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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.


Week 1: Due Tuesday January 30

  • Complete a practice Calc 1 section of the comps exam
  • Use LaTeX to typeset your answers for the Calc 1 exam; you should include a \maketitle command that gives a title and your name and the date.
  • Fill out this short survey on how comfortable you feel with each topic on the comps study guide.  Use 1 for topics you don’t remember at all, and 5 for topics you feel completely comfortable with.  (Please try to complete this by Saturday)

Week 2: Due Tuesday February 6

  • Complete a practice Calc 2 section of the comps exam.
  • Read the solutions to the Calc 1 practice section.
  • Typeset a theorem according to these guidelines
  • Think about any questions you want to ask about Calc 2 material.
  • Sign up for talks in this signup sheet.  I plan to do about 3/day for the next five classes, in more or less the order they’re listed.
    • You will give a 8-10 minute talk, that reminds everyone of how the relevant topic works and gives a couple examples.
    • If you’re not sure what material you need to include, please talk to me.
    • You must send me a brief summary of what you want to discuss by 4PM on the Sunday before your talk.  You will lose points if I do not get this summary by the deadline.

Week 3: Due Tuesday February 13

  • Complete a practice Linear section of the comps exam.
  • Read the solutions to the Calc 2 practice section.
  • Think about questions you want to ask about linear algebra material.
  • Write an abstract and an outline for a paper.
    • The abstract should be in a \begin{abstract} ... \end{abstract} block.
    • You should use sections and subsections to make the headings you would want in your paper.
    • The ultimate paper you will write will explain the background of some theorem, give definitions, and state and prove the theorem, and should be about 3-4 pages.  (You do not need to have a complete paper by next week; you need to have an abstract and an outline of such a paper).
  • Talks for February 13:
    • Vena: Optimization
    • Andrew McCall: Integration by Parts
    • Nick: Geometry of Vectors, Dot Product, norms
    • Simon: Lines, Planes, Distances, Projections

Week 4: Due Tuesday February 20

  • Submit feedback on last week’s talks on this form.
    • Note: feedback will be anonymous to each other but not to me.  You don’t need to give me feedback on anything, but I do welcome it.  You do need to give feedback on each of the other four talks.
  • Read the solutions to the practice linear section.
  • Complete a practice multivariable section.
    • Yes, there are ten problems.  Do all ten.
    • Problem 13 has a major error.  Rather than doing the problem as written, try to identify the error.
  • Write and LaTeX a proof for the theorem you have chosen for your paper.  (This is probably the theorem you chose two weeks ago, and that you wrote the outline for last week).
    • I want to see the theorem stated clearly using the {thm} environment, and the proof written clearly with the {proof} environment.
  • Talks for February 20:
    • Luis: Equations of Lines, Planes, Curves, and Surfaces
    • Jimmy: Systems of Linear Equations
    • Suzette: Matrices and Determinants
    • Silvia: Eigenvectors and Eigenvalues

Week 5: Due Tuesday February 27

  • Talks for February 27:
    • Bryan: Operators and Quantifiers
    • Sophia: Sets, subsets, power sets, and products

Week 6: Due Tuesday March 6

  • Talks for March 6:
    • Myriam: Induction
    • Paige: Number Theory
    • Andrew Poggione: counting

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.  There is a study guide available here.

We have a number of practice exams from previous years available.

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.

Occidental Undergraduate Summer Research

Occidental has an undergraduate research program to sponsor you doing research with a professor.  You would need to find a professor to mentor you; the program comes with a $4000 stipend and subsidized (but not free) summer housing.  The deadline is February 9.

National Science Foundation Research Experience for Undergraduates.

The NSF REU  program 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.  Deadlines are typically in February and March.


The AMS has an info page rounding up several summer internship opportunities.  The MAA also has a page of internship opportunities.  I’ll try to add more as I find them.