MAD2104 Discrete Math I

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Syllabus, MAD2104 01-02, Summer 2018
Syllabus, MAD2104 01-06, Spring 2018

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MAD2104 Course Notes
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Quick reference
Equivalency Laws
Rules of Inference

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Chapter 2

Using logical operators (from 2.1)
Symbolize a verbal proposition (from 2.1)
Constructing truth tables (from 2.1)
Bit strings (from 2.1)
Tautologies, truth tables (from 2.2)
More of tautologies, truth tables (from 2.2)
Verbal equivalencies, negations, variations (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)
Disjunctive Normal Form (from 2.2)
Predicates and Quantifiers (from 2.3)
Negate simple verbal quantified statements (from 2.3)
More Predicates and Quantifiers (from 2.3)
Predicates, Quantifiers, DeMorgan's Laws (from 2.3)

Chapter 3

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)

Chapter 5: Number Theory

Modular congruence
Division algorithm
a mod m
Modular arithmetic
Definitions, theorems
Relatively prime
Euler φ function
Fermat's Little Theorem
Euclidean algorithm (no calculator version)
Euclidean algorithm (calculator required)
Proofs (Chapters 4 and 5)
GCD as a linear combination
Multiplicative inverse mod m
Solve linear congruence
RSA (calculator helpful)

Chapters 1.1 and 4.1 Set Mathematics

Set math definitions terminology
Sets, elements, subsets
Set operations
Sets and set ops, 4.1
Indexed sets, 4.1

More Chapter 3
Well ordered sets, 3.3
Proof by induction, 3.3, 4.1

Chapter 7

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