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Problems and proofs in numbers and a...

Millman, Richard S.

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Problems and proofs in numbers and algebra

Record Type:	Electronic resources : 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:

515832
Number theory.

LC Class. No.: QA241

Dewey Class. No.: 512.7

Problems and proofs in numbers and algebra
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100 1 $a Millman, Richard S. $3 2134861
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 : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
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 515832
650 0 $a Proof theory. $3 543782
650 0 $a Algebra. $3 516203
650 1 4 $a Mathematics. $3 515831
650 2 4 $a General Algebraic Systems. $3 897364
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Mathematical Logic and Foundations. $3 892656
700 1 $a Shiue, Peter J. $3 2134862
700 1 $a Kahn, Eric Brendan. $3 2134863
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856 4 0 $u http://dx.doi.org/10.1007/978-3-319-14427-6
950 $a Mathematics and Statistics (Springer-11649)