MAD2104 Discrete Math I

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Syllabus, MAD2104 01-04, Fall 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)
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)
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 1.1 Definitions in Set Mathematics

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

Chapter 2 Propositional Logic

Predicates and Quantifiers (from 2.3)
More Predicates and Quantifiers (from 2.3)
Compound statements with quantified terms (combines 2.1, 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)

TEST 3 TOPICS BEGIN HERE

Chapters 1.1, 4.1 Set Mathematics

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

Chapter 3 Arguments and proof

Methods of Proof, 3.2 (also includes concepts from Chapter 5)

Chapter 5: Number Theory

Modular congruence
Modular arithmetic
GCD as a linear combination
Multiplicative inverse mod m
Solve linear congruence
Fermat's Little Theorem
RSA (calculator helpful)

Chapter 7 Relations

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

TEST 3 TOPICS END HERE

More Chapter 3

Proof by induction, 3.3, 4.1

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