Math 192r: Mechanics and Overview

Lecturer: Prof. James Propp (propp at math dot harvard dot edu), 
	visiting from the University of Wisconsin.  
Phone: 617-495-4744 
Office: Science Center 435 

Course Assistant: Andy Cotton (acotton@fas.harvard.edu)

Lectures: Tuesdays and Thursdays, 2:30-4:00 in Sever 103
Lecturer's consulting hours: 
	Tuesdays 1:30-2:00, Science Center 435
	Wednesdays, 1:30-2:00, Cafe Algiers
	and by appointment
Course Assistant's sections: Mondays, 5-6 p.m., Science Center 309.
Course Assitant's consulting hours: Wednesdays, 8-9 a.m.,
	fourth floor lounge of Science Center.
Course web-sites:
	www.math.harvard.edu/~propp/192/
	www.courses.fas.harvard.edu/~math192

My goal is to inculcate two things: knowledge of the basic tools of
algebraic combinatorics, and an ability to wield those tools
opportunistically the way a researcher does.  As in most math courses,
you'll be learning facts and mastering techniques, but you'll also have
opportunities to explore problems for which you haven't been given all
the tools yet, for which you'll need to use a mix of rigorous and
non-rigorous reasoning.  Additionally, you'll have opportunities to
communicate ideas orally and in writing.

Letter grades will be awarded to students on the basis of their
performance in three domains: in-class participation (10%), homework
(50%), take-home exams (50%), with the lowest 10% being dropped.  (Note
that there are no in-class tests.)

Class participation:
      * Attendance (I plan to start 5 minutes past the hour) 
      * I expect you to have done the assigned reading, or the
        assigned skimming.  This will make for a more lively class,
        since you'll be less busy scribbling everything down; you'll be
        able to get the big picture and ask questions.  
      * There are many ways to participate: answering a question
        (correctly or not) in a way that propels the discussion
        forward; asking a good question; giving a clarification,
        synthesis or recapitulation.

Homework:
      * There will be 6 hours per week of homework, on average.  
      * Some problems will call for discovery and exploration, with
        judicious use of empirical reasoning; others will call for
        rigorous solution.  
      * Students are expected to learn to write short programs (ten lines
        or fewer) in a symbolic algebra system like Maple, Mathematica,
        or Macsyma.  When a homework problem involves writing code, the
        code should be emailed to me.  
      * Homework sets and take-homes will be graded not just on the basis
        of correctness but also on the basis of clarity.  
      * Collaboration is encouraged, but you must try the problems on
        your own first, and write up your solutions independently of one
        another.  Also, write down the names of people you worked with
        (there is no penalty for working with others, but there is if
        you do so without acknowledging them).  
      * Please staple your assignments.  
      * You can submit homework by email, but NOT in Word.  
      * Concerning late homework: To be fair to the grader and to the other
        students, it's important that the homeworks be graded promptly
        and all at the same time.  So if you hand in a paper late, and
        it doesn't get to the grader in time, you'll get a zero for
        that assignment.  (I'll only make exceptions for unusual
        circumstances.  If you've got such a circumstance, please tell
        me ahead of time if you can.) 
      * The lowest 10% of each student's homework grade is dropped.

Take-home exams:
      * One due in the middle of the term (November 1), the other due at
        the end of Reading Period.  
      * No collaboration with each other, but you can consult with me.  
      * When there's a take-home, there won't be homework.

Prerequisites: High school algebra, linear algebra, basic combinatorics.
If you know what a ring is, you'll recognize lots of examples in this 
course; but we won't use any of the general theory of rings.

Reading:
      * "Concrete Mathematics" by Graham, Knuth, and Patashnik,
        pp. 47-56, 153-172, 196-204, 243-255, 276-280, 283-290,
        306-346, 387-396.  
      * "generatingfunctionology" by Wilf,
        pp. 1-17, 35-36, 40-41, 91-93, 98-99, 108-111.  
      * "East Side, West Side" by Wilf,
        pp. 1-15, 23-28, 36-39, 44-46.  (Like the previous Wilf book,
        it's on the web for free.) You'll find links to both books on
        the course web-page.  
      * Handouts from other books, which I'll give you.  The main three are:
        "Enumerative Combinatorics" by Stanley; 
        "Constructive Combinatorics" by Stanton and White; and 
        "Combinatorial Matrix Theory" by Brualdi and Ryser.

All lectures for this course (including "make-up lectures" that I'll
create for days when I can't give ordinary lectures) will be available
over the Web throughout the semester.

No class on Tuesday, 9/18 and Thursday, 9/27.  There will, however, be
video lectures on the Web.

Suggestions for ways in which the course can be improved are welcome at
any time.