A Guide to Elementary Number Theory
Published on 25. March 2010
Book
Hardback
152 pages
978-0-88385-347-4 (ISBN)
Description
Covers the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through a traditional text.
More details
Language
English
Place of publication
Washington DC
United States
Target group
College/higher education
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 237 mm
Width: 159 mm
Thickness: 17 mm
Weight
330 gr
ISBN-13
978-0-88385-347-4 (9780883853474)
Schweitzer Classification
Person
Underwood Dudley was born in New York City in 1937. He has bachelor's and master's degrees from the Carnegie Institute of Technology and received the Ph.D. degree (number theory) from the University of Michigan in 1965. He taught at the Ohio State University and at DePauw University, from which he retired in 2004. He is the author of three books on mathematical oddities, The Trisectors, Mathematical Cranks, and Numerology, an elementary number theory text, and is the editor of two collections of mathematical pieces. He has edited the College Mathematics Journal, the Pi Mu Epsilon Journal, and two of the Mathematical Association of America's book series. He has served as the MAA's Pólya lecturer and has received its Distinguished Service Award. He is a member of the MAA, the American Mathematical Society, and the Society for Industrial and Applied Mathematics.
Content
Introduction
1. Greatest common divisors
2. Unique factorization
3. Linear diophantine equations
4. Congruences
5. Linear congruences
6. The Chinese Remainder Theorem
7. Fermat's Theorem
8. Wilson's Theorem
9. The number of divisors of an integer
10. The sum of the divisors of an integer
11. Amicable numbers
12. Perfect numbers
13. Euler's Theorem and function
14. Primitive roots and orders
15. Decimals
16. Quadratic congruences
17. Gauss's Lemma
18. The Quadratic Reciprocity Theorem
19. The Jacobi symbol
20. Pythagorean triangles
21. x4+y4/=z4
22. Sums of two squares
23. Sums of three squares
24. Sums of four squares
25. Waring's Problem
26. Pell's Equation
27. Continued fractions
28. Multigrades
29. Carmichael numbers
30. Sophie Germain primes
31. The group of multiplicative functions
32. Bounds for PI(x)
33. The sum of the reciprocals of the primes
34. The Riemann Hypothesis
35. The Prime Number Theorem
36. The abc conjecture
37. Factorization and testing for primes
38. Algebraic and transcendental numbers
39. Unsolved problems
Index
About the author.
1. Greatest common divisors
2. Unique factorization
3. Linear diophantine equations
4. Congruences
5. Linear congruences
6. The Chinese Remainder Theorem
7. Fermat's Theorem
8. Wilson's Theorem
9. The number of divisors of an integer
10. The sum of the divisors of an integer
11. Amicable numbers
12. Perfect numbers
13. Euler's Theorem and function
14. Primitive roots and orders
15. Decimals
16. Quadratic congruences
17. Gauss's Lemma
18. The Quadratic Reciprocity Theorem
19. The Jacobi symbol
20. Pythagorean triangles
21. x4+y4/=z4
22. Sums of two squares
23. Sums of three squares
24. Sums of four squares
25. Waring's Problem
26. Pell's Equation
27. Continued fractions
28. Multigrades
29. Carmichael numbers
30. Sophie Germain primes
31. The group of multiplicative functions
32. Bounds for PI(x)
33. The sum of the reciprocals of the primes
34. The Riemann Hypothesis
35. The Prime Number Theorem
36. The abc conjecture
37. Factorization and testing for primes
38. Algebraic and transcendental numbers
39. Unsolved problems
Index
About the author.