Proof Patterns
This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity.

The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

1121152314
Proof Patterns
This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity.

The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

54.99 In Stock
Proof Patterns

Proof Patterns

by Mark Joshi
Proof Patterns

Proof Patterns

by Mark Joshi

Overview

This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity.

The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Product Details

ISBN-13: 9783319162492
Publisher: Springer International Publishing
Publication date: 03/19/2015
Edition description: 2015
Pages: 190
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

About the Author

Mark Joshi, a leading mathematician in analysis and financial mathematics, published several successful textbooks and over sixty research papers in mathematics. He is known for his innovative viewpoints and intuitive style.

Table of Contents

Induction and complete induction.- Double Counting.- The pigeonhole principle.- Divisions.- Contrapositive and contradiction.- Intersection-enclosure and Generation.- Difference of invariants.- Linear dependence, fields and transcendence.- Formal equivalence.- Equivalence extension.- Proof by classification.- Specific-generality.- Diagonal tricks and cardinality.- Connectedness and the Jordan curve theorem.- The Euler characteristic and the classification of regular polyhedra.- Discharging.- The matching problem.- Games.- Analytical patterns.- Counterexamples.
From the B&N Reads Blog
Page 1 of

Related Subjects

Science & Technology
Mathematics
Number Theory
Science & Technology
Mathematics
Number Theory

Customer Reviews