MATH:3900 (22M:096) Introduction to Mathematics Research:

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.

Click here for rest of syllabus including grading scheme

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.

Tentative ScheduleHW/Announcements
Week 1
1/20 Introduction to Topological Data Analysis: Grid cells
Icon Quiz 1 (Due 1/21)
HW 1 (Due 1/28)
1/22 Discuss Preparatory Lecture 1: The Euler characteristic (20:32 min)
FY: Mobius band, Klein bottle
Jeff Weeks: "Shape of Space" book, 2013 video (60 min), software, games
The Geometry Center Shape of Space Video (11 min)
FYI: Grid cells - raw data
Week 2
1/27 Discuss Preparatory Lecture 2: Addition and Free Abelian Groups (17:53 min),  Worksheet 1,  answers
Intro to Data Analysis slides 		Icon Quiz 2 (Due 1/26)
Icon Quiz 3 (Due 1/28)
1/29 Discuss Preparatory Lecture 3: Modular Arithmetic (9:40 min)  Worksheet 2,  
Installing R and Rstudio, tips, pptx
Start discussing On the Local Behavior of Spaces of Natural Images, Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, Afra Zomorodian, International Journal of Computer Vision January 2008, Volume 76, Issue 1, pp 1-12.
slides
FYI: Van Hateren's Natural Image Database
Topology and data, G Carlsson (2009), section 2.4, p. 269 - 278
Week 3
2/3 Discuss Preparatory Lecture 4: Addition and Free Vector Spaces (21:26 min)
 Worksheet 3, Continue image analysis discussion 		Icon Quiz 4 (Due 2/2)
Icon Quiz 5 (Due 2/4)
HW 2 (Due 2/4)
2/5 Discuss Preparatory Lecture 5: Triangulations and Simplicial Complexes (28:19 min)
 Worksheet 4, Continue image analysis discussion
Week 4
2/10 Discuss Preparatory Lecture 6: Creating a Simplicial Complex from Data (28:15 min), Intro to Swirl, Equivalence relations and partitions, worksheet 5 Icon Quiz 6 (Due 2/9)
2/12
Week 5
2/17 Files for R intro 2 Intro draft including 2, 8, 10 (Due 2/17)
2/19 Homology example
Week 6
2/24 Create Your Own Homology HW 4 (Due 2/26)
2/26 Barcodes (pptx), pptx with notes
Week 7
3/3 Review HW 5 (Due 3/3)
3/5 Midterm (Answers)
Week 8
3/10 Persistence Diagrams, circle.R
3/12 circle2.R
*****Spring Break****
Week 9
3/24 Review/ethics
3/26
Week 10
3/31 Mapper slides, Python mapper Intro draft including 3, 8, 10 and commented R code (Due 3/31)
4/2 mapper 2
Week 11
4/7 Topology of Viral Evolution 2 well-written pages plus comments from the Writing Center (due 4/9)
4/9 Zig-zag persistence
Week 12
4/14 Finding generators, clustering, witness complexes
4/16 Lab
Week 13
4/21 slides HW 6: 2 well-written pages plus comments from the Writing Center (due 4/22)
HW 7 (due 4/23)
Draft of your project which should be at least 50% done.
4/23 slides
Week 14
4/28 slides
4/30 slides
Week 15
5/4 Student presentations HW 9 (due 5/5) Summarize May 4th presentations
HW 10 (due 5/7) Summarize May 6th presentations
5/6 Student presentations
Final Exam Week
5/13 Final exam Wed 5/13/2015 8:00 PM - 8:50 PM in 221 JH

Homework

HW 1 (due Tuesday 3/3, 2 points): Add your info (picture, name, interests) to our course wiki class list

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

Answers to HW 4

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)

Answers to HW 5

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,