Explorations in analysis, topology, and dynamics : an introduction to abstract mathematics
著者
書誌事項
Explorations in analysis, topology, and dynamics : an introduction to abstract mathematics
（The Sally series, . Pure and applied undergraduate texts ; 44）
American Mathematical Society, c2020
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注記
Includes index
内容説明・目次
内容説明
This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigour as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually.
Material on topology (e.g. of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.
目次
Real numbers and sequences
An introduction to point-set topology and continuity
Differential calculus
Integral calculus
Discrete dynamical systems
Iterating algorithms and represenations of real numbers
Appendix A: Definitions, proofs, and mathematical language
Appendix B: Sets and functions between sets
Appendix C: Graphs
Appendix D: Hints to selected problems
Index.
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