580 -Syllabus

January 12, 2009

Mathematics 580: Topics in Set Theory: Combinatorial Set Theory.

Section 1.
Andres Caicedo.
Time: MWF 3:40-4:30 pm.
Place: Education building, Room 330.
Office Hours: By appointment. See this page for details.

We will cover diverse topics in combinatorial set theory, depending on time and the interests of the audience, including partition calculus (a generalization of Ramsey theory), cardinal arithmetic, and infinite trees. Time permitting, we can also cover large cardinals, determinacy and infinite games, or cardinal invariants (the study of sizes of sets of reals), among others. I’m open to suggestions for topics. 

Recommended background: Knowledge of cardinals and ordinals. A basic course on set theory (like 502: Logic and Set Theory) would be ideal but is not required.

Textbook: There is no official textbook. The following suggested references may be useful, but are not required:

  • Set theory. By T. Jech. Springer (2006), ISBN-10: 3540440852  ISBN-13: 978-3540440857
  • Set theory. An introduction to independence proofs. By K. Kunen. North Holland (1983), ISBN-10: 0444868399  ISBN-13: 978-0444868398
  • Set theory for the working mathematician. By K. Ciesielski. Cambridge U. Press (1997), ISBN-10: 0521594650  ISBN-13: 978-0521594653
  • Set theory. By A. Hajnal and P. Hamburger. Cambridge U. Press (1999), ISBN-10: 052159667X  ISBN-13: 978-0521596671
  • Discovering modern set theory. By W. Just and M. Weese. Vol I. AMS (1995), ISBN-10: 0821802666 ISBN-13: 978-0821802663. Vol II. AMS (1997), ISBN-10: 0821805282 ISBN-13: 978-0821805282
  • Problems and theorems in classical set theory. By P. Komjath and V. Totik. Springer (2006), ISBN-10: 038730293X  ISBN-13: 978-0387302935
  • Notes on set theory. By Y. Moschovakis. Springer (2005), ISBN-10: 038728723X  ISBN-13: 978-0387287232

Grading: Based on homework.

I will use this website to post any 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.


305 -Syllabus

January 12, 2009

Mathematics 305: Abstract Algebra I.

Section 1.
Instructor: Andres Caicedo.
Time: MWF 10:40-11:30 am.
Place: Education building, Room 221.
Office Hours: By appointment. See this page for details.

Text: Redfield, Robert H. Abstract Algebra. A concrete introduction. Addison Wesley, 2001. ISBN: 0-201-43721-X. If needed, I will provide references for additional topics not covered by the textbook.

Contents:  The usual syllabus for this course lists

Introduction to abstract algebraic systems – their motivation, definitions, and basic properties. Primary emphasis is on group theory (permutation and cyclic groups, subgroups, homomorphism, quotient groups), followed by a brief survey of rings, integral domains, and fields.

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