Dr. Mann's M367L, Spring 2010
Applied Topology
57090


Lectures     MWF 10:00 - 11:00 am in RLM 5.120
 
Lecturer                   Jennifer K. Mann, Ph.D.
Office: RLM 10.128
Office Hours: MF 11-12, W 12-1
Email: jmann@math.utexas.edu
Phone: 512-471-1140
Website: http://www.ma.utexas.edu/users/jmann/
 
Text               Students will be given several articles and directed to web resources. Additionally, some reading assignments will require students to use the books held in the PMA reserves for this course.

Honor Code          The core values of the University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the University is expected to uphold these values through integrity, honesty, trust, fairness, and respect toward peers and community.

Grading      
A (100-90), B (89-80), C (79-70), D (69-60), F (59-0) (no plus/minus grades)
40% Class Participation (attendance is mandatory)
25% Quizzes/Homework
35% Project/Presentation

Course Website       http://www.ma.utexas.edu/users/jmann/M367L.html
 
Course Description
Topology has a variety of scientific applications. We will study these applications in the following contexts: the human brain, RNA, proteins, DNA computing, and DNA topology. Under DNA topology I plan to discuss supercoiling, catenation, knotting, tangle theory, topoisomerases, replication, recombination, and difference topology. The intent of this course is to bring together mathematicians, biologists, biophysicists, biochemists, and biomedical engineers. Thus, this course will be an introduction to interdisciplinary research at the interface of mathematics and biology. We will cover in class both the mathematics used in the applications and any necessary biological background.

Prerequisite
Interest in biological applications of mathematics

Blackboard
Blackboard is used heavily in this course. Assignments, grades, course documents, and web resources are provided to the students via Blackboard.

Services available to students
The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-6441 TTY. At the beginning of the semester, please notify the instructor of your specific needs.

Topics and Important Dates
January
20 First class
22 Last day of the official add/drop period; DNA Structure
25 DNA Structure
27 DNA Topology: Supercoils, Catenanes, Knots
29 DNA Topology; Quiz 1
February
1 Lk = Tw + Wr
3 Last add day; DNA Replication
5 Biochemical Topology; Quiz 2
8 Topoisomerases, Supercoiling, Intercalators, Gyrase
10 Topo II, Topo IV, Reverse Gyrase, Topo V, Topo VI
12 Topoisomerases & Transcription, Topoisomerase Animations; Quiz 3
15 Last free Q drop; Topo II Structure
17 DNA Recombination: General Recombination
19 Site-specific Recombination; Quiz 4
22 Site-specific Recombination: Int
24 Site-specific Recombination: Hin
26 Genome Comparisions; DNA Extraction
March
1 Consequences of DNA Knotting; Quiz 5 Due
3 Introduction to Knot Theory: Part I
5 Introduction to Knot Theory: Part II
8 Polynomial Knot Invariants: Alexander-Conway Polynomials
10 Alexander-Conway Polynomials Continued; Jones Polynomial; Quiz 6 Due
12 Discussion of Project Guidelines and Expectations; HOMFLY Polynomial
15 - 20 Spring Break
22 Knot Theory Software & Websites Introduction
24 UT Counseling; Bacteriophage Introduction
26 Joe Ojile: Viral Molecular Motor; Mathematica Knot Theory Package; Quiz 7 Due
29 Chris Burchsted: Graphs & RNA Topologies; Mathematica: LinKnot
31 KnotPlot
April
2 KnotPlot
5 Mathematical Models of Topoisomerase; Quiz 7 Solutions Presented
7 Lucas Bertolini: Synthetic DNA Structures; Quiz 6 Solutions Presented
9 Danaan Thome: Tangled in Kinetoplasts; Mathematical Models of Topoisomerase Continued
12 Taylor Smith: DNA Origami; Tying a Molecular Knot with Optical Tweezers; Papers Due
14 Quiz 8 Due; In-class Quiz 9; Chalkboard Proof "If L_1=L_2, then Lk(L_1)=Lk(L_2)."
16 Stuart Sevier: Topological Quantum Computing
19 Becky Scofield: Topology & the Heart; Introduction to Tangles
21 Nancy Okeudo: A Tubular-Shaped DNA Model; Introduction to Tangles Contd.
23 Lee McCuller: Knot Physics of Vibrated Granular Chains; Difference Topology
26 Jessica Bright: Long Tangled Filaments; Difference Topology Contd.
28 Quiz 10 Due; RNA Geometry & Topology
30 Mathematical Classifications of RNA Structures
29th Last academic drop
May
3 Protein Geometry & Topology
5 Daniel Davee: Topology & Geometry of Spacetime; Mitotic Chromosomes
7 Last class day; Quiz 11 Due; Brain Topology


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