Fall 2013      MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology

Instructor:  Dr. Isabel K. Darcy
Department of Mathematics
University of Iowa
Office:B1H MLH
Phone: 335- 0778
Email: idarcybiomath AT gmail.com
Course URL:http://homepage.math.uiowa.edu/~idarcy/AppliedTopology.html
DEO Contact Information: Dan Anderson, 14 MLH, dan-anderson@uiowa.edu

To join a live lecture, e-mail me (idarcybiomath AT gmail.com) for the URL. If you are in Iowa City, we meet in 212 CEF.

The live lecture part of this course will meet MWF 16:30 - 17:20 GMT (11:30am - 12:20pm CDT, Iowa time). The live lectures will be recorded.

Goal: To prepare students and other researchers for the IMA Thematic Year on Scientific and Engineering Applications of Algebraic Topology, but all interested participants are welcome to register for free or for official credit. Workshop attendance is not required. Students, if they so choose, will also have the opportunity to analyze real data in collaboration with those who generated the data, with the potential to publish their results. Both pure and applied students/researchers are welcome to take this course. A variety of backgrounds often results in greater depth of analysis when analyzing real world problems. This course will be individualized to meet the interests and background of each participant.

NOTE: You can take this ONLINE course for FREE or you can register via a big ten university. See REGISTER for more information.

Office hours: MWF 15:40 - 16:20 GMT (10:40 - 11:20 CDT), M 2:00 - 3:00 am GMT (9pm - 10pm CDT) and by appointment. Office hours will be held in our online classroom (same URL for entering class). I am also available via google+, skype, and in person at UI.

Course Description: 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. We will begin this course with an exploration of Topological Data Analysis. Participants will have the opportunity, if they so choose, to analyze real data in collaboration with those who generated the data, with the goal of publishing at least one article on your results. If you have data you would like analysed, please let me know. In October we will focus on Modern Applications of Homology and Cohomology. We will cover necessary mathematical background for this workshop. In November, we will focus on Topological Structures in Computational Biology and will explore the world of DNA, RNA, and proteins.

Target Audience: Anyone interested in topological data analysis including graduate students, faculty, industrial researchers in bioinformatics, biology, business, computer science, cosmology, engineering, imaging, mathematics, neurology, physics, statistics, etc.

Prerequisite: This course assumes scientific maturity. Due to the applied nature of this course, we welcome a variety of scientific backgrounds and interests. A variety of backgrounds often results in greater depth of analysis when analyzing real world problems. Group projects will be encouraged, but not required. While one person might want to focus on mathematical details, another person might want to focus on a particular application. Those without a background in algebraic topology can learn the basics via a few short online videos.

Advantanges/disadvantages of taking this course for official credit: I expect all material including lectures will be available to all whether or not one takes it for official credit. Only students officially enrolled in this course will have their work graded, but I hope to provide feedback to anyone who requests it, as much as time allows; but if there are time constraints, my priority must be given to students officially enrolled in this course. See Grading system for how grading will fit the individual needs and interests of those officially enrolled.
NOTE: The level of this class will be aimed at students officially enrolled in this class. The participation of anyone interested in this subject matter is very welcome (and beneficial to all) whether or not officially enrolled. However, since some students will be taking this course for official credit, I need to make sure that this course meets their needs. Hence I may have a few meetings that will include only officially enrolled students plus possibly others who are "sponsored" by an officially enrolled student. It is likely that students will form study groups and including all/most students from these study groups could be beneficial to students who are officially enrolled.

Why take a course in applied algebraic topology:

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

For those interested in teaching: You will be able to answer the question, "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).

Format of course:

We will have a combination of live online introductory lectures, more specialized lectures, and discussion periods. Participation during these lectures is strongly encouraged. We will also have a few pre-recorded short supplementary lectures. Most lectures will have an online quiz focusing on the basics. This includes both live online lectures as well as pre-recorded short supplementary lectures. Homework problems will be posted online. Participants will also post their homework answers online for community grading (see below). Students can choose to work in small groups on a class project analyzing real data. This course will be individualized to meet the interests and background of each participant. Thus grading for students officially enrolled will be based on points earned and not percentage. While one student may earn most of their points via HW and quizzes, another person may choose to focus on project(s). Students are encouraged to collaborate on HW and project(s).

