### MAD2104 Discrete Math I

Syllabus, MAD2104 01-06, Spring 2019

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Equivalency Laws
Rules of Inference

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Chapter 2 Propositional Logic

Using logical operators (from 2.1)
Bit strings (from 2.1)
Symbolize a verbal proposition (from 2.1)
Tautologies, truth tables (from 2.2)
More of tautologies, truth tables (from 2.2)
Verbal equivalencies, negations, variations (from 2.2)
Disjunctive Normal Form (from 2.2)
Using Equivalency Laws (from 2.2)
Name That Law! (from 2.2)
Proving/disproving Equivalencies (from 2.2)
Proving Equivalencies (from 2.2)
Predicates and Quantifiers (from 2.3)
More Predicates and Quantifiers (from 2.3)
Negate simple verbal quantified statements (from 2.3)
Compound statements with quantified terms (combines 2.1, 2.3)
Predicates, Quantifiers, DeMorgan's Laws (from 2.3)

Chapter 1.1 Definitions in Set Mathematics

Set math definitions, notation
Sets, elements, subsets
Sets, elements, subsets
Set operations

Chapter 3 Arguments and proof

Simple verbal arguments (from 3.1)
Validity of symbolic arguments, using truth tables (from 3.1)
More Rules of Inference, Fallacies (from 3.1)
Inference, deduction (from 3.1)
Constructing validity proofs (from 3.1)
Rules of inference, quantifiers (from 3.1)
Other quantified arguments (from 3.1)
More complicated quantified arguments (from 3.1)
Still more complicated quantified arguments (from 3.1)
Methods of Proof, 3.2 (also includes concepts from Chapter 5)
Proof by induction, 3.3, 4.1
Well ordered sets, 3.3

Chapter 5: Number Theory

Definitions, theorems
Modular congruence
Modular arithmetic
GCD as a linear combination
Multiplicative inverse mod m
Solve linear congruence
Fermat's Little Theorem
Euler φ function

Chapter 4.1: More set math

More set math definitions terminology, 1.1, 4.1
Sets and set operations, 4.1
Indexed sets, 4.1

Chapter 7 Relations

Relations
Digraphs
Properties of relations
Properties of relations - The Sequel
Proofs (Chapter 7)

Chapters 1.2 and 4.2: Functions

Definitions and whatnot
Intro to Functions 1.2
Intro to Functions 1.2
Floor/ceiling functions 1.2
Floor/ceiling functions 1.2
Floor function 1.2
Ceiling function 1.2
Ceiling function 1.2
Floor function 1.2
Characteristic function 1.2
Characteristic function 1.2
Function properties, 4.2
Function properties, 4.2
Prove injection, surjection, 4.2
Calculate function composition, 4.2
Prove injection, surjection, 4.2

Chapter 6: Graph Theory

Graph theory definitions et c.
Name that graph
Bipartite graphs
Degree sequence
Special graphs
Handshaking theorem