SPRING 2008

Math 414-01/714-01 (flier)::

Studying DNA Topology with Mathematical and computational
methods

T-Th 2:10-3:25, Room 211 Thornton Hall

Instructor: Mariel Vazquez; mariel@math.sfsu.edu

Office Hours: TH 3:30-4:30, or by appointment

Description: Students from mathematics, computer science and biology will be introduced to mathematical and computational techniques used to analyze DNA structure. Strong interaction between math and biology is emphasized. 414 and 714 are paired courses. The expectations for graduate students will be higher than for undergraduates, and evaluations will be done accordingly.

Prerequisite and requirements. Math 228 (Calculus III) with a grade of C or better. Math 325 (Linear Algebra) or instructor's consent.

Number of Units: 3 units

 Syllabus (pdf file)

Materials:

  Required Text: DNA Topology by Bates and Maxwell

  Lectures

  Lecture notes will be posted here after each class where a powerpoint presentation is used.

Lecture 1 (January 24, 2008)

Lecture 2 (January 29, 2008)

Lecture 3 (January 31, 2008)

Lecture 4 (February 12, 2008)

Lecture 4 part II  (February 12-14, 2008)

Lectures 5 and 6: On February 14th and 19th there was an introduction to Matlab and exercices worked in class. This is not included in a ppt presentation

Lecture 7  (February 21, 2008)

Lectures 8-9  (February 26-28, 2008)

Invited lecturer Rob Scharein. Introduction to Knot Theory and to KnotPlot  (March 4th, 2008)

March 6th, 2008  First Midterm

Lectures 10-11  (March 11-13, 2008) 

Lectures 12-13  (March 18-20, 2008); this is to be complemented with your lecture notes.

March 25-27: Spring Break, no lectures

Lecture 14 (April 1st, 2008); research talk on DNA packing in bacteriophages by Professor Arsuaga.

Lectures 15-16 (April 3 and 8, 2008);  methods for computing the writhe of a polygonal chain, end of bacteriophage talk. (Professor Arsuaga)

Lecture 17 (April 10th, 2008); Visit to Professor Pasion's laboratory.

Lecture 18 (April 15th, 2008); Directional twist, directional writhe, Lk-Tw_Wr (White's theorem, Twist number

Lecture 19 (April 17th, 2008); Another formalist for Tw and Wr. Twist number calculations.

Lecture 20 (April 22nd, 2008); Introduction to Knot Theory (from hand-out); knot definition, knot equivalence, elementary moves, reidemeister moves.

Lecture 21 (April 24th, 2008); Knot Theory ; review of knots and links, knot equivalence, elementary moves, connected sum.

Lecture 22 (April 29th, 2008); Knot Theory; alternating knots, properties of the connected sum, Reidemeister moves and theorem.

Lecture 23 (May 1st, 2008); Knot Theory; Knot invariants, gauss codes

May 6th, second midterm (Supercoiling and Knotting)

Lecture 24 (May 8th, 2008); Enzymes that change the topology of DNA.

  There will be two midterms and one final project. Grades will be computed as follows: 20% homework, 40% midterms, 40% final project

  Homework

Homework 1 (Due February 5, 2008)

Questions for Homework are in the slides for Lecture 4 and Lecture 4 part II (due February 19, 2008)

Homework 3 (Due February 28, 2008)

Homework 4 (Due March 13, 2008)

Homework 5 (Due April 3, 2008)

Homework 6 (Due April 24, 2008)

Homework 7 (Due May, 2008)