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

Gabor Toth

ISBN 10: 3030750531 / ISBN 13: 9783030750534

Published by Springer Nature Switzerland, 2022

About this Item

Elements of Mathematics | A Problem-Centered Approach to History and Foundations | Gabor Toth | Taschenbuch | xv | Englisch | 2022 | Springer Nature Switzerland | EAN 9783030750534 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Seller Inventory # 123939606

Bibliographic Details

• Title: Elements of Mathematics | A Problem-Centered Approach to History and Foundations
• Publisher: Springer Nature Switzerland
• Publication Date: 2022
• Language: English
• ISBN 10: 3030750531
• ISBN 13: 9783030750534
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 28D millimeters 235 millimeters width by 155 millimeters height by 28 millimeters depth
• Weight: 913 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

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.

About the Author

Gabor Toth is Distinguished Professor of Mathematics at Rutgers University, Camden. His research interests include convex geometry and differential geometry, in particular, harmonic maps and minimal immersions. Beyond mathematics, he teaches Ancient Egyptian Grammar and the history of precolonial Africa. He regularly trains gifted high school students for mathematical contests in Princeton. His previous books include Measures of Symmetry for Convex Sets and Stability, Glimpses of Algebra and Geometry, and Finite Möbius Groups, Spherical Minimal Immersions, and Moduli.