Topological Data Analysis

Spring 2015 Section 0001: 11:00A - 12:15P TTh 221 JH

**Instructor: ** Dr. Isabel K. Darcy,
Department of Mathematics and AMCS,
University of Iowa

**Office:**B1H MLH

**Phone:** 335- 0778

**Email**: **idarcybiomath+3900 AT gmail.com** or isabel-darcy AT uiowa.edu

**Office hours:** Monday 10:30am - 12:00noon, Thursday 12:30pm - 2:00pm, and by appointment.

Midterm this Thursday 3/5 in class.

Problem session Wednesday 3/4 at 1:30pm in 221 MLH

Extra office hours Wednesday 3/4 at 10:30am - 11:40am and 2:30pm - 3:45pm+
in my office
B1H
MLH

+ means that I can stay later if we don't finish by 3:45pm.

Answers to HW 4 and Answers to HW 5

TENTATIVE CLASS SCHEDULE-ALL DATES SUBJECT TO CHANGE (click on date/section for pdf file of corresponding class material):

Note: It helps to see concepts multiple times. Thus week 1 material may be the most challenging. Week 1 will introduce you to topological data analysis using a non-standard example (non-standard examples can be very helpful when modeling data in the real world). Thus week 1 material will only appear on an exam IF also covered in a later week. But having a partial understanding of week 1 will help with later weeks.

**HW 2 (due Thursday Feb 5 beginning of class, 2 points):** Download a data set and answer the following questions:

1.) Where did you get your data?

2.) Briefly describe your data

3.) What format is your data in (eg excel, text, etc.)?

4.) How many data points are in your data set?

5.) Does your data live in a fixed dimension and if so, what is that dimension?

**HW 3 (due Tuesday 3/3, 10 points)**

Do a few Swirl
submodules (1 point each for up to 10 submodules of any combination of
Swirl
courses).

**HW 4 (due Thursday Feb 26 in class, 6 points)**

Calculate the following for all i for the simplicial complex from class:

1.) Find C_i, B_i, Z_i

2.) Find the matrix corresponding to each boundary map (from C_i to
C_{i-1})

3.) Find H_i

**HW 5 (due Tuesday March 3 beginning of class, 24 points)
**
Complete the linked worksheet
(p. 1: 6 pts,
p. 2: 2 pts,
p. 3: 2 pts,
p. 4: 5 pts,
p. 5: 5 pts,
p. 6: 4 pts)

**HW 6 (due Wednesday April 22, 2 points) **

2 well-written pages plus comments from the Writing Center

**HW 7 (due Thursday April 23, 25 points) **

Draft of your project which should be at least 50% done.

**HW 8 (due ?, 2 points) **

Survey

**HW 9 (due Wednesday May 5, 5 points) **

Summary of May 4th presentations.

**HW 10 (due Friday May 7, 5 points) **

Summary of May 6th presentations.

HW 11 (Due Monday May 11, 2 points): Choose 4 lectures from the first 7 weeks of class AND 4 additional lectures from weeks 8 14 that you found most interesting (in terms of what should be on the final exam).

Final exam Wed 5/13/2015 8:00 PM - 8:50 PM in 221 JH

Study midterm, worksheets, homework, and lectures with a focus on ??

Review session Tuesday at ??

Office hours Tuesday at ?? and Wednesday at ??

**Design your own HW (Due 4/30, 30 points)**

One possibility: Attend a conference and present a poster. For example,

- The 1st Annual Meeting of SIAM Central States Section, Missouri S&T Campus, Rolla, Missouri, April 11-12, 2015 (abstracts due March 10)
- Midwest Undergraduate Data Analytics Competition (MUDAC), Department of Mathematics and Statistics at Winona State University, Winona, MN, April 11-12, 2015.
- Midwest Undergraduate Mathematics Symposium (MUMS), Simpson College Mathematics Department, Indianola, Iowa, April 10 - 11, 2015 (Apply for travel funds ASAP, abstracts due March 27).
- Present a poster at the UI Sonia Kovalevsky High School Mathematics Day, April 11th, 2015
- 11th Annual UI Spring Undergraduate Research Festivals (SURF) SURF 2015 - Wednesday, April 8th from 4:30-6:30PM, 2nd Floor Atrium UCC (Deadline to register - March 25th)
- UI College of Engineering Research Open House & Student Recognition Luncheon April 16 & 17, 2015 (Deadline for submission: February 28, 2015)