of Mathematics, and in 2000, he received the MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. He was named the 2006í2008 George Pólya Lecturer by the MAA.
Dr. Benjamin’s research interests include combinatorics, game theory, and number theory, with a special fondness for Fibonacci numbers. Many of these ideas appear in his book (co-authored with Jennifer Quinn), Proofs That Really Count: The Art of Combinatorial Proof published by the MAA. In 2006, that book received the Beckenbach Book Prize by the MAA. Professors Benjamin and Quinn are the co-editors of Math Horizons magazine, published by MAA and enjoyed by more than 20,000 readers, mostly undergraduate math students and their teachers.
Professor Benjamin is also a professional magician. He has given more than 1,000 “mathemagics” shows to audiences all over the world (from primary schools to scienti¿ c conferences), where he demonstrates and explains his calculating talents. His techniques are explained in his book Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks. Proli¿ c math and science writer Martin Gardner calls it “the clearest, simplest, most entertaining, and best book yet on the art of calculating in your head.” An avid games player, Dr. Benjamin was winner of the American Backgammon Tour in 1997.
Professor Benjamin has appeared on dozens of television and radio programs, including the Today Show, CNN, and National Public Radio. He has been featured in Scienti¿ c American, Omni, Discover, People, Esquire, The New York Times, the Los Angeles Times, and Reader’s Digest. In 2005, Reader’s Digest called him “America’s Best Math Whiz.”
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Book Contents :-
Biscuits of Number Theory written by
Arthur T Benjamin, Ezra Brown
cover the following topics.
l. A Dozen Questions About the Powers of Two.
2. From 30 to 60 is Not Twice as Hard .
3. Reducing the Sum of Two Fractions .
4. A Postmodern View of Fractions and Reciprocals of Fermat Primes . .
5. Visible Structures in Number Theory
6. Visual Gems of Number Theory
7. A New Proof of Euclid
8. On the Infinitude of the Primes.
9. On the Series of Prime Reciprocals
10. Applications of a Simple Counting Technique
11. On Weird and Pseudoperfect Numbers.
12. A Heuristic for the Prime Number Theorem
13. A Tale of Two Sieves
Part-III Irrationality and Continued Fractions
14. Irrationality of the Square Root of Two-A Geometric Proof
15. Math Bite: Irrationality of
16. A Simple Proof that n is Irrational.
17. n,e and Other Irrational Numbers
18. A Short Proof of the Simple Continued Fraction of e
19. Diophantine Olympics and World Champions: Polynomials and Primes Down Under
20. An Elementary Proof of the Wallis Product Formula for Pi
21. The Orchard Problem.
Part-IV Sums of Squares and Polygonal Numbers
22. A One-Sentence Proof that every Primep 1 (mod 4) is a Sum of TwoSquares
23. Sum of Squares
24. Sums of Squares
25. A Short Proof of Cauchyls Polygonal Number Theorem
26. Genealogy of Pythagorean Triads.
Part-V Fibonacci Numbers
27. A Dozen Questions About Fibonacci Numbers .
28. The Fibonacci Numbers-Exposed
29. The Fibonacci Numbers-Exposed More Discretely.
Part-VI Number-Theoretic Functions
30. Great Moments of the Riemann zeta Function
31. The Collatz Chameleon.
32. Bijecting Eulerls Partition Recurrence.
33. Discovery of a Most Extraordinary Law of the Numbers Concerning the Sum of Their Divisors.
34. The Factorial Function and Generalizations Manjul Bhargava.
35. An Elementary Proof of the Quadratic Reciprocity Law
Part-VII Elliptic Curves, Cubes And Fermat,s Last Theorem
36. Proof Without Words: Cubes and Squares.
37. Taxicabs and Sums of Two Cubes
38. Three Fermat Trails to Elliptic Curves
39. Fermat,s Last Theorem in Combinatorial Form
Lester Ford Award.
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