Tuesday, Thursday 6-7:15 pm, 406 Mathematics Building
September 9th to December 12th
All important course announcements will appear here. So check back regularly.
Our first meeting together will be September 13 in Room 406 (through the math help room)
Instructor: Matt DeLand (x45886, 206 Mathematics, deland@math.columbia.edu)
Faculty Supervisor: Cathy O'Neil (518 Mathematics, oneil@math.columbia.edu
Undergraduate Secretary: Mary Young (410 Mathematics, my@math.columbia.edu
Office Hours: TBA and by Appointment
Text: The Knot Book by Colin Adams. Published by the American Mathematical Society. ISBN 0821836781. There should be copies available in the book store before long. Also there are two copies on reserve in the mathematics library.
Course description: This course is intended to simultaneously develop your understanding of an advanced subject matter in mathematics and improve your ability to lecture to a classroom.
Prerequisites: Two years of calculus and at least one year of additional math courses, as well as the permission of the director of undergraduate studies.
Policies: Here are some standard policies to keep in mind:
Homework: Homework will be assigned weekly, just to make sure you're keeping up. (The emphasis is on your lecture.)
Resources: Help is always available from the Help Room, me, or the TA.
If there's something you don't understand -- ASK.
Exams:There will be no exams
Grading and requirements:
Each student will prepare talks to be given to the seminar, under the supervision of the graduate mentor. You are required to hand in lecture notes and meet with the graduate mentor at least one day before your scheduled presentation. It is your responsibility to schedule this meeting. Attendance is mandatory (failure will result in decreased grade).
| Date | Speakers | Topics Covered | Homework | Date Due |
|---|---|---|---|---|
| Sep 9 | Organizational Meeting | If there is an administrative question, please be in contact with myself, Professor O'Neill, or Mary Young as soon as possible | ||
| Sep 13 | Arthur P. Ian S. | Introduction Prime Knots | ||
| Sep 15 | Nicole P. Ilya V. | Dowker Notation (2.2) Tangles, Conway Notation (2.3) | ||
| Sep 20 | John K. John L. | Unknotting Numbers (3.1) Bridge and Crossing Numbers (3.2-3) | Homework 1 Page 1 Page 2 | September 27 |
| Sep 22 | Jake A. John A. | Surfaces without Boundry(4.1) | ||
| Sep 27 | Ilya V. Whitney B. | Tricolorization and Planar Graphs (1.5,2.4) Surfaces with Boundry(4.2) | Homework 2 | Oct 4 |
| Sep 29 | Arthur P. Nicole P. | Genus and Seifert Surfaces (4.3) Torus Knots (5.1) | ||
| Oct 4 | John K. John L. | Satellite Knots and Hyperbolic Knots (5.2-3) Braids(5.4) | Homework 3 | Oct 11 |
| Oct 6 | Jake A. John A. | Almost Alternating Knots (5.5) Bracket and Jones Polynomial(6.1) | ||
| Oct 11 | Whitney B. Ilya V. | Polynomials of Alternating Knots (6.2) Alexander and HOMFLY Polynomials (6.3) | Homework 4 | Oct 18 |
| Oct 18 | Arthur P. Nicole P. | Example Day Links in Graphs (8.1) | No Homework This Week | |
| Oct 20 | John K. John L. | Knots in Graphs (8.2) Polynomials of Graphs (8.3) | ||
| Oct 25 | Jake A. John A. | Example Day Three Manifolds (9.1-9.2 1/2) | Homework 5 | Nov 1 |
| Oct 27 | Whitney B. Ilya V. | Three Manifolds (9.2 1/2 - 9.3) Topology Day | ||
| Nov 1 | Arthur P. Nicole P. | Braid Representations Higher Dimensional Knotting | ||
| Nov 3 | John K. | Matrix Invariants and Homology (see me for materials!) | Homework 6 | Nov 8 |
| Nov 8 | No Class | |||
| Nov 15 | John L. Jake A. | Continue Matrix Invariants | Homework 7 | Nov 15 |
| Nov 17 | John A. Whitney B. | More on Matrix Invariants Introduction to Probability | ||
| Nov 22 | Ilya V. Arthur P. | Conditional Probability Discrete Random Variables and Expected Value | ||
| Nov 29 | Nicole P. John K. | Bernoulli and Binomial Random Variables Poisson Random Variables | ||
| Dec 1 | John L. Jake A. | Other Discrete Distributions Continuous Random Variables | ||
| Dec 6 | John A. Whitney B. | Normal and Exponential Random Variables More Continuous Distributions | ||
| Dec 8 | Matt -- Last Day/Class Party | Whatever he wants |
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