£63.19

Introduction to Mathematics: Number, Space, and Structure (Pure and Applied Undergraduate Texts)

Higher Education

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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.

Key Features

Introduction To Mathematics: Number, Space, And Structure Pure And Applied Undergraduate Texts

Product Type: Abis Book

Brand: Language: English

Product Specifications

Format: paperback
ASIN: 1470471884
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Education > Higher Education
Domain: Amazon UK
Release Date: 30 September 2023
Listed Since: 23 June 2023

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Introduction to Mathematics: Number, Space, and Structure (Pure and Applied Undergraduate Texts)

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