NOTE: ALL HOMEWORK AND IN CLASS WORK HAS BEEN REMOVED. THESE LINKS ARE BROKEN.
| Day |
Topic |
Homework Due |
| Week 1: Introduction, Logic |
| Tuesday 1/16 |
Introduction to the class
Propositions
Truth Tables
Compound Propositions: and, or, exclusive or
Implications
|
Fill out this form to be considered for an override. |
| Thursday |
Propositional logic cont.
Translating logical expressions into English
slides for week 1 |
|
| Week 2: Logic and Inference |
| Tuesday 1/23 |
Predicate logic
Logical Quantifies: for all, there exists
solutions to in class work
|
|
| Thursday |
Nested Quantifiers
The rules of inference
Rules of inference
solutions to in class work
slides for week 2
|
Homework 1 due |
| Week 3: Proofs |
| Tuesday 1/30 |
Direct proofs
Proof by contraposition
in class work
|
|
| Thursday |
Proof by contradiction
in class work
slides for week 3
|
|
| Friday 2/2 |
DROP DEADLINE - Last day to drop without paying tuition and receiving a W on transcript. |
|
| Week 4: Sets |
| Tuesday 2/6 |
Introduction to sets
Set descrition: roster method and set builder notation
Important numerical sets
Intervals
Equality of sets
Subsets and proper subsets
Venn diagrams
in class work
|
|
| Thursday |
Introduction to cardinality
Power sets
n-tuples and ordered pairs
Cartesian product
in class work
slides for week 4
|
Homework 2 due |
| Week 5: Exam |
| Tuesday 2/13 |
Review
Propositional logic: propositions, truth tables, logical equivalence, tautologies, DeMorgan's laws, translating into sentences
Predicate logic: quantifiers, DeMorgan's laws, nested quantifiers, translating into sentences
Rules of inference: reasoning about hypotheses and conclusions, applying rules of inference
Proofs: direct proof, proof by contraposition, proof by contradiction
Set Theory: set builder notation, subsets, Venn diagrams, cardinality, power sets, Cartesian product
Rules of inference
Exam practice questions |
|
| Thursday |
Exam 1 |
|
| Week 6: Sets cont. |
| Tuesday 2/20 |
Set operations
Union
Intersection
Difference
Symmetric Difference
Complement
Proofs with sets
Set identities and logical equivalences
in class work |
|
| Thursday |
Functions or "mappings"
Domain, codomain, and range
One-to-one and onto functions
Invertible functions
in class work
slides for week 6
|
|
| Week 7: Sequences |
| Tuesday 2/27 |
Composition of functions
Introduction to sequences
Arithmetic sequences
Geometric sequences
in class work |
|
| Thursday |
Sequences cont.
Recurance relation, sequences and recursion
Introduction to summations
in class work
slides for week 7 |
|
| Week 8: Number Theory |
| Tuesday 3/5 |
Division
Modulo
Dividend, divisor, quotient, and remainder
Congrugence
in class work
|
Homework 3 due |
| Thursday |
Base in mathematics
Representing numbers in different bases (ie: decimal, hexadecimal, octal, binary)
Bases, operations, and algorithms
in class work
slides for week 8 |
|
| Week 9: SPRING BREAK |
| Week 10: Number Theory |
| Tuesday 3/19 |
Primes and greatest common divisors
in class work
Sieve of Eratosthenes demo
|
|
|
| Thursday |
Primes and least common multiples
in class work
slides for week 9 |
Homework 4 due |
| Week 11: Exam |
| Tuesday 3/26 |
Review
Set theory: set operations (union, intersection, difference, symmetric difference, complement), subsets, proofs of set equivalences.
Sequences and sums: recursive and explicit definitions of sequences, recurrance relations, summations, nested summations
Number theory: divisibility, modulo operator, congruence, base conversions, primes, gcd, lcm, and related proofs
Exam practice questions |
|
| Thursday |
Exam 2 |
|
| Week 12: Number Theory |
| Tuesday 4/2 |
Euclidean algorithm for gcds
Bezout's Theorem
Inverses
Solving Congruences
in class work
slides for week 12
|
|
| Thursday |
CLASS CANCELED |
|
| Week 13: Number Theory cont. |
| Tuesday 4/9 |
Chinese remainder theorem
Solving systems of congruences
solution to problem 9c on Exam 2
in class work
|
|
| Thursday |
Introduction to relations
Binary relations
in class work
slides for week 13 |
|
| Week 14: Relations and Graphs |
| Tuesday 4/16 |
Guest professor: PhD student Jaime Gould
Relations continued.
Properties of relations: reflexive, symmetric, antisymmetric, and transitive
Combining relations
in class work |
|
| Thursday |
n-ary relations
Properties of relations in matrix and graph representations
Closures
in class work
slides for week 14
|
|
| Week 15: Relations and Graphs |
| Tuesday 4/23 |
Paths in graphs
Powers of relations
Transitive closure
in class work |
Homework 5 due |
| Thursday |
Computing transitive closure
Boolean product
Begin final exam review
No new slides for this week. see week 14 slides |
|
| Week 16: Exam |
| Tuesday 4/30 |
Final exam review
Exam is cumulative, but will emphasize material covered after exam 2
Exam practice questions |
|
| Thursday |
Final Exam |
|
