Problems and proofs in numbers and algebra /

Problems and proofs in numbers and algebra /

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Bibliographic Details
Author / Creator:	Millman, Richard S., 1945- author.
Imprint:	Cham : Springer, 2015.
Description:	1 online resource (x, 223 pages) : illustrations
Language:	English
Subject:	Number theory. Proof theory. Algebra. Algebra. Number theory. Proof theory. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11091943

Hidden Bibliographic Details
Other authors / contributors:	Shiue, Peter Jau-Shyong, 1941- author. Kahn, Eric Brendan, author.
ISBN:	9783319144276 3319144278 9783319144269 331914426X 9783319144269
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references. Online resource; title from PDF title page (SpringerLink, viewed February 17, 2015).
Summary:	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 ℓ́ℓproveℓ́ℓ or ℓ́ℓsolveℓ́ℓ 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.℗ℓ 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.
Other form:	Print version: Millman, Richard S. Problems and Proofs in Numbers and Algebra Cham : Springer International Publishing,c2015 9783319144269
Standard no.:	10.1007/978-3-319-14427-6

Description
Summary:	Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. 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. In the past, PNA has been taught in a "problem solving in middle school" course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.
Physical Description:	1 online resource (x, 223 pages) : illustrations
Bibliography:	Includes bibliographical references.
ISBN:	9783319144276 3319144278 9783319144269 331914426X