Syllabus, MAD2104 01-06, Spring 2019

MAD2104 Course Notes

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Equivalency Laws

Rules of Inference

If you find bugs or errors, please report them to Mr. Wooland. Screen snapshots would be helpful in that case.

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)

Set math definitions, notation

Sets, elements, subsets

Sets, elements, subsets

Set operations

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

Definitions, theorems

Modular congruence

Modular arithmetic

GCD as a linear combination

Multiplicative inverse mod

Solve linear congruence

Fermat's Little Theorem

Euler

RSA (calculator helpful)

More set math definitions terminology, 1.1, 4.1

Sets and set operations, 4.1

Indexed sets, 4.1

Relations

Digraphs

Properties of relations

Properties of relations - The Sequel

Proofs (Chapter 7)

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

Graph theory definitions et c.

Name that graph

Bipartite graphs

Degree sequence

Special graphs

Handshaking theorem