COMPREHENSIVE COMPUTER LEARNING: MICROSOFT OFFICE 2010
CONTENTS ALGORITHMS, NUMBERS, AND MACHINES WHAT IS AN ALGORITHM? INTEGER ALGORITHMS AND COMPLEXITY PRIME TESTING REAL NUMBERS MORE PRIME TESTING PRIME FACTORIZATION LOGARITHMS GREATEST COMMON DIVISOR MACHINE REPRESENTATION OF NUMBERS APPROXIMATION ERRORS BASE 2, 8, AND 16 NUMERICAL SOLUTIONS NEWTON’S METHOD FOR SQUARE ROOTS THE BISECTION ALGORITHM EXERCISES SETS, SEQUENCES, AND COUNTING NAÏVE SET THEORY THE DIABOLICAL LIBRARIAN OPERATIONS ON SETS AND CARDINALITY THE PIGEONHOLE PRINCIPLE SEQUENCES THE CHARACTERISTIC SEQUENCE OF A SUBSET COUNTING NUMBER OF K-SEQUENCES ON AN N-SET NUMBER OF SUBSETS OF AN N-SET NUMBER OF K-PERMUTATIONS ON AN N-SET N-FACTORIAL NUMBER OF K-SUBSETS OF AN N-SET PASCAL’S TRIANGLE COUNTING ALGORITHMICALLY (WITHOUT A FORMULA) IN?NITE SEQUENCES AND COMPLEXITY FUNCTIONS THE TOWERS OF HANOI BAD COMPLEXITY FUNCTIONS BOOLEAN EXPRESSIONS, LOGIC, AND PROOF THE GREEDY ALGORITHM AND THREE COOKIE PROBLEMS THE GREEDY ALGORITHM BOOLEAN EXPRESSIONS AND TRUTH TABLES THE NEGATION OPERATOR THE CONJUNCTION OPERATOR THE DISJUNCTION OPERATOR THE CONDITIONAL OPERATOR THE BICONDITIONAL OPERATOR PREDICATES AND QUANTI?ERS VALID ARGUMENTS EXAMPLES OF PROOFS DIRECT PROOF INDIRECT PROOF CANTOR’S DIAGONALIZATION PROCESS MATHEMATICAL INDUCTION STRONG INDUCTION PROOFS PROMISED IN CHAP 1 RUSSIAN PEASANT MULTIPLICATION IS CORRECT RESOLVING THE CAKE CUTTING CONUNDRUM CASTING OUT NINES EUCLID’S ALGORITHM FOR GCD IS CORRECT THE PROOF PROMISED IN CHAP 2 SEARCHING AND SORTING SEARCHING SEARCHING AN ARBITRARY LIST SEARCHING A SORTED LIST BRANCHING DIAGRAMS A SECOND VERSION OF BINARY SEARCH SORTING SELECTION SORTS EXCHANGE SORTS BINARY TREES WITH (AT LEAST) N! LEAVES PARTITION SORTS COMPARISON OF SORTING ALGORITHMS TIMINGS AND OPERATION COUNTS GRAPHS AND TREES INTRODUCTION DEGREES EULERIAN GRAPHS HAMILTONIAN GRAPHS PATHS, CIRCUITS, AND POLYGONS SUBGRAPHS DETERMINED BY PATHS TREES TRAVERSALS EDGE-WEIGHTED GRAPHS SHORTEST PATHS DRAWING AND COLORING BIPARTITE GRAPHS PLANAR GRAPHS SOME HISTORY OF THE FOUR COLOR THEOREM DIRECTED GRAPHS INTRODUCING DIRECTIONS STRONG CONNECTIVITY TOPOLOGICAL SORTING SHORTEST PATHS IN DIGRAPHS (ACYCLIC OR NOT) DISTANCE FUNCTION DIJKSTRA’S ALGORITHM FLOYD-WARSHALL ALGORITHM THE MAXIMUM FLOW PROBLEM MATCHINGS IN BIPARTITE GRAPHS RELATIONS: ESPECIALLY ON (INTEGER) SEQUENCES RELATIONS AND REPRESENTATIONS MATRIX REPRESENTATION DIRECTED GRAPH REPRESENTATION PROPERTIES OF RELATIONS EQUIVALENCE RELATIONS MATRIX AND DIGRAPH OF AN EQUIVALENCE RELATION ORDER RELATIONS MATRIX AND DIGRAPH OF A PARTIAL ORDER MINIMAL AND MAXIMAL ELEMENTS RELATIONS ON FINITE SEQUENCES DOMINATION LEXICOGRAPHIC ORDER RELATIONS ON IN?NITE SEQUENCES ASYMPTOTIC DOMINANCE AND BIG-OH NOTATION ASYMPTOTIC EQUIVALENCE AND BIG-THETA NOTATION ASYMPTOTIC RANKING STRONG ASYMPTOTIC DOMINANCE AND LITTLE-OH NOTATION SEQUENCES AND SERIES EXAMPLES DE?NED BY RECURRENCE EQUATIONS SOLVING FIRST-ORDER LINEAR RECURRENCE EQUATIONS THE FIBONACCI SEQUENCE ALGORITHMS FOR THE FIBONACCI SEQUENCE THE GOLDEN RATIO THE FIBONACCI SEQUENCE AND THE GOLDEN RATIO THE ORDER OF THE FIBONACCI SEQUENCE THE COMPLEXITY OF EUCLID’S ALGORITHM FOR GCD SOLVING SECOND-ORDER LINEAR RECURRENCE EQUATIONS IN?NITE SERIES ZENO’S PARADOXES FORMAL DE?NITIONS OF CONVERGENCE OF SEQUENCES AND SERIES GENERATING SEQUENCES AND SUBSETS GENERATING SEQUENCES IN LEXICOGRAPHIC-ORDER GENERATING ALL K-SEQUENCES ON {1N} AVERAGE-CASE COMPLEXITY GENERATING SUBSETS OF {1N} AS INCREASING SEQUENCES GENERATING PERMUTATIONS IN LEXICOGRAPHIC-ORDER GENERATING ALL K-PERMUTATIONS OF {1N} IN LEX-ORDER DISCRETE PROBABILITY AND AVERAGE-CASE COMPLEXITY PROBABILISTIC MODELS SAMPLE SPACES PROBABILITY FUNCTIONS THE SPECIAL CASE OF EQUALLY LIKELY OUTCOMES CONDITIONAL PROBABILITY COMBINATIONS OF EVENTS INDEPENDENT EVENTS MUTUALLY EXCLUSIVE EVENTS RANDOM VARIABLES AND EXPECTED VALUES EXPECTED FREQUENCY EXPECTED VALUES PROBABILITY DISTRIBUTIONS STANDARD DISTRIBUTIONS AND THEIR EXPECTED VALUES THE UNIFORM DISTRIBUTION THE BINOMIAL DISTRIBUTION THE GEOMETRIC DISTRIBUTION CONDITIONAL EXPECTED VALUES CONDITIONAL EXPECTATION APPLYING EXPECTATION TO LINEAR SEARCH APPLYING EXPECTATION TO QUICKSORT TURING MACHINES THE CHURCH-TURING THESIS UNIVERSAL TURING MACHINE: AS A COMPUTATIONAL MODEL THE HALTING PROBLEM