MAD2104 Discrete Math I

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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)
Bitwise operations (from 2.1)
Tautologies, truth tables (from 2.2)
More of tautologies, truth tables (from 2.2)
Disjunctive Normal Form (from 2.2)
Verbal equivalencies, negations, variations (from 2.2)
Name That Law! (from 2.2)
Using Equivalency Laws (from 2.2)
Using Equivalency Laws, proving/disproving claims (from 2.2)
Proving Equivalencies (from 2.2)
Predicates and Quantifiers (from 2.3)
Negate simple verbal quantified statements (from 2.3)
Compound statements with quantified terms (combines 2.1, 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)
Rules of inference, quantifiers (from 3.1)

TEST 1 TOPICS END HERE

Constructing validity proofs (from 3.1)
Other 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

Proof by induction, 3.3, 4.1, 4.3 (recently updated to include 4.3)
Well ordered sets, 3.3

Chapter 7

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

Chapters 1.2, 4.2, 4.3: Functions

Definitions and whatnot
Intro to Functions 1.2
Intro to Functions 1.2
Floor/ceiling functions 1.2
Floor/ceiling functions 1.2
Characteristic function 1.2
Characteristic function 1.2
Function properties, 4.2
Function properties, 4.2
Prove injection, surjection, 4.2
Calculate recursive function, 4.3
Calculate f n, 4.3
Calculate f n, 4.3
Bit strings and structural induction (4.3)

Chapter 6
Graph theory definitions et c.
Name that graph
Bipartite graphs
Degree sequence
Special graphs
Handshaking theorem


Other things from Chapters 3 and 4
Bit strings, structural induction, 4.3

Other
Solve linear recurrence relation