
Introduction to Mathematics
Number, Space, and Structure
Scott A. Taylor(Author)
American Mathematical Society (Publisher)
Published on 30. September 2023
Book
Paperback/Softback
436 pages
978-1-4704-7188-0 (ISBN)
Description
This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of mathematical history and culture. Early chapters integrate an introduction to sets, logic, and beginning proof techniques with a first exposure to more advanced mathematical structures. The middle chapters focus on equivalence relations, functions, and induction. Carefully chosen examples elucidate familiar topics, such as natural and rational numbers and angle measurements, as well as new mathematics, such as modular arithmetic and beginning graph theory. The book concludes with a thorough exploration of the cardinalities of finite and infinite sets and, in two optional chapters, brings all the topics together by constructing the real numbers and other complete metric spaces. Designed to foster the mental flexibility and rigorous thinking needed for advanced mathematics, Introduction to Mathematics suits either a lecture-based or flipped classroom. A year of mathematics, statistics, or computer science at the university level is assumed, but the main prerequisite is the willingness to engage in a new challenge.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
284 gr
ISBN-13
978-1-4704-7188-0 (9781470471880)
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Schweitzer Classification
Person
Scott A. Taylor, Colby College, Waterville, ME
Content
Sets
Sets with structure
Logic, briefly
Basic proof techniques, briefly
Building sets
Optional: Set theory axiomatics
Equivalence relations
Functions
Advanced proof techniques
The sizes of sets
Sequences: From numbers to spaces
New numbers from completed spaces
Axioms
A summary of proof techniques
Typography
Bibliography
Index.
Sets with structure
Logic, briefly
Basic proof techniques, briefly
Building sets
Optional: Set theory axiomatics
Equivalence relations
Functions
Advanced proof techniques
The sizes of sets
Sequences: From numbers to spaces
New numbers from completed spaces
Axioms
A summary of proof techniques
Typography
Bibliography
Index.