Note: Schedule is subject to change.
Week 1: Introduction, Logic
DAY
TOPIC
HOMEWORK DUE
Monday 8/18
Introduction to the class
Class Introduction slides
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Wednesday 8/19
Propositional logic
Propositions
Truth tables
Logic operators: not, and, or, exclusive or
Implications: conditional
Reading: Chapter 1, Sections 1.1-1.2
Friday 8/21
Implications cont.: biconditional
Quiz
Week 2: Logic and Inference
DAY
TOPIC
HOMEWORK DUE
Monday 8/25
Logical Equivalences
DeMorgan's laws
Reading: Chapter 1, Section 1.3
Wednesday 8/27
Predicate logic
Quantifiers: for all, there exists
Reading: Chapter 1, Sections 1.4 -1.5
Friday 8/29
Quantifiers cont.
Quiz
Week 3: Logic and Inference cont.
DAY
TOPIC
HOMEWORK DUE
Monday 9/1
NO CLASS, Labor Day
Wednesday 9/3
The rules of inference
Reading: Chapter 1, Sections 1.6
Friday 9/5
Rules of inference cont.
Quiz
DROP DEADLINE SEPT 6
Last day to drop without paying tuition and receiving a W on transcript.
Week 4: Logic and Inference cont.
DAY
TOPIC
HOMEWORK DUE
Monday 9/8
Rules of inference cont.
Wednesday 9/10
Rules of inference cont.
Friday 9/12
NO CLASS
In-Class Assignment Due at end of class
Week 5: No Class
DAY
TOPIC
HOMEWORK DUE
Monday 9/15
NO CLASS
Homework 1 due Tuesday
Wednesday 9/17
NO CLASS
Friday 9/19
NO CLASS
Week 6: Proofs
DAY
TOPIC
HOMEWORK DUE
Monday 9/22
Proofs
Direct proofs
Reading: Chapter 1, Section 1.7
Wednesday 9/24
Proofs cont.
Proofs by contraposition
Reading: Chapter 1, Section 1.8
Friday 9/26
Division
Dividend, divisor, quotient, and remainder
Modulo
Congruence
Quiz
Reading: Chapter 4, Section 4.1
Week 7: Number Theory
DAY
TOPIC
HOMEWORK DUE
Monday 9/29
Base in mathematics
Representing numbers in different bases (ie: decimal, hexadecimal, octal, binary)
Bases, operations, and algorithms
Reading: Chapter 4, Section 4.2
Wednesday 10/1
Review
Propositional logic: propositions, truth tables, logical equivalence, tautologies, DeMorgan's laws, translating into sentences
Rules of inference: reasoning about hypotheses and conclusions, applying rules of inference
Predicate logic: quantifiers, DeMorgan's laws, translating into sentences
Proofs: direct proof, proof by contraposition, proof by contradiction
Number theory: divisibility, modulo operator, congruence, base conversions, primes, gcd, lcm, Euclidean algorithm. Number theory proofs
Friday 10/3
Review
Propositional logic: propositions, truth tables, logical equivalence, tautologies, DeMorgan's laws, translating into sentences
Rules of inference: reasoning about hypotheses and conclusions, applying rules of inference
Predicate logic: quantifiers, DeMorgan's laws, translating into sentences
Proofs: direct proof, proof by contraposition, proof by contradiction
Number theory: divisibility, modulo operator, congruence, base conversions, primes, gcd, lcm, Euclidean algorithm. Number theory proofs
Week 8: Exam
DAY
TOPIC
HOMEWORK DUE
Monday 10/6
Exam 1
Exam 1
Homework 2 due Tuesday
Wednesday 10/8
NO CLASS
Friday 10/10
FALL BREAK
Week 9: Number Theory Cont.
DAY
TOPIC
HOMEWORK DUE
Monday 10/13
Review exam 1 problems
Wednesday 10/15
Primes.Greatest common divisors and least common multiples.
Reading: Chapter 4, Section 4.3-4.4
Friday 10/17
Primes.Greatest common divisors and least common multiples. Cont.
Reading: Chapter 4, Section 4.3-4.4
Week 10: Number Theory cont. and Sets
DAY
TOPIC
HOMEWORK DUE
Monday 10/20
Euclidean algorithm for gcds
gcds as Linear Combinations.
Reading: Chapter 4, Section 4.3-4.4
Wednesday 10/22
Euclidean algorithm for gcds
gcds as Linear Combinations.
