The mathematical neighborhoods of school mathematics

著者

書誌事項

The mathematical neighborhoods of school mathematics

Hyman Bass ; assistance of Jason Brasel

American Mathematical Society, 2023

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注記

Includes index

内容説明・目次

内容説明

The Mathematical Neighborhoods of School Mathematics visits regions beyond, but proximal to and accessible from school mathematics. Its aim is to give readers a glimpse of not just the rich diversity and adaptability of mathematics, but, most importantly, its interconnections and overall coherence, a perspective not easily available from the school curriculum. This aim entailed assembling a variety of substantial mathematical domains that do not typically cohabit the same volume. The book begins with an in-depth treatment of topics in the school curriculum, often with novel approaches and connections. A unifying thread is the group theoretic study of addition and multiplication in the various number systems of school mathematics. The exposition is mathematically rigorous, including proofs of many fundamental theorems not otherwise easily available in mathematically accessible form. The Mathematical Neighborhoods of School Mathematics is intended to be a conceptual contribution to mathematics education. It will be a valuable resource in professional development of mathematics teachers, and in mathematical enrichment programs, for both students and teachers. In this regard, many of the chapters are relatively self-contained. It could also serve as a text for undergraduate mathematics majors with an interest in teaching. The exceptional Chapter 11 presents some novel instructional designs for problem-solving activities meant to cultivate ""connection-oriented mathematical thinking.

目次

Basic notation and background Division with remainder, place value, and order of magnitude Modular congruence and base-$B$ expansions of rational numbers Discrete real additive groups Primes and factorization Group theory and Euclidean isometry groups Rings and fields Polynomials Combinatorics Discrete calculus Complex numbers Mathematical connections Index

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