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Problems and proofs in numbers and algebra

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 th...

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Detalles Bibliográficos
Autores principales: Millman, Richard S, Shiue, Peter J, Kahn, Eric Brendan
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-14427-6
http://cds.cern.ch/record/1996708
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author Millman, Richard S
Shiue, Peter J
Kahn, Eric Brendan
author_facet Millman, Richard S
Shiue, Peter J
Kahn, Eric Brendan
author_sort Millman, Richard S
collection CERN
description 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.
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spelling cern-19967082021-04-21T20:26:47Zdoi:10.1007/978-3-319-14427-6http://cds.cern.ch/record/1996708engMillman, Richard SShiue, Peter JKahn, Eric BrendanProblems and proofs in numbers and algebraMathematical Physics and MathematicsDesigned 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.Springeroai:cds.cern.ch:19967082015
spellingShingle Mathematical Physics and Mathematics
Millman, Richard S
Shiue, Peter J
Kahn, Eric Brendan
Problems and proofs in numbers and algebra
title Problems and proofs in numbers and algebra
title_full Problems and proofs in numbers and algebra
title_fullStr Problems and proofs in numbers and algebra
title_full_unstemmed Problems and proofs in numbers and algebra
title_short Problems and proofs in numbers and algebra
title_sort problems and proofs in numbers and algebra
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-14427-6
http://cds.cern.ch/record/1996708
work_keys_str_mv AT millmanrichards problemsandproofsinnumbersandalgebra
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