Reading: Chapter 4, Section 4.3-4.4
Friday 10/24
Chinese remainder theorem. Introduction to sets
Set description: roster method and set builder notation
Important numerical sets
Intervals
Equality of sets
Subsets and proper subsets
Venn diagrams
Reading: Chapter 2, Section 2.1-2.2
Week 11: Sets cont. and Time Complexity of Algorithms
DAY
TOPIC
HOMEWORK DUE
Monday 10/27
Power sets
n-tuples and ordered pairs
Cartesian product
Introduction to set operations
Reading: Chapter 2, Section 2.3-2.4
Wednesday 10/29
Introduction to cardinality. Set operations
Union
Intersection
Difference
Symmetric Difference
Complement
Reading Chapter 2, Section 2.5-2.6
Friday 10/31
The growth of functions and complexity of algorithms.
Reading: Chapter 3, Section 3.2-3.3
Week 12: Induction, recursion and sequences
DAY
TOPIC
HOMEWORK DUE
Monday 11/3
Introduction to induction.
Reading: Chapter 5, Section 5.1-5.2
Wednesday 11/5
Sequences and recursion.
Reading: Chapter 5, Section 5.3-5.5 Homework 3 Due
Friday 11/7
Sequences and recursion. Cont
Reading: Chapter 5, Section 5.3-5.5
Week 13: Relations cont. and Exam 2
DAY
TOPIC
HOMEWORK DUE
Monday 11/10
Introduction to Counting and Combinatorics
Product rule
Sum rule.
Reading: Chapter 6, Section 6.1-6.3
Wednesday 11/12
Review
Number Theory: Euclidean algorithm, finding inverses, Chinese Remainder Theorem
Sets: set builder notation, Venn diagrams, cardinality, power set and Cartesian product, subsets and proper subsets, set operations: union, intersection, complement, difference, set identities, proofs with sets
Functions: functions as mappings from one set to another, domain and co-domain, one-to-one, onto, one-to-one correspondence, invertible
Sequences and Sums: calculating terms in a sequence given a definition, arithmetic and geometric sequences, recurrence relations, solutions to recurrence relations, finding a definition given the sequence, calculating basic sums
Friday 11/14
Exam 2
Week 14: Relations cont.
DAY
TOPIC
HOMEWORK DUE
Monday 11/17
Bayes’ Theorem and Recurrence relations.
Reading: Chapter 7, Section 7.3
Reading: Chapter 8, Section 8.1-8.2
Wednesday 11/19
Recurrence relations cont.
Reading: Chapter 8, Section 8.3-8.5
Friday 11/21
Graphs, Euler and Hamilton paths, shortest-path problems.
Reading: Chapter 10, Section 10.5-10.8
Week 15: Trees cont. and State Machines
DAY
TOPIC
HOMEWORK DUE
Monday 11/24
Introduction to trees and boolean algebra
Reading: Chapter 11, Section 11.1-11.2
Wednesday 11/26
State machines.
Reading: Chapter 13, Section 13.1-13.5 Homework 4 Due
Friday 11/28
THANKSGIVING BREAK
Week 16: Final Exam
DAY
TOPIC
HOMEWORK DUE
Monday 12/1
Review
Propositional logic: propositions, truth tables, logical equivalence, tautologies, DeMorgan's laws, translating into sentences
Rules of inference: reasoning about hypotheses and conclusions, applying rules of inference
Predicate logic: quantifiers, DeMorgan's laws, translating into sentences
Proofs: direct proof, proof by contraposition, proof by contradiction
Number theory: divisibility, modulo operator, congruence, base conversions, primes, gcd, lcm, Euclidean algorithm. Number theory proofs, Euclidean algorithm, finding inverses, Chinese Remainder Theorem
Sets: set builder notation, Venn diagrams, cardinality, power set and Cartesian product, subsets and proper subsets, set operations: union, intersection, complement, difference, set identities, proofs with sets
Functions: functions as mappings from one set to another, domain and co-domain, one-to-one, onto, one-to-one correspondence, invertible
Sequences and Sums: calculating terms in a sequence given a definition, arithemetic and geometric sequences, recurrance relations, solutions to recurrance relations, finding a definition given the sequence, calculating basic sums
Counting and Combinatorics: product rule, sum rule.
Wednesday 12/3
Final Exam part 1
Final Exam part 1
Friday 12/5
Final Exam part 2
Final Exam part 2