Elements of Mathematics : A Problem-Centered Approach to History and Foundations

Language: English

Published by Springer, 2022

3030750531 / 9783030750534

Series: Book 164 of 170 - Undergraduate Texts in Mathematics

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Druck auf Anfrage Neuware - Printed after ordering - This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed.Beginning with a thorough treatment of the natural numbers via Peano's axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff's axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections between topics.Elements of Mathematics is ideal for students seeking a deep and engaging mathematical challenge based on elementary tools. Whether enhancing the early undergraduate curriculum for high achievers, or constructing a reflective senior capstone, instructors will find ample material for enquiring mathematics majors. No formal prerequisites are assumed beyond high school algebra, making the book ideal for mathematics circles and competition preparation. Readers who are more advanced in their mathematical studies will appreciate the interleaving of ideas and illuminating historical details.

Seller Inventory # 9783030750534

Title
Elements of Mathematics : A Problem-Centered Approach to History and Foundations
Author
Gabor Toth
Publisher
Springer
Publication year
2022
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3030750531
ISBN 13
9783030750534
Item weight
913 grams
Dimensions
235x155x28 mm
Series
Book 164 of 170: Undergraduate Texts in Mathematics

AHA-BUCH GmbH

Einbeck, Germany

5-star seller

AbeBooks seller since August 14, 2006

Shipping rates from Germany to U.S.A.

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