Problems and Proofs in Numbers and Algebra

by Richard S. Millman
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Richard S. Millman Problems and Proofs in Numbers and Algebra
Richard S. Millman - Problems and Proofs in Numbers and Algebra

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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.


Richard S. Millman
Peter J. Shiue
Eric Brendan Kahn

Further information

Illustrations Note:
9 SW-Abb., 21 Tabellen

Provides a foundation for solving proofs and problems as a transition to more abstract algebra and mathematics

Readers learn problem solving abilities concerning proofs through numbers and algebra

Problems and theorems are focused on many diverse areas of number theory and algebra

Media Type:
Springer International Publishing
Biography Artist:

Richard S. Millman,Ph.D., Director, Center for Education Integrating Science, Mathematics, and Computing (CEISMC) Georgia Institute of Technology Atlanta, GA 30332-0282

Peter J. Shiue Department of Mathematical Sciences University of Nevada, Las Vegas 4505 Maryland Pkwy Las Vegas, NV 89154-4020

Eric Brendan Kahn Department of Mathematics, Computer Science, and Statistics Bloomsburg University 400 East Second Street Bloomsburg, PA 17815

"Aimed at introducing postcalculus students to higher mathematics by way of solving rigorous problems and learning how to prove. ... the content is less focused on basic mathematical concepts seen in upper-division college mathematics coursework and more so on topics that teachers might present in their classrooms, and on interesting applications ... . Teachers of mathematics at the secondary level would be well served by taking a course based on this text. Summing Up: Recommended. Upper-division undergraduates through faculty." (D. S. Larson, Choice, Vol. 53 (1), September, 2015)
Number of Pages:

Master Data

Product Type:
Paperback book
Release date:
6 October 2016
Package Dimensions:
0.256 x 0.156 x 0.006 m; 0.32 kg
Manufacturer Part Number:
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