Instructor: Fred Goodman
Office: 325G McLean Hall
Phone: 335-0791 (office), 331-1939 (mobile)
Office Hours: MW 12:30-1:30 and by appointment.
Course goals:
Knowledge of enumerