Elements of Mathematics

Name: Elements of Mathematics
Brand: Springer Nature Switzerland AG
SKU: 9783030750534
Price: 212.61 PLN
Availability: InStock

A Problem-Centered Approach to History and Foundations

Autor: Gabor Toth

Język:

Oprawa: Miękka

Wydawca: Springer Nature Switzerland AG

Dostępność: Dostępna u dostawcy

Wysyłamy za 8-11 dni

212.61 zł

This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundament...

Informacje o książce

Autor

Gabor Toth

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2022

strony

527

EAN

9783030750534

Enbook ID

41442996

Wydawca

Springer Nature Switzerland AG

Waga

892

Wymiary

235 x 154 x 36

Pełny opis

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.

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Elements of Mathematics

A Problem-Centered Approach to History and Foundations

Informacje o książce

Pełny opis

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