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eBook Elements of Number Theory (Undergraduate Texts in Mathematics) download

by John Stillwell

eBook Elements of Number Theory (Undergraduate Texts in Mathematics) download ISBN: 0387955879
Author: John Stillwell
Publisher: Springer; 2003 edition (December 13, 2002)
Language: English
Pages: 256
ePub: 1994 kb
Fb2: 1564 kb
Rating: 4.9
Other formats: docx lit rtf txt
Category: Math Sciences
Subcategory: Mathematics

This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers.

Ships from and sold by Book-Net. This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals. The development of these ideas, and the transition from ancient to modern, is the main theme of the book.

Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level.

Another excellent exposition by John Stilwell of l mathematics, with no further .

Another excellent exposition by John Stilwell of l mathematics, with no further requirement. For the rest of us. If "Elements of Number Theory" is recommended before diving into Dedekind's "Theory of Algebraic Integers", this one is great to prepare yourself for Emil Artin.

John Stillwell is Professor of Mathematics at the University of San Francisco.

This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving . Elements of Number Theory Undergraduate Texts in Mathematics.

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. Издание: иллюстрированное.

Elements Of Number Theory book. Start by marking Elements Of Number Theory (Undergraduate Texts In Mathematics) as Want to Read

Elements Of Number Theory book. This book is intended to complement my Elements oi Algebra, and. Start by marking Elements Of Number Theory (Undergraduate Texts In Mathematics) as Want to Read: Want to Read savin. ant to Read.

FREE delivery worldwide! Description for Elements of Number Theory (Undergraduate Texts in. .This book features material suitable for a one-semester course.

FREE delivery worldwide! Description for Elements of Number Theory (Undergraduate Texts in Mathematics) Hardcover. Focuses on solutions of equations in integers, which is the central problem of number theory. It contains exercises at the end of every section, so that each idea or proof receives immediate reinforcement. Series: Undergraduate Texts in Mathematics. Num Pages: 256 pages, biography. BIC Classification: PBH. Category: (UU) Undergraduate. Dimension: 241 x 162 x 21. Weight in Grams: 546. Product Details.

The Real Numbers: An Introduction to Set Theory and Analysis. Naive Lie Theory (Undergraduate Texts in Mathematics). Reverse Mathematics: Proofs from the Inside Out. Numbers and Geometry.

For example, the proof.

Most mathematics departments in North America offer a course in elementary num-. However, since the advent of public key cryptography with its important applications of elementary. The text has a number of unusual and attractive features. For example, the proof. given for the law of quadratic reciprocity is not the 1844 lattice point counting argument.

Undergraduate Texts in Mathematics. Lc Classification Number. The author's concept (history mostly as the means of approaching mathematics) remains a matter of interest for both the mathematician and the historia.

Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.

Comments: (5)
Khiceog
Stillwell's book Elements of Number Theory presents a grand picture, starting with solving integer equations, and then working into general solutions of the Pell Equation. He covers basic ground, but without the generally random approach that most Number Theory books present.

In particular, he stresses repeatedly the importance of Unique Factorization, and in many ways his book is a build up to how Unique Factorization is "saved" in general algebraic structures by Prime Ideals. That by itself makes it worthwhile, because it is bringing in very important topics from Modern Algebra that are used in modern number theory. This is especially true because that angle is missing from several introductory texts on the subject (such as Dudley's classic text).

Great exercises, clear writing, and motivating discussion also gives the reader all important context. Too many number theory books show random results which, while pleasing, seem arbitrary. Here is a coherent development of deep ideas and a striking big picture. I am definitely glad to have it on my shelf.
Brajind
I enjoy the algebraic approach to number theory.
Lyrtois
After reading the first couple of chapters of Mr. Stillwell's book on number theory I've made plans to purchase his other college-level textbooks, including Elements of Algebra, Real Numbers, Four Pillars of Geometry, and, recently, Reverse Mathematics. I'm a mathematically-minded CS student and my interests fit very nicely with Mr. Stillwell's, plus I enjoy his style tremendously. Book is perfect for self-study.
Contancia
This is a very pleasant introduction to number theory. Each chapter is preceded by a preview and concluded by a discussion to make the main ideas clear and well-motivated and to show how things fit in the big picture by discussing the historical development. The book starts with the very basics and moves via some pearls like the four square theorem and quadratic reciprocity to a culmination with algebraic number theory. A readable and elementary introduction to algebraic number theory is especially valuable today because, as Stillwell argues in his preface, this is the proper setting in which to learn of rings and ideals. Nowadays, of course, the custom is to pull these concepts out of a hat in the mysterious context of "abstract algebra" where there is no apparent reason to introduce them whatsoever. Fortunately, Stillwell has provided us with an equally enjoyable book on algebra, so now we can only hope that some day the curricula will change accordingly.
CopamHuk
One of the best introductory books I've seen. It is concise, and yet very illuminating and down to earth, leading very nicely into the beginnings of algebraic number theory.