國立虎尾科技大學 |

Problems and proofs in numbers and algebra

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Problems and proofs in numbers and algebra/ by Richard S. Millman, Peter J. Shiue, Eric Brendan Kahn.
Author:	Millman, Richard S.
other author:	Shiue, Peter J.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	x, 223 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Number theory. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-14427-6
ISBN:	9783319144276 (electronic bk.)

Problems and proofs in numbers and algebra
Millman, Richard S.

Problems and proofs in numbers and algebra[electronic resource] /by Richard S. Millman, Peter J. Shiue, Eric Brendan Kahn. - Cham :Springer International Publishing :2015. - x, 223 p. :ill., digital ;24 cm.

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. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge.

ISBN: 9783319144276 (electronic bk.)

Standard No.: 10.1007/978-3-319-14427-6doiSubjects--Topical Terms:

527883
Number theory.

LC Class. No.: QA241

Dewey Class. No.: 512.7

Problems and proofs in numbers and algebra
LDR:02950nam a2200301 a 4500 001 836513
003 DE-He213
005 20150922105231.0
006 m d
007 cr nn 008maaau
008 160421s2015 gw s 0 eng d
020 $a 9783319144276 (electronic bk.)
020 $a 9783319144269 (paper)
024 7 $a 10.1007/978-3-319-14427-6 $2 doi
035 $a 978-3-319-14427-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA241
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 512.7 $2 23
090 $a QA241 $b .M655 2015
100 1 $a Millman, Richard S. $3 1066702
245 1 0 $a Problems and proofs in numbers and algebra $h [electronic resource] / $c by Richard S. Millman, Peter J. Shiue, Eric Brendan Kahn.
260 $a Cham : $c 2015. $b Springer International Publishing : $b Imprint: Springer,
300 $a x, 223 p. : $b ill., digital ; $c 24 cm.
520 $a 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. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge.
650 0 $a Number theory. $3 527883
650 0 $a Proof theory. $3 579943
650 0 $a Algebra. $2 gtt $3 579870
650 1 4 $a Mathematics. $3 527692
650 2 4 $a General Algebraic Systems. $3 672227
650 2 4 $a Number Theory. $3 672023
650 2 4 $a Mathematical Logic and Foundations. $3 669393
700 1 $a Shiue, Peter J. $3 1066703
700 1 $a Kahn, Eric Brendan. $3 1066704
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-14427-6
950 $a Mathematics and Statistics (Springer-11649)