Syllabus, MAD2104 01-04, Fall 2018 (under construction)

Syllabus, MAD2104 01-02, Summer 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)

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)

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)

Modular congruence

Division algorithm

a mod m

Modular arithmetic

Definitions, theorems

Relatively prime

Euler

Euclidean algorithm (no calculator version)

GCD as a linear combination

Multiplicative inverse mod

Solve linear congruence

Fermat's Little Theorem

Euclidean algorithm (calculator required)

Proofs (Chapters 4 and 5)

RSA (calculator helpful)

Proof by induction, 3.3, 4.1

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

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