 # Discrete mathematics and its applications

[This text] is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.-Pref
xxi, 787, 9, 8, 83, 1, 18 pages : illustrations (some color) ; 26 cm
9780072424348, 9780071198813, 9780071233743, 0072424346, 0071198814, 0071233741
49719375
The foundations: logic and proof, sets, and functions : Logic ; Propositional equivalences ; Predicates and quantifiers ; Nested quantifiers ; Methods of proof ; Sets ; Set operations ; Functions
The fundamentals: algorithms, the integers, and matrices : Algorithms ; The growth of functions ; Complexity of algorithms ; The integers and division ; Applications of number theory ; Matrices
Mathematical reasoning, induction, and recursion : Proof strategy ; Sequences and summations ; Mathematical induction ; Recursive definitions and structural induction ; Recursive algorithms ; Program correctness
Counting : The basics of counting ; The pigeonhole principle ; Permutations and combinations ; Binomial coefficients ; Generalized permutations and combinations ; Generating permutations and combinations
Discrete probability : An introduction to discrete probability ; Probability theory ; Expected value and variance
Advanced counting techniques : Recurrence relations ; Solving recurrence relations ; Divide-and-conquer algorithms and recurrence relations ; Generating functions ; Inclusion-exclusion ; Applications of inclusion-exclusion
Relations : Relations and their properties ; n-ary relations and their applications ; Representing relations ; Closures of relations ; Equivalence relations ; Partial orderings
Graphs : Introduction to graphs ; Graph terminology ; Representing graphs and graph isomorphism ; Connectivity ; Euler and Hamilton paths ; Shortest-path problems ; Planar graphs ; Graph coloring
Trees : introduction to trees ; Applications of trees ; Tree traversal ; Spanning trees ; Minimum spanning trees
Boolean algebra : Boolean functions ; Representing Boolean functions ; Logic gates ; Minimization of circuits
Modeling computation : Languages and grammars ; Finite-state machines with output ; Finite-state machines with no output ; Language recognition ; Turing machines
Appendixes : A.1. Exponential and logarithmic functions ; A.2. Pseudocode