Coupon
Elements of Number Theory
by John Stillwell


Overview - This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois.  Read more...

 
Hardcover
  • $59.95

Add to Cart + Add to Wishlist

In Stock Online.

Free Shipping is not available for this item.
 
> Check In-Store Availability

In-Store pricing may vary

 
 
New & Used Marketplace 16 copies from $31.26
 
 
 

More About Elements of Number Theory by John Stillwell
 
 
 
Overview
This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts- rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the- ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factorization in the arithmetic of certain generalized "inte- gers," Kummer created in the 1840s a new kind of number to overcome the difficulty. He called them "ideal numbers" because he did not know exactly what they were, though he knew how they behaved.

 
Details
  • ISBN-13: 9780387955872
  • ISBN-10: 0387955879
  • Publisher: Springer
  • Publish Date: December 2002
  • Page Count: 256
  • Dimensions: 9.3 x 6.4 x 0.9 inches
  • Shipping Weight: 1.2 pounds

Series: Undergraduate Texts in Mathematics

Related Categories

Books > Mathematics > Number Theory

 
BAM Customer Reviews