Proof Patterns

• Main Author: Joshi, Mark (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Geometry.; Number theory.; Topology.; Combinatorics.; Mathematics > Study and teaching.; Number Theory.; Analysis.; Mathematics Education.

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...

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.