000			02813cam a22002775i 4500
001			137495
003			ISI Library, Kolkata
005			20170403154722.0
008			141224s2015 nyu 000 0 eng
020			_a9783319144269
040			_aISI Library
082	0	4	_a512.7 _223 _bM655
100	1		_aMillman, Richard.
245	1	0	_aProblems and proofs in numbers and algebra / _cRichard Millman.
260			_aCham : _bSpringer, _c2015.
300			_ax, 223 pages ; _c24 cm.
504			_aIncludes bibliographical references.
505	0		_aI. The Integers 1. Number Concepts, Prime Numbers, and the Division Algorithm 2. Greatest Common Divisors, Diophantine Equations, and Combinatorics 3. Equivalence Classes with Applications to Clock Arithmetics and Fractions II. The Algebra of Polynomials and Linear Systems 4. Polynomials and the Division Algorithm 5. Factoring Polynomials, Their Roots, and Some Applications 6. Matrices and Systems of Linear Equations.
520			_aDesigned to facilitate the transition from undergraduate calculus and differential equations to learning about proofs, this book helps students develop the rigorous mathematical reasoning needed for advanced courses in analysis, abstract algebra, and more. Students will focus on both how to prove theorems and solve problem sets in-depth; that is, where multiple steps are needed to prove or solve. This proof technique is developed by examining two specific content themes and their applications in-depth: number theory and algebra. This choice of content themes enables students to develop an understanding of proof technique in the context of topics with which they are already familiar, as well as reinforcing natural and conceptual understandings of mathematical methods and styles. The key to the text is its interesting and intriguing problems, exercises, theorems, and proofs, showing how students will transition from the usual, more routine calculus to abstraction while also learning how to prove or solve complex problems. This method of instruction is augmented by examining applications of number theory in systems such as RSA cryptography, Universal Product Code (UPC), and International Standard Book Number (ISBN). The numerous problems and examples included in each section reward curiosity and insightfulness over more simplistic approaches. Each problem set begins with a few easy problems, progressing to problems or proofs with multi-step solutions. Exercises in the text stay close to the examples of the section, allowing students the immediate opportunity to practice developing techniques.
650		0	_aNumber theory.
650		0	_aProof theory.
650		0	_aAlgebra.
700	1		_aShiue, Peter J., _eauthor
700	1		_aKahn, Eric Brendan, _eauthor
942			_2ddc _cBK
999			_c421452 _d421452