(499)Summary of week eight and nine

Hi all,

By now, you have seen all the potential topics, here they are:

Dr. Zhu: capstone-projects_zhu

Dr. Cook: capstone-projects_cook

Dr. Simic-Muller: capstone-projects_simicmuller

Dr. Edgar: capstone_edgar

Dr. Stuart: capstone_stuart

Dr. An: capstone_an

Dr. Benkhalti: capstone-topics_benkhalti

Dr. Jones: capstone_jones

Dr. Heath: capstone_heath

Think about what you might be interested in, and go ask for more details. Your proposal of the capstone project is due Dec, 9, last day of class.

On Nov 16, we will have peer presentations, please expect to stay for 30 minutes longer or so, as this will be the only time we have to finish the presentation. You should grade for 3 or 4 talks, and grading sheet will be handed out to you before the presentation. You will be grading for randomly chosen students.

If you like to revise any of your previous work, please let me know. I will be happy to meet you and help you with it. The deadline for revision of your previous work is Nov 30.

Last and this week, our seminars are more career oriented, as  we had alumni panel and career connection presentation. Start making your resume in LaTeX, and the resume is due Nov 23rd.


(499) Summary of Week Six/Seven

Hi all,

Last week, Dr. Zhu, Dr. Cook and Dr. Simic-Muller presented their potential capstone topics. Please look at the topics and think about them. They might not look directly related to your topic, but you might still need to use related content in your research. Here are the topics:

Dr. Zhu’s topic: capstone-projects_zhu

Dr. Cook’s topic: capstone-projects_cook

Dr. Simic-Muller’s topic: capstone-projects_simicmuller

We did more peer review of your paper, and this should be the last paper peer review.

This week, our speaker is Dr. Susan Massey.  Please write a one page report on the talk, following our standard format. If you like to know more about her research, please use our library resources.

For now, your assignments are:

  1. Write a 5~10 page report on “Hair and Beyond”. For this paper, please focus on the mathematical content. Use the Breaks as your hints for theorems and proof guides. You have all taken 317, so I expect to see some careful proofs in your paper.
  2. On the 26th, you are giving a beamer talk of 5~10 minutes. It is always better to prepare more than what you might have the time to talk about. If you want to do practice talks with me, let me know. I am here on Monday and Wednesday (not Friday, Oct 21, apparently we have a mid-semester break! )

On the 26th, we have more faculty members presenting their topics. Please be in class on time.

(499) Summary of Week Five

This week we had our first seminar. Our speaker is Donsub Rim, and the paper of the talk can be found here.  You should skim through the paper even if you don’t understand most of it, as it is of the format and length we aim for. If you are interested in writing your capstone on applied mathematics, or if you like to implement graphs in your capstone paper, this paper is a good example of such content. Please write a report on the talk, with comments on the talk: what are the things you liked about the talk, and would like to use when you give the capstone talk, etc.

On Oct 12, we will be peer reviewing your second reading report and summing up the comments I got from your first peer review. Two major things I noticed: correct format and mathematical content is crucial for you to receive a high review. So please keep editing your second paper aiming towards these goals.

I am not on campus on Friday, Oct 14. Email me if you have any questions or would like to meet during other times.

(499)Summary of Week Four

Hi all,

This week in class, we did anonymous peer reviews of your report on Fermat’s last theorem. Here are some of the things we learned:

Tips to make a paper look nice:

  1. Use the right format.
  2. Have a personalized title.
  3. Use Theorem (and other) packages in your LaTex file to make it look more clear.
  4. A longer paper is better than a short one.
  5. Have a clear distinction between Abstract and Introduction.


Things we want to avoid:

  1. Too much background and not enough content.
  2. Only one paragraph, no clear structure.
  3. Too much computation or program, but no explanation.
  4. Not putting effort in the work.

What if your work has a large amount of computation or programming? Sum up your computation briefly, or write a pseudo-code in the main body of the paper, then attach the big computation or your program in the appendix.

Your assignment this week is to keep working on your report of paper of your choice. Please try to revise your paper based on the feedback of peer review. We will review  these paper in two weeks.

In the meantime, please start making two beamer documents, both your Fermat’s last theorem beamer and your paper beamer. They are intended for 5 minute talks.

Next week, we are having our first seminar. The talk will be on Inverse problems, and you might not understand all the details of the talk. Try to organize the information such as important results, applications, motivation of the problem, some reference and things you don’t understand but would like to know more. By next Friday, I expect a brief report on the talk in the standard format (abstract, intro, etc.).

Finally,  here are some papers with titles that might be good or bad, you can be the judge.

This one certainly grabbed my eyes; this title only Grothendieck can get away with (also notice he was saying “I” instead of “we” the whole paper. But again, this is Grothendieck, and we are not him); I am not sure if I recommend this title; and you probably want to be more specific than this one.



(499)Summary of Week Two

Hi all,

This week we are setting up your hardwares for the course. We will use Latex as our writing software and Sage for file sharing and collaborating.

Please make sure to check out the Latex beamer Dr.Edgar created. You can also find useful links about Latex here.

For Sage, please make sure to create an account on Sagemathcloud, create a project for your capstone class, and add me as your collaborator. From now on, you can hand in all your assignments directly by putting files in your project. I expect to see your autobiography by this Friday written in Latex if you have not handed to me yet in class.

I handed out some material on Fermat’s last theorem, and this is your first project of read-write-talk.

Your assignment this week is : write a one page report on the reading material in Latex, and share it with me on Sage. It is due on Wednesday, 9/21. 

In the meantime, check out the videos on Numberphile on Fermat’s last theorem, as well as some other videos on cool math facts/theorems/unsolved problems. You might find some inspiration for your capstone project. One cool video I really enjoyed is this.

Summary of Week One

Hi all,

Hope your first week is starting smoothly!

Here is what we did on the first day:

We very briefly went over the syllabus and calendar, and we talked about what the capstone is all about and what you should expect from it, here is a beamer on the topic: beamer (modified from Prof. Simic-Muller’s beamer last year). Let me know if you want the .tex file of this file.

Your assignment this week is to write a math autobiography and hand it in to me by the end of next class. I expect to have a general idea of your math background after reading your autobiography: what classes did you like, what you still like to learn, what you plan to do after graduate, what might be some of the topics you like to work on, etc.

If you already know LaTeX, then type it up in LaTeX; if not, that’s OK, type it up in Word, or other softwares.

We agreed on optional office hours on Fridays: 13.45-15.45, but still let me know if you like to work together during different hours.