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

**Course URL:** Home/Schedule

**Course wiki:** wiki

**DEO Contact Information:**
Dan Anderson, 14 MLH, dan-anderson@uiowa.edu

**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

**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) :

- A: 500 points or more + at least 95% class attendance + 80% average on both midterm and quizzes
- A-: 485 - 499 points + at least 95% class attendance + 75% average on both midterm and quizzes
- B+: 475 - 484 points + at least 93% class attendance + 70% average on both midterm and quizzes
- B: 440 - 474 points + at least 93% class attendance + 65% average on midterm and quizzes
- B-: 425 - 439 points + at least 93% class attendance + 60% average on midterm and quizzes
- C: 375 - 424 points + at least 85% class attendance + 50% average on midterm and quizzes
- D: 350 - 375 points + at least 75% class attendance + 40% average on midterm and quizzes
- D-: 330 - 349 points + at least 75% class attendance + 40% average on midterm and quizzes

**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.

**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.