598 -Syllabus

August 19, 2009

Math 598: Graduate Student Seminar.

Instructor: Andres Caicedo.
Contact Information: See here.
Time: W 2:40-3:30 pm.
Place: Mathematics/Geosciences building, Room 124120.
Office Hours: MW 10:40-11:30 am.

Text:

  • Steenrod, Norman; Halmos, Paul; Schiffer, Menahem; Dieudonné, Jean. How to write mathematics. AMS (1973).
  • Krantz, Steven. A primer of mathematical writing. AMS (1997).

Although they are not required, I also recommend:

  • Higham, Nicholas. Handbook of writing for the mathematical sciences. SIAM (1993).
  • Lamport, Leslie. LaTeX: A Document Preparation System (2nd Edition). Addison-Wesley (1994).

These are books that will likely be useful to you for years.

Content: The goal of this Seminar is to get you acquainted with what Mathematical Research and Mathematical Writing are about, in general, and with mathematical research at BSU in particular. As you go through the Masters program, you are expected to become familiar with a specific field of mathematics, to obtain the required background knowledge and skills in order to do research in that field, and to write a Masters thesis, that you can think of as your first endeavor into the world of mathematical research.

Roughly, we will spend two meeting talking about research in different degrees of generality.

Then we will talk about mathematical writing. I recommend that you start right away reading the short essays from the first book listed above, I will later indicate what chapters to read from Krantz book.

An important component of mathematical writing nowadays is some degree of dexterity with the TeX program, and so we will talk about it and practice for a little bit. You are expected to write your thesis using LaTeX, so the sooner you become familiar with it, the easier this will be. You will need to write (Using LaTeX) a short summary of a journal paper of your choice (we will talk more about this during the first meeting).

Afterwards, you will have the chance to do a short presentation on  the journal paper you have chosen.

Finally, the faculty will give some talks on their own research. This may be a good opportunity for you to see first hand the faculty who will most likely be your advisors, and topics similar to those that may end up being part of your thesis.

Grading:

  • Attendance 40%.
  • Presentation 30%.
  • Summary 30%.

(It is unusual in graduate courses to grade attendance, but the success of this seminar definitely depends on it.)

I will use this website to post additional information, and encourage you to use the comments feature. If you leave a comment, please use your full name, which will simplify my life filtering spam out.


502- Syllabus

August 19, 2009

Math 502: Logic and Set Theory.

Instructor: Andres Caicedo.
Contact Information: See here.
Time: MWF 12:40-1:30 pm.
Place: Mathematics/Geosciences building, Room 124.
Office Hours: MW 10:40-11:30 am. 
Text: Just, Winfried and Weese, Martin. Discovering Modern Set Theory. Vol I: The Basics. American Mathematical Society (1996).

Contents: Math 502 is intended to provide an introduction to mathematical logic and set theory. I will supply additional notes and references for the material on logic, roughly corresponding to the first five weeks of lecture.  We will cover propositional and predicate (first-order) logic, completeness, compactness, and the basic theorems of model theory, before jumping into set theory proper. There, we will study the Zermelo-Fraenkel axioms, including the axiom of choice, with an emphasis on the development of the theory of ordinals and cardinals, and the notion of transfinite recursion. Depending on time, additional topics may be covered.  

Grading: Based on homework. 

I will use this website to post additional information, and encourage you to use the comments feature. If you leave a comment, please use your full name, which will simplify my life filtering spam out.