Math 499. Senior Seminar: Great Theorems of Mathematics
MWF 9:00 - 9:50 am in Young Hall 207
Office Hours: MW between 11 to 12:00 pm, and W from 2:30 to 3:30pm. You can also arrange a meeting by appointment.
Young Hall 105
Phone Ext.: #6187
All homework assignments and their due dates are now listed in the homework page.
No class on September 16.
This New Yorker article written by Steven Strogatz gives a very nice background (and explanation) on Einstein's proof of the
Pythagorean theorem (proof 5 in class). Strogatz wrote a wonderful series of articles in the New York Times explaining math to a general audience. It is titled
Elements of Math.
I made some changes to the syllabus.
Schedule for the Presentations.
The main book we'll use is:
Journey through Genius by William Dunham.
Goals of the Class
The goals of this class are the following:
- Showcase the connections between different areas of mathematics.
- Prepare you to know how to give a class-style lecture.
- Prepare you to write mathematics professionally (using LaTeX).
- Prepare you to give a presentation in Beamer (a package in LaTeX).
- Connect with the recreational side of mathematics.
- Be able to read mathematical papers of a level just below research level.
The course grade will be based on:
The class will form into groups of 2 (or 3 if necessary). The groups will be assigned two chapters from the book Journey through Genius and
they will present each chapter to the class over two class periods (two class periods per chapter). The students not presenting will have to attend and they will provide
feedback to the presenters by the next class session. I will also get a copy of this feedback.
For the second presentation, students should go beyond the text and be ready for questions that can come up for a person reading the text. For example,
some questions from Chapter 2 which are relevant are:
The grade for an individual with regard to the class presentation will depend on the presentations (25%) and the feedback they
provide to the other teams (10%).
- The chapter talks about the "collapsible" compass and how Euclid proved that you did not need to assume that you could fix a compass to a length to
use it elsewhere. How does Euclid's proof work (note this proof is not in the book, you'd have to find it elsewhere or figure it out on your own).
- The book mentions proposition I.5 is known as the "bridge of fools" because the diagram vaguely resembles a bridge and many people have trouble
understanding the proof. What was the diagram? What is the proof?
Schedule for the Presentations.
The presentations will be two-a-day from October 3 to October 14 in the same order as the team presentations. The schedule is here.
- Each student will find an article they like from the series of anthologies The best writing on mathematics edited by Mircea Pitici. The whole
series is on reserve. The 2011 edition is also available as an ebook, which can make things easier for the student.
- The student will send their top three picks to me via email by September 25. After I collect all picks, I will assign a student with an article they ranked.
- The student will then write a Beamer presentation and give a 15 minute presentation about the article in class. A Beamer presentation is like
PowerPoint but written with LaTeX. It has the advantage of making mathematical formulas prettier.
- Every student will give feedback on the presentations of the other students.
The grade for an individual with regard to the Beamer presentation will depend on the presentation itself (15%) and the feedback they provide to the other
students (5%). Note that this presentation is not a team presentation. Using Beamer correctly will be part of the grade.
For the paper, you have to find a subject on your own and write about it. The assignment has the following rules:
Your assignment also includes reading the drafts of three other students and give them feedback so that they can improve their final draft.
The comments you write should be written seriously and be helpful.
- First, pick a mathematical subject. It can be a cool puzzle, an interesting game (that involves thinking), an application of mathematics to
some field (maybe an application of math to sports) or an exciting theorem.
- Once you pick your subject, find three references to give you background on that subject.
- Send the subject and the three references to my email by November 1st . I will then approve the topic, if it is suitable.
If not, you have to find one right away. I suggest you have three subjects in case I don't approve one of them.
- Once you have my approval, write a paper talking about the subject. Your paper should be between 3 and 5 pages long (double-spaced with 12
point font). You can use the "Best Writing In Mathematics" articles as examples of how to write good math articles.
You are welcome to include pictures and you should include a bibliography. The first draft is due on November 14.
- The paper has to be written in LaTeX. You will send me the .tex file and you will print 4 copies of your pdf (1 for me and 3 for 3 students).
- After getting feedback from your peers (by November 21), you will write a final draft and turn it in on December 7.
The grade for an individual with regard to the paper will depend on the first draft (10%), the final draft (10%) and the feedback they provide to the other
students (5%). The aesthetic presentation of the paper will be weighed in as part of the grade.
LaTeX and Beamer
As described above, the final paper should be written in LaTeX (and compiled to a pdf) and the individual presentation should be written in a special LaTeX package
called Beamer (also compiled to a pdf). Below I include links to useful manuals, websites and also templates for LaTeX and Beamer.
- Slides from a talk on LaTeX created by Vadim Ponomarenko of San Diego State University.
The TeX source code for the slides. (Right-click to Save Link As).
- LaTeX on Wikibooks. A very useful online manual.
- For PC users, you can use TeXnicCenter to compile.
You'll need to install MiKTeX. After you install MikTeX, you wil also have TeXWorks in your computer. You can use
this compiler instead of TeXnicCenter if you prefer. Or find your own.
- For Mac users the things to install are different. You can use MacTeX or find one of your liking online.
- Another option is to compile things online in Share LaTeX. Many of my students have liked how easy
it was to use.
- Similar to ShareLatex, the computing software Sage which is free online also has a LaTeX compiler online.
- Example of a TeX file of mine in TeX and the corresponding pdf.
- Example of a Beamer file of mine in TeX and the corresponding pdf.
Working in groups, students will prepare a short sketch of a mathematical paradox or a puzzle to present in the annual
Halloween Colloquium of the Math/CS Department. The colloquium is at Noon on October 31.
The groups will have to present to me their plans at least a week before the Halloween Colloquium and do a trial run in class
on Friday October 28th.
The grade for an individual with regard to the Halloween Colloquium will depend on the presentation itself (10%).
I will post a homework assignment for each presentation from Journey Through Genius. Students need only turn in
homework assignments for 5 of the assignments, they get to choose which ones they want to turn in.
To pass the course, students have to take an assessment exam on the day of the final, which is on Tuesday December 13 from 8:30am to 11:30am. The assessment counts for 0% of the grade, but if a
student fails to do it, he/she will not pass the class.
The Writing Center offers free tutorial assistance, information, and
resources for every stage of the writing process.
In the online scheduler you can set up an appointment with a writing center tutor.
You can also set up a standing appointment (to meet every week at a set time) and you can also have access to a lot of resources the writing center has
If you believe that you need accommodations for a disability, please consult with The Learning and Teaching Center.
Since accommodations may require early planning and are not retroactive,
please contact the center as soon as possible. For details about the services for students with disabilities and the accomodations
process, visit http://www.lakeforest.edu/academics/resources/disability/.
You are also welcome to contact me privately to discuss your academic needs. However, all disability-related
accommodations must be arranged through Teryn Robinson at the Learning and Teaching Center.
Last modified on October 4, 2016.