Learning Discrete Mathematics with ISETL

1 Numbers, Programs, and ISETL.- 1.1 Preview.- 1.2 Overview of ISETL.- 1.3 Integers.- 1.4 Integer Operations.- 1.5 Special Binary Integer Operators.- 1.5.1 Extending Binary Operators.- 1.5.2 Greatest Common Divisor.- 1.5.3 Modular Arithmetic.- 1.6 Random Integers.- 1.7 Floating-Point, Rational, and Real Numbers.- 1.8 Floating-Point Operations.- 1.9 Other Simple Data Types.- 2 Propositional Calculus.- 2.1 Preview.- 2.2 Boolean Variables and Expressions.- 2.3 Reasoning and Boolean Expressions.- 2.4 Methods of Proof.- 2.5 Predicate Calculus: First Pass.- 2.6 Propositions as Objects.- 3 Sets and Tuples.- 3.1 Preview.- 3.2 Introduction to Sets.- 3.3 Set Operations.- 3.4 Set Formation.- 3.5 Tuples and Tuple Operations.- 3.6 One-Liners.- 3.6.1 Proofs.- 3.6.2 Prime Numbers.- 3.7 The Compound Operator.- 4 Functions.- 4.1 Preview.- 4.2 Representations of Functions.- 4.2.1 Programs.- 4.2.2 Funcs.- 4.2.3 Tuples and Strings.- 4.2.4 Smaps.- 4.3 Function Operations.- 4.3.1 Evaluation and Equality of Functions.- 4.3.2 Images and Pre-images.- 4.3.3 Arithmetic with Functions.- 4.3.4 Composition of Functions.- 4.3.5 The Inverse of a Function.- 4.3.6 The Partial Sum Operator.- 4.3.7 Collections of Functions.- 4.3.8 Functions of Several Variables.- 4.4 Applications of Functions.- 4.4.1 Data Bases.- 4.4.2 Counting Onto Functions.- 4.4.3 Finite State Automata.- 5 Predicate Calculus.- 5.1 Preview.- 5.2 Single-Level Quantification.- 5.3 Two-Level Quantification.- 5.4 Three-Level Quantification.- 5.5 Quantification in Math and CS.- 5.5.1 Continuity of Functions.- 5.5.2 The Chemical Factory Problem.- 5.5.3 Abstract Algebra.- 5.5.4 Statements About Programs.- 6 Combinatorics, Matrices, Determinants.- 6.1 Preview.- 6.2 Combinatorics.- 6.2.1 The Multiplication and Addition Principles.- 6.2.2 Permutations.- 6.2.3 Combinations.- 6.3 Matrices.- 6.3.1 Representation of Matrices.- 6.3.2 Operations on Matrices.- 6.3.3 Matrix Inversion.- 6.4 Determinants.- 7 Mathematical Induction.- 7.1 Preview.- 7.2 Proposition Valued Functions of N.- 7.3 Modus Ponens.- 7.4 Implication Valued Functions of N.- 7.5 Making Proofs by Induction.- 7.6 Variations on the Induction Theme.- 7.6.1 Double Induction.- 7.6.2 Strong Induction.- 7.6.3 Recursively Defined Sequences.- 8 Relations and Graphs.- 8.1 Preview.- 8.2 Relations and Their Representations.- 8.3 Properties of Relations.- 8.4 Digraphs.- ISETL order form.