Elements of mathematics : a problem-centered approach to history and foundations / Gabor Toth.
Tóth, Gábor, Ph. D., author.
2021
QA39.3 .T68 2021
Available Online

Linked e-resources

Linked Resource Online Access
Concurrent users Unlimited
Authorized users Authorized users
Document Delivery Supplied Can lend chapters, not whole ebooks

Details

Title Elements of mathematics : a problem-centered approach to history and foundations / Gabor Toth.
Author Tóth, Gábor, Ph. D., author.
ISBN 9783030750510 (electronic bk.)
3030750515 (electronic bk.)
9783030750503
3030750507
DOI https://doi.org/10.1007/978-3-030-75051-0
Published Cham : Springer, [2021]
Copyright ©2021
Language English
Description 1 online resource : illustrations (some color)
Item Number 10.1007/978-3-030-75051-0 doi
Call Number QA39.3 .T68 2021
Dewey Decimal Classification 510
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed October 5, 2021).
Series Undergraduate texts in mathematics. Readings in mathematics.
Available in Other Form Print version: 9783030750503
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
All Resources
0. Preliminaries: Sets, Relations, Maps
1. Natural, Integral and Rational Numbers
2. Real Numbers
3. Rational and Real Exponentiation
4. Limits of Real Functions
5. Real Analytic Plane Geometry
6. Polynomial Expressions
7. Polynomial Functions
8. Conics
9. Rational and Algebraic Expressions and Functions
10. Exponential and Logarithmic Functions
11. Trigonometry
Further Reading
Index.

Browse Subjects

Show more subjects...

Statistics

from
to
Export