The goal of this course is to prepare students for the IMA Thematic Year on Scientific and Engineering Applications of Algebraic Topology. Thus the format of this course will vary during IMA workshops.

During non-workshop periods: We will meet 2.5 hours each week as a group (take the survey to determine time). We will have a combination of introductory lectures, more specialized lectures, and discussion periods.

Note: To participate in discussions, students will need headphones (or a high quality echo canceling mic such as the Phoenix Audio DUET MT202-PCO USB Speakerphone).

In addition to meetings by appointment, I will have 3 hours per week of online office hours. In addition, I am normally signed into skype and gchat/gvideo/google+, so students who use skype or gmail can contact me whenever I am online.

During IMA workshop periods: I will hold office hours/discussion periods both at the IMA as well as online. You should attend as many workshops as possible, but workshop attendance is not required.

Students attending IMA workshops should focus on actively participating in these workshops including interacting with a variety of participants. I will arrange group meals for students to interact with speakers as well as other participants. You can register and/or apply for funding for the following workshops at the URLs below:

Students who are unable to attend a workshop should view workshop videos. The number of videos viewed will depend on your interests. You can view these videos either

  1. During the scheduled talk, you can listen to the lectures live by going to the URL: http://ima.umn.edu/videos/ee3180.html
  2. After the recording has been posted. IMA videos are posted at the URL: http://ima.umn.edu/videos/
    Most recordings are posted within 24 hours. Some are even posted the same day.

Click on the talk title under the workshop schedule for abstracts and talk material. IMA workshop schedules during the Fall 2013 semester:

Grading system for students officially enrolled in this course:

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, and project(s). While one student may earn most of their points via HW and quizzes, another person may choose to focus on project(s). Participants are encouraged to collaborate on HW and project(s).

Quizzes (approximately 200 points possible): Most lectures will have a short online quiz associated to them. This includes both live online lectures as well as pre-recorded short supplementary lectures. Quizzes will focus on the basics and important points. While I recommend that you take a quiz after each lecture or on a weekly basis, the due date will be the Sunday before the start of the associated IMA workshop (due dates will be clearly indicated on ICON). A few quizzes will have a due date before a particular lecture. 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.

Homework (approximately 200 points possible): HW problems will be posted on the web. Students will also be expected to post their answers on the web for community grading. You can earn HW points by doing HW, helping someone else with their HW, or validating their HW (more info will be posted later on the HW wiki page).

Project: I would expect a standard class project would earn 300 points, but a truely exceptional project could earn 600 points (but only 400 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. Participants will have the opportunity to analyze real data in collaboration with those who generated the data, with the goal of publishing at least one article on your results. Less rigorous projects are also possible. For more information on the project, click here.

Please let me know if you would like to earn points using other methods (e.g. creating software, writing teaching material for undergraduate or graduate related courses, presenting posters, etc.). Writing software (or teaching material or etc) can also be suffient to earn an A in this course, regardless of HW/quiz grades. I am happy to personalize this course to meet each participant's needs.

The following grades can be earned via the following points. For those officially registered for this course, I will keep you informed if you are not on track to earn an A in this course. Collaboration is encouraged on everything except quizzes.

If you register for 2 units:

If you register for 3 units: 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.

Register:

How to officially register for this course:

If you are a University of Iowa student: Register as you would any grad course.

If you are a student at a Big Ten University: You can register through your own university via the Committee on Institutional Cooperation (CIC). You can apply through your university to become a CIC Traveling Scholar. A list of big ten universities can be found at list of CIC Member Universities

All others: Go to URL http://www.continuetolearn.uiowa.edu/readytoenroll/index.asp

How to register for free version: Fill out the survey or e-mail me (idarcybiomath AT gmail DOT com).

Note: To participate in discussions, students will need headphones (or a high quality echo canceling mic such as the Phoenix Audio DUET MT202-PCO USB Speakerphone).

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