Math 2602 Home Page

Math 2602 Linear and Discrete Mathematics Section F, Spring 2014

Handout

Click here for the handout from the first day.

Instructors

Prof. Dan Margalit

TAs: Rebecca Winarski, J.D. Walsh

Book

Class Meetings

Lecture: Tuesday and Thursday, 12:05-1:25, CULC 102.
Section F1 (Winarski): Monday and Wednesday 1:05-1:55, CULC 423.
Section F2 (Walsh): Monday and Wednesday 1:05-1:55, CULC 129.

Office Hours

Prof. Margalit: Monday 3-4, Tuesday and Thursday after class, and by appoinment in Skiles 244.
Rebecca Winarski: Wednesday 12-1, Skiles 152
J.D. Walsh: Monday 12-1, Skiles 149

Course Objectives

The main goals of this course are to learn how to prove mathematical statements, to solve mathematical problems, and to apply and analyze known theorems and algorithms in the subject areas of combinatorics, number theory, and graph theory.

T-Square

The course T-Square site includes links to the course Grade book, Piazza site, and Announcements.

Clickers

The course will use Turning Point clickers. Student scores are based solely on their response rates. It is the student's responsibility to maintain a working clicker and to have it registered on T-Square.

Piazza

Piazza will be available on T-Square as an optional tool for online discussions about the course material.

Homework

Homework will primarily assigned via WebWork. It is generally due on Tuesday night at midnight and covers the previous week's material. Multiple attempts are usually allowed. Some weeks, there will be problems that are not graded, and hence do not count towards the final score.

Quizzes

Quizzes, again assigned via WebWork, are given before each class meeting, and are intended to check comprehension of the reading/viewing material. Multiple attempts are not allowed on the questions. For the quizzes you will be learning new material that has not yet been covered in class.

Write to Becca if you still need to sign up for a WebWork account. Send your gtlogin, recitation number (1 or 2), your email address, and your full name.

Reading, Viewing, Notes, Schedule, and Exams

Meeting 9

Date	Topics	Text Sections	Videos	Notes
Jan 7	Statements	0.1	Statements Converse / contrapositive Negation Negation of conditional Quantifiers	Meeting 1
Jan 9	Proofs	0.2	Direct proof Proof by contradiction Proof by contraposition Proof by cases Infinitude of the primes	Meeting 2
Jan 14	Truth tables / Logic	1.1-1.2	Truth Tables Truth Tables for Conditional Statements Truth Tables for Conditional Statements Truth Table with 3 statements Tautologies Contradictions Logical Equivalence with truth tables Logical Equivalence without truth tables	Meeting 3
Jan 16	Binary relations	2.3-2.4	Binary Relations Equivalence Relations Equivalence Classes Properties of Equivalence Classes	Meeting 4
Jan 21	Functions	3.1-3.2		Meeting 5
Jan 23	Cardinality	3.3	Cardinality of Sets Infinite Sets Different Infinities	Meeting 6
Jan 28	Congruence	4.4-4.5	Congruence Reducing modulo n Linear Congruence Equations Chinese Remainder Theorem	Meeting 7
Jan 30	Midterm 1	0.1-0.2, 1.1-1.2, 2.3-2.4, 3.1-3.3		Solutions
Feb 4	Snow day
Feb 6	Induction	5.1	Proof by Induction Proof by Induction	Meeting 8 Induction
Feb 11	Snow day
Feb 13	Snow day
Feb 18	Recursive sequences	5.2-5.3	Arithmetic Sequences Geometric Sequences Recurrence Relations	Recurrence relations
Feb 20	Algorithms / Complexity	8.1-8.3	What is an algorithm? Big O Order of complexity	Meeting 10 Big O
Feb 25	Inclusion-exclusion	6.1-6.2	Inclusion-Exclusion Multiplication and Addition Principles	Basics of counting
Feb 27	Midterm 2	4.4-4.5, 5.1-5.3, 8.1-8.3		Solutions
Mar 4	Pigeonhole principle	6.3	Pigeonhole Principle	Meeting 12
Mar 6	Permutations / Combinations	7.1-7.2	Permutations Combinations	Meeting 13 Permutations and Combinations
Mar 11	Probability	7.3	Basic Probability Probability (coin flips) Probability (more than 2 outcomes)	Meeting 14
Mar 13	Bayes' Rule	7.4	Conditional Probability Bayes' Theorem Bayes' Theorem and Cancer Screening	Meeting 15
Mar 25	Repetitions	7.5	Permutations with Repetition	Meeting 16
Mar 27	Binomial Theorem	7.7	Pascal's triangle and binomial coefficients Introducing Pascal's triangle Patterns in Pascal's triangle	Meeting 17
Apr 1	Graphs	9.1-9.3	Konigsberg Bridge Problem Graph Definitions Bipartite Graph Sum of degrees is twice the number of edges Graph Isomorphism	Meeting 18
Apr 3	Midterm 3	6.1-6.3, 7.1-7.5, 7.7		Solutions
Apr 8	Euler / Hamilton Paths	10.1-10.2		Meeting 19
Apr 10	Shortest Paths	10.4	Weighted Graphs Dijkstra's Algorithm	Meeting 20
Apr 15	Trees	12.1-12.2	Trees	Meeting 21
Apr 17	Spanning Trees	12.3	Spanning Trees Krushkal's Algorithm Prim's Algorithm	Meeting 22
Apr 22	Planar Graphs	13.1	Planar Graphs	Meeting 23
Apr 24	Graph Coloring	13.2	Graph Coloring	Meeting 24
Apr 29	Final Exam	0.1-0.2, 1.1-1.2, 2.3-2.4, 3.1-3.3 4.4-4.5, 5.1-5.3, 8.1-8.3 6.1-6.3, 7.1-7.5, 7.7 9.1-9.3, 10.1-10.2, 10.4, 12.1-12.3, 13.1-13.2		Practice exam
				Course notes

Grading

Final grades will be computed according to the following scale:

Quizzes 15%

Clickers 10%

Homework 25%

Midterms 30%

Final Exam 20%

Absences

As a general rule, absences are excused for official Georgia Tech business only. I reserve the right to ask for a letter from the Dean of Students. In general, internships and interviews are not grounds for excused absences. If you have an official excuse for absence for an exam, you will be excused from that exam without penalty, meaning that your other exams will count for a larger portion of your grade.

Resources

---T-Square

---Math Labs, in Clough 280. Math 2602 TAs will be available on Mon 1-2, Tue 11-12, Wed 2-3, and Thu 3-4.

---Center for Academic Success, Drop in tutoring and one-on-one tutoring

---ADAPTS, Disabilities Services Program

---Honor code

Math 2602

Linear and Discrete Mathematics

Section F, Spring 2014