Introduction to mathematical structures and profits. /
Larry J. Gertein
- New York: Jones and Barlett Publishers, 1996.
- x, 350 p.: ill.; 24cm.
Contents: Logic: Statements, propositions and theorems -- Logical connectives and truth tables -- Conditional statements -- Proofs: structures and strategies -- Logical equivalence -- Applications: A Brief introduction to switching circuits -- Sets: Fundamentals -- Russell's paradox -- Quantifiers -- Set inclusion -- Union, intersection and complement -- Indexed sets -- The Power set -- Ordered pairs and cartesian products -- Set decomposition: partitions and relations -- Mathematical induction and recursion -- Functions: Definitions and examples -- Surjections, injections, bijections, sequences -- Composition of functions -- Finite and Infinite sets: Cardinality: Fundamental counting principles -- Comparing sets, finite or infinite -- uncountable sets -- More on infinity -- Languages and finite automata -- Permutations and Combinations: Combinatorial problems -- The Addition and product rules -- Introduction to permutations -- Permutations and geometric symmetry -- Decomposition into cycles -- Computing the order of a permutation; A Card - Shuffling example -- Odd and even permutations; Applications to configurations -- Binomial and multinomial coefficients