MAD2104 Discrete Math I

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Syllabus, MAD2104 01-04, Fall 2018 (under construction)
Syllabus, MAD2104 01-02, Summer 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 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)
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)
Negate simple verbal quantified statements (from 2.3)
More Predicates and Quantifiers (from 2.3)
Predicates, Quantifiers, DeMorgan's Laws (from 2.3)
Compound statements with quantified terms (combines 2.1, 2.3)

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)

Chapter 5: Number Theory

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

More Chapter 3

Proof by induction, 3.3, 4.1

Chapter 1.1, Chapter 4.1 Set Mathematics

Sets, elements, subsets
Sets, elements, subsets
Set operations
Set math definitions terminology
Sets and set ops, 4.1
Indexed sets, 4.1
Verify/disprove set inclusion, 4.1
Bit strings and sets, 4.1

Chapter 7 Relations

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