Book of Proof
Virginia Commonwealth University, Math Department, 2009 - Proof theory - 306 pages
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.
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answer approach assume begin bijective called cardinality Cartesian Chapter choices column combine concerns conditional statement conjecture Consider contains contradiction countably infinite course defined definition described direct proof disprove divides divisible divisors Draw elements entry equal equation equivalence classes equivalence relation exactly example exists expression fact factorization false Figure formula function f Given gives idea illustrate implies induction injective integer involves irrational laws least letters logic look mathematical means multiple natural number Notice Observe perfect number positive possible prime prime numbers proof Proposition prove rational real number reason reflexive relation sentence shown sides solution subset Suppose surjective symbols symmetric techniques theorem things transitive true truth table understand universal values write