Syllabus, MAD2104 01-06, Spring 2018

MAD2104 Course Notes

Answers for selected Course Notes exercises

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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)

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)

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)

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)

Modular congruence

Division algorithm

a mod m

Modular arithmetic

Definitions, theorems

Relatively prime

Euler

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

Solve linear congruence

RSA (calculator helpful)

Set math definitions terminology

Sets, elements, subsets

Set operations

Sets and set ops, 4.1

Indexed sets, 4.1

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

Well ordered sets, 3.3

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

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

Calculate

Bit strings and structural induction (4.3)

Graph theory definitions et c.

Name that graph

Bipartite graphs

Degree sequence

Special graphs

Handshaking theorem

Bit strings, structural induction, 4.3

Solve linear recurrence relation