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lehman e mathematics computer science 2017

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Textbook in PDF format Proofs What is a Proof Propositions Predicates The Axiomatic Method Our Axioms Proving an Implication Proving an “If and Only If” Proof by Cases Proof by Contradiction Good Proofs in Practice The Well Ordering Principle Well Ordering Proofs Template for Well Ordering Proofs Factoring into Primes Well Ordered Sets Logical Formulas Propositions from Propositions Propositional Logic in Computer Programs Equivalence and Validity The Algebra of Propositions The SAT Problem Predicate Formulas Mathematical Data Types Sets Sequences Functions Binary Relations Finite Cardinality Induction Ordinary Induction Strong Induction Strong Induction vs Induction vs Well Ordering State Machines States and Transitions The Invariant Principle Partial Correctness & Termination The Stable Marriage Problem Recursive Data Types Recursive Definitions and Structural Induction Strings of Matched Brackets Recursive Functions on Nonnegative Integers Arithmetic Expressions Induction in Computer Science Infinite Sets Infinite Cardinality The Halting Problem The Logic of Sets Does All This Really Work Structures Number Theory Divisibility The Greatest Common Divisor Prime Mysteries The Fundamental Theorem of Arithmetic Alan Turing Modular Arithmetic Remainder Arithmetic Turing’s Code (Version ) Multiplicative Inverses and Cancelling Euler’s Theorem RSA Public Key Encryption What has SAT got to do with it Directed graphs & Partial Orders Vertex Degrees Walks and Paths Adjacency Matrices Walk Relations Directed Acyclic Graphs & Scheduling Partial Orders Representing Partial Orders by Set Containment Linear Orders Product Orders Equivalence Relations Summary of Relational Properties Communication Networks Routing Routing Measures Network Designs Simple Graphs Vertex Adjacency and Degrees Sexual Demographics in America Some Common Graphs Isomorphism Bipartite Graphs & Matchings Coloring Simple Walks Connectivity Forests & Trees Planar Graphs Drawing Graphs in the Plane Definitions of Planar Graphs Euler’s Formula Bounding the Number of Edges in a Planar Graph Returning to K and K; Coloring Planar Graphs Classifying Polyhedra Another Characterization for Planar Graphs Counting Sums and Asymptotics The Value of an Annuity Sums of Powers Approximating Sums Hanging Out Over the Edge Products Double Trouble Asymptotic Notation Cardinality Rules Counting One Thing by Counting Another Counting Sequences The Generalized Product Rule The Division Rule Counting Subsets Sequences with Repetitions Counting Practice Poker Hands The Pigeonhole Principle Inclusion-Exclusion Combinatorial Proofs Generating Functions Infinite Series Counting with Generating Functions Partial Fractions Solving Linear Recurrences Formal Power Series Probability Events and Probability Spaces Let’s Make a Deal The Four Step Method Strange Dice The Birthday Principle Set Theory and Probability Conditional Probability Monty Hall Confusion Definition and Notation The Four-Step Method for Conditional Probability Why Tree Diagrams Work The Law of Total Probability Simpson’s Paradox Independence Mutual Independence Probability versus Confidence Random Variables Random Variable Examples Independence Distribution Functions Great Expectations Linearity of Expectation Deviation from the Mean Markov’s Theorem Chebyshev’s Theorem Properties of Variance Estimation by Random Sampling Confidence in an Estimation Sums of Random Variables Really Great Expectations Random Walks Gambler’s Ruin Random Walks on Graphs Recurrences Recurrences The Towers of Hanoi Merge Sort Linear Recurrences Divide-and-Conquer Recurrences A Feel for Recurrences Glossary of Symbols

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lehman e mathematics computer science 2017