Syllabus, MAD2104 01-04, Fall 2018

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)

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)

Set math definitions, notation

Sets, elements, subsets

Sets, elements, subsets

Set operations

Predicates and Quantifiers (from 2.3)

More Predicates and Quantifiers (from 2.3)

Compound statements with quantified terms (combines 2.1, 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)

Set math definitions terminology

Sets and set operations, 4.1

Indexed sets, 4.1

Sets, elements, subsets

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

Modular congruence

Modular arithmetic

GCD as a linear combination

Multiplicative inverse mod

Solve linear congruence

Fermat's Little Theorem

RSA (calculator helpful)

Relations

Digraphs

Properties of relations

Properties of relations - The Sequel

Proofs (Chapter 7)

Proof by induction, 3.3, 4.1

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