Course description:  

 

 

 

The format of the class will normally (but not always) be as follows.  Each topic will be introduced by a lecture with ‘gaps’ to be filled in by the class.  There will be several unanswered questions to be worked on before the next class.   In that class  you will discuss those questions, and frequently others, in small groups.  After these discussions the class will write up solutions to the problems.   

 

Grading: 

 

Homework 25%, Prelims 25%, Final 30%, Class participation 20%


Prelims: 

 

There will be at least one prelim and one final.  The date of the prelim will be determined shortly after the beginning of the semester. 

 

Lecture topics;

 

Topics will probably include (but may not be limited to) combinatorial designs, finite projective planes, combinatorial geometries, matroids, Möbius inversion on finite posets, Polya theorem of counting.

 

Some of the above topics will requre knowledge of either groups, or vector spaces whose scalars are finite fields.  While vector spaces are a prerequisite for the course, vector spaces whose scalars are finite fields are not.  Similarly, knowledge of groups is not a prerequisite for the course.  So we will carefully go over what you need to know on these two topics in class.  

 

Much of this content is in the text.  Some is not and will only be covered in class.  If you miss such a class it is your repsonsibility to get the content some other way.   

Homework:

 

There will be weekly homework, but the assignments will be shorter than what you might expect in a 4000-level math class.  The assignments will be designed to be finished in 3 or 4 days, but will not be due until until one week after they are available.  Since the specific questions on the homework will be determined by what happens during the discussion groups, homework will not be available until the week before it is due.  

 

Hw assignments will be posted here:

 

hw1 - due 2/4

hw2 - due 2/13

 

Discussion questions

 

Discussion questions will be posted here.

 

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