Proof Patterns

by Mark Joshi

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.

206 pages, Paperback

Published March 21, 2015