Elements of Mathematics
Gabor Toth
Broschiertes Buch

Elements of Mathematics

A Problem-Centered Approach to History and Foundations

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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, an...