MARC 主機 00000cam 2200457Ki 4500
001 898086761
003 OCoLC
005 20151030025011.0
008 141212s2015 sz b 000 0 eng d
020 331914426X
020 9783319144269
035 (OCoLC)898086761|z(OCoLC)911263411
040 YDXCP|beng|cYDXCP|dBTCTA|dOCLCQ|erda|dUNL|dOCLCF|dCDX|dAS
|dMATH
050 QA241|b.M54 2015
082 04 512.7/4|223
100 1 Millman, Richard S.,|d1945-|eauthor
245 10 Problems and proofs in numbers and algebra /|cRichard S.
Millman, Peter J. Shiue, Eric Brendan Kahn
264 1 Cham :|bSpringer,|c[2015]
264 4 |c©2015
300 x, 223 pages ;|c24 cm
336 text|btxt|2rdacontent
337 unmediated|bn|2rdamedia
338 volume|2rdacarrier
504 Includes bibliographic references
520 Designed 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 Number theory
650 0 Proof theory
650 0 Algebra
650 7 Algebra.|2fast|0(OCoLC)fst00804885
650 7 Number theory.|2fast|0(OCoLC)fst01041214
650 7 Proof theory.|2fast|0(OCoLC)fst01078942
700 1 Shiue, Peter Jau-Shyong,|d1941-|eauthor
700 1 Kahn, Eric Brendan,|eauthor