Course Goals
 To prepare you for Part 1 of the Comprehensive Exam by helping you to review and develop mastery of the five fundamental courses of the math major: Differential and Integral Calculus, Multivariable Calculus, Discrete Mathematics, and Linear Algebra.
 To help you develop your abilities to communicate your ideas, especially your mathematical and technical ideas, through writing and through speech.
 To help you become informed about the range of opportunities available to you as math majors, both over the next year and after you graduate.
You can find a link to the syllabus here.
Assignments:
Presentations:
I have posted the rubric I will use to evaluate your presentations. I encourage you to send me drafts of your slides or come in and talk to me about your presentation before you give it.
 Week 9: April 6
 Nina
 Sherry
 Max
 Hugh
 Eustacio
 Elliott
 Erik
 Week 10: April 13
 Shuyu
 David
 Ellen
 Emerson
 Eva
 Lyra
 Week 11: April 20
 Dylan
 Sara
 Week 12: April 27
 Ian
 Katie
 Tristan
 Ethan Cohen
 YoungJun
 Ethan Vu
 Will
Week 8: Thursday March 30
 Hand in a draft of your paper.
 About three pages.
 Has:
 title and author (use LaTeX
\maketitle)
 abstract (use
\begin{abstract}
blah\end{abstract}
 motivation/context
 definitions
 theorem statement (use
\begin{thm}
stuff\end{thm}
)  proof (use
\begin{proof}
stuff\end{proof}
).
 title and author (use LaTeX
 Paper Rubric
 Email me talk topic
 Possibly volunteer for April 6 talk date.
Week 7: Thursday March 23
 Choose a theorem from a 300level math class you have taken. Use LaTeX to write a statement and proof of the theorem. Aim for about 1 to 1.5 pages.
 Print five copies and bring them to class.
 Answer the survey I will send out.
 Try to make a two or three page Beamer presentation. (You don’t need to turn this in; I just want you to figure out how the basics work).
Week 6: Thursday March 16
 The Comps Exam is Tuesday, March 14.
 Please study!
 You will have three hours for all five sections of the exam.
 The exam is held in a five hour window from noon to 5PM on Tuesday, March 14, in Fowler 113.
 If you currently have a resume (or can complete one in less than ten minutes, or need to have it finished by the end of the week anyway since you’re applying to something), email a copy of your resume to Julia Marquez at the Hameetman Career Center. Please mention in the subject line that you are part of the math junior seminar.
 No other homework this week, but we will have class in the usual time.
Week 5: Thursday March 2
 By Sunday noon, submit feedback on the talks this past Thursday. How have they changed since the start of term?
 Read the solutions to the practice Multi section.
 Complete a practice discrete section of the comps exam. (You don’t need to submit the extra problems, but they are good practice).
 Choose two problems and use LaTeX to typeset your answers; you should include a
\maketitle
command that gives a title and your name and the date.  Some of you to prepare a short (four to fiveminute) presentation on a discrete math topic. List of topics and signup form.
 If you are presenting on Discrete, submit your notes to me by email by Wednesday noon.
Week 4: Thursday February 23
 By Sunday noon, submit feedback on the senior comps talks. For each speaker, one thing you thought they did well, and one thing they could have improved.
 If you couldn’t make some of the talks, submit for each one you did attend, and then also reflect on the talks in Junior seminar as last week.
 Read the solutions to the practice Linear section.
 Complete a practice multivariable section of the comps exam.
 Choose two problems and use LaTeX to typeset your answers; you should include a
\maketitle
command that gives a title and your name and the date.  Some of you to prepare a short (four to fiveminute) presentation on a multivariable calculus topic. List of topics and signup form to be posted soon. Everyone needs to do three of the five weeks.
 If you have done three talks, do not do any more
 If you have only done one talk so far, make sure you sign up for one this week.
Week 3: Thursday February 16
 By Sunday noon, submit feedback on the senior comps talks. For each speaker, one thing you thought they did well, and one thing they could have improved.
 If you couldn’t make some of the talks, submit for each one you did attend, and then also reflect on the talks in Junior seminar as last week.
 Read the solutions to the practice Calc 2 section.
 Complete a practice linear section of the comps exam.
 Choose two problems and use LaTeX to typeset your answers; you should include a
\maketitle
command that gives a title and your name and the date.  Some of you to prepare a short (four to fiveminute) presentation on a Linear Algebra topic. List of topics and signup form to be posted soon. Everyone needs to do three of the five weeks. If you did both Calc 1 and Calc 2, please do not sign up for a linear talk.
 Email me any questions or bits of the subject you’re confused about; after presentations I’ll field any other questions on the subject that people want to ask.
 Be aware that the next round of senior comps talks, which you must attend, are this Thursday afternoon at 4:30 in Fowler 112. Be prepared to give feedback on those talks.
Week 2: Due Thursday February 9
 Read the solutions to the practice Calc 1 section.
 Complete a practice Calc 2 section of the comps exam.
 Choose one problem and use LaTeX to typeset your answer; you should include a
\maketitle
command that gives a title and your name and the date.  12 of you to prepare a short (four to fiveminute) presentation on a Calc 2 topic. List of topics and signup form. Everyone needs to do three of the five weeks, so you need to do at least one of Calc 1 and Calc 2.
 Email me any questions or bits of the subject you’re confused about; after presentations I’ll field any other questions on the subject that people want to ask.
 Be aware that the first of the senior comps talks, which you must attend, are this Thursday afternoon at 4:30 in Fowler 112. Be prepared to give feedback on those talks.
Due Sunday February 5
 Send me two things you saw that you thought were good, and two things you thought could be improved, from last week’s talks.
Week 1: Due Thursday February 2
 Complete a practice Calc 1 section of the comps exam
 Choose one problem and use LaTeX to typeset your answer; you should include a
\maketitle
command that gives a title and your name and the date.  12 of you to prepare a short (four to fiveminute) presentation on a Calc 1 topic. List of topics and signup form are now available. Everyone needs to do three out of the five weeks.
 Email me any questions or bits of the subject you’re confused about; after presentations I’ll field any other questions on the subject that people want to ask.
Comps Part 1
Part 1 of the Comprehensive Exam will be held the week after Spring Break (exact date coming soon). We hope that you will use part of your spring break to help you prepare for the exam.
The exam covers the required topics from the five fundamental courses. You can download the topics lists from Occidental’s website.
We have a number of practice exams from previous years available.
 2004 and 2005

 Calculus 1 solutions
 Calculus 2 Solutions
 Linear solutions
 Multivariable solutions
 Discrete solutions
 2006
 2008
Mathematical Communication
You may find the introduction to LaTeX I wrote elsewhere on this site helpful.
Future Opportunities
I encourage everyone to look for a job/internship/research opportunity this summer. This will improve your resume, and also give you a better idea what sorts of things you might want to do after you graduate. Many of these opportunities will pay you reasonably well.
National Science Foundation Research Experience for Undergraduates.
One very good source of these is the NSF REU program, which funds experiences where a group of undergraduates from different institutions gather and do research on a math topic for ten weeks over the summer; typically the students also receive a stipend of several thousand dollars.
A list of programs running this summer is available here.