(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.




(115)Review problems

Hi all,

we have our first test on Thursday, Oct 6. The following is a set of review problems that is never due. But you can hand them in for extra credits.

1.2: 6,7,11,18,23,24,31,33,38,43

1.3: 1,3,7,11,22,24,43

2.1: 13,15,19,25,29(Hint: c=a\pi r)

2.2: 5,6,15,31,41

2.3: 15,56

3.1: 2,4,5,14,20,22,26,28,46,54,59,60,63,65(drawing a picture might help)




(152)Homework 4(Due 10/6)

Hi all,

Our first test is on Oct 4, Tuesday. Here are some problems for you to review for the content:

4.9: 8,12,17

5.1: 23,25,26(a),29(a)

5.2: 20,30,32(do not evaluate),34,38

5.3: 10,14,18,33(Substitution would be easier),40

5.4: 15,16,33

5.5: 15,17,25,40,48

7.1: 1,2,5,7(split the integral into two),20

(115) Summary of lines

Hi all,

Last week we spent some time on lines, and with all the different forms you learned, I think it might be a good time to sum them up a little.

To find a line, you need two pieces of information: the direction of the line, and the position of the line, it doesn’t matter how you get these information. Like making a burger, you need some bread and some patty, it doesn’t matter where you buy the bread and patty.

The position of a line is always given by a point on the line. It might be the y-intercept, or just any generic point (x_1,y_1) on the line.

The direction of a line is given by slope (or undefined, in case the line is vertical). It might be directly given to you, and there are many ways of grabbing this information:

  1. Any two points (x_1,y_1) and (x_2,y_2) on the line gives the slope by \frac{y_2-y_1}{x_2-x_1}
  2. The line is parallel to a line you already know. For example, if your line is parallel to 3x+2y=5, you know your line has slope -\frac{3}{2}, as parallel lines have the same slope.
  3. The line is perpendicular to a line you already know. For example, if your line is perpendicular to 3x+2y=5, you know your line has slope \frac{2}{3}, as perpendicular lines have slopes that multiple to be -1.

(499)Summary of Week Three

Hi all,

I hope you all had a fruitful week. This week we talked about how to use online sources to find articles and books you need for your capstone project, and how to prevent plagiarism.

Do take advantage of the Interlibrary loan system, and don’t be shy if you need anything. If you are not sure whether you are plagiarizing, look at the article I gave you, use that as a check list.

You assignment this week is to search for an article online, and write a one-page report on it. Please use the template I gave you, or any template that has the following components: abstract, introduction, main body, conclusion and reference. Get used to the format, and this will make your life a lot easier next semester.

If you didn’t have all the components in your report on Fermat’s last theorem, please go back and add the missing part(s) in your report. I will be reading your reports over the weekend, and we will peer review your reports in our class next Wednesday anonymously. Please bring your peer review for paper sheet: peer_review_paper. And when you review, please be kind and constructive.

Finally, some of you told me some stories in Fermat’s last theorem were really sad, so here is a happy story related to the theorem.

Alright, that’s it for now. Let me know if you have any questions!

(152)Homework 3(Due 9/29)

Hi all,

Starting this Thursday, we are moving on to integration techniques, so this week’s homework is largely for reviews.

4.9: 32,36,62

5.1: 22

5.2: 19,22(Only write down the Riemann sum, do not evaluate),33

5.3: 9,12,13

5.4: 32,35,44 (be careful with absolute values),52

5.5: 1-6,7,9

(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.