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 or isabel-darcy AT
Course URL: Home/Schedule
Course wiki: wiki
DEO Contact Information: Dan Anderson, 14 MLH,

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

Course Description: Research experience; students study an elementary topic of active research, then work either individually or in groups under faculty supervision. The Spring 2015 course will focus on topological data analysis. Topology has many applications. It allows one to recognize shapes, but allows for distortions. Hence topology has been used to study the shape of noisy data. At minimum persistent homology can be used to cluster data when it is unclear what threshold should be used for determining connections such as when constructing a brain network. But holes in data can have significant meaning. For course schedule, see Schedule

Prerequisite: Linear algebra (may be taken concurrently with consent of instructor).

Objectives and Goals of the Course: To learn introductory research skills. This course will be individualized to meet the interests and background of each participant.

Why take a course in applied algebraic topology:

For those interested in pure mathematics, statistics, computer science: We need researchers with expertise in a variety of areas of mathematics. There are many interdisciplinary researchers (including me) who enjoy collaborating with others in order to apply deeper analysis to real life applications.

For those interested in teaching: You will be able to answer the question, "What is topology and how can topology be applied to real world problems?" Moreover, applied topology has been used to introduce students to abstract mathematics while applying this mathematics to real world problems. There is a lot of data out there for researchers at all levels, including undergraduates, to analyze.

For those interested in applications: That is what this course is about (and you will get to analyze real data).

Texts: None

Grading system:

In order to meet the interests and background of each participant, grades will be based on a point system as opposed to percentages. Each point you earn will be added to your grade You can earn points via HW, quizzes, exams, and project(s).

Quizzes and Homework (approximately 150 points possible): Many lectures will have a short online quiz associated to them. Quizzes will focus on the basics and important points. Note, you do not need to take and/or pass all quizzes. Each point you earn on a quiz will be added to your point grade.

Midterm: 100 points. Tentative date: Thursday Feb 26th.

Pseudo-Optional Final Exam: 50 points. Note: If you have sufficient points for your desired grade, you do not need to take the final exam. However, do not make any assumptions regarding the points you expect to earn.

Project: Points can be earned throughout the semester. I would expect a standard excellent class project would earn 300 points total, but a truely exceptional project could earn 600 points (but only 500 are needed for an A). Writing an article that is almost/somewhat ready for submitting for publication to a good journal will be sufficient for earning an A in this class, regardless of HW and quiz grade. Most, if not all, projects will focus on analyzing data as described on the project webpage; but other ideas are welcome.

Please let me know if you would like to earn points using other methods (e.g. creating software, writing teaching material, presenting posters, etc.).

The following grades can be earned via the following combination of points. Collaboration is encouraged on everything except quizzes and exams.

Standard grading system (see note below regarding class attendance) :

NOTE regarding class attendance: Class attendance is required, but if you need to miss a class, fill out the UI absence form and e-mail it to me. You may be required to make up some of the material missed during class, but I expect your grade will not be penalized in most cases. Substitutions may also be possible for more advanced students.

NOTE: You may substitute your final exam grade for your midterm grade.

This course will be individualized to meet the interests and background of each participant, so if you would like to propose your own individualized grading system, please let me know.

GRADING All work must be shown in order to receive credit.  If no work is shown, you may receive zero credit even if your answer is correct.

Locations of exams TBA.  You are required to bring identification to all exams.   Calculators may NOT be allowed.  You are required to pick up your exams and keep them until the end of the semester.  Exams will be cumulative.

If there is a mistake in grading, you must report this mistake within one week from when the exam, homework, etc. has been handed back to the class (whether or not you picked up your exam, homework, etc).

Attendance and absences: Your attendance at each scheduled class meeting is expected.  You are  responsible for material covered in class and announcements made during class; these may include changes in the syllabus.

Student Collaboration: You may collaborate with other students on homework and projects;   however, each individual student is responsible for turning in your own homework in your own words.  Copying is not collaboration and will be prosecuted under scholastic dishonesty.  Any significant collaboration should be acknowledged.

The University policies on scholastic dishonesty will be strictly enforced.

Resources for Students:

Students may find the Writing Center and the Speaking Center very useful for this course:

From Writing Center website: Suggestions and feedback on all kinds of writing, from course papers to creative pieces and multimedia projects.

You an obtain feedback via individual appointments, online submissions or weekly appointments (for weekly appointments, space is limited so sign up NOW if you are interested).

From Speaking Center website: We work with a range of students from many disciplines on such issues as: effective participation in class discussions, crafting and delivering oral presentations, understanding unfamiliar cultural references, interview skills, creative performances, and speech anxiety.

The College of Liberal Arts and Sciences Policies and Procedures