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

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Autor: Gabor Toth
Lehekülgede arv: 527
Ilmumisaasta: 2021
Kauba ID: 18232479

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

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. 1st ed. 2021.

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

Kauba ID: 18232479
Kategooria: Majandusalased raamatud
Tootepakendite arv: 1 tk.
Paki suurus ja kaal (1): 0,3 x 0,3 x 0,1 m, 0,2 kg
Kirjastus: Springer Nature Switzerland AG
Raamatu keel: Inglise keel
Tüüp: Matemaatika
Autor: Gabor Toth
Lehekülgede arv: 527
Ilmumisaasta: 2021

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