عنوان

Problems and proofs in numbers and algebra

(Number (ISBN

9783319144269

Country Code

IR

Number

10373

.Language of Text, Soundtrack etc

انگلیسی

Country of publication

IR

Title Proper

Problems and proofs in numbers and algebra

General Material Designation

[Book]

First Statement of Responsibility

/Richard S. Millman, Peter J. Shiue, Eric Brendan Kahn.

Place of Publication, Distribution, etc.

Cham

Name of Publisher, Distributor, etc.

Springer International Publishing : Imprint: Springer

Date of Publication, Distribution, etc.

, 2015.

Specific Material Designation and Extent of Item

X, 223 pages 9 illustrations

Text of Note

Language: انگلیسی

Text of Note

Print

Text of Note

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.

Entry Element

Algebra

Entry Element

Mathematical logic.

Entry Element

Number theory.

Class number

Book number

Millman, Richard S, author.

Kahn, Eric Brendan, author.

Shiue, Peter J, author.

Country

ایران

Agency

دانشگاه محقق اردبیلی

Date of Transaction

20231204

old catalog

p

BL

270410

1

a

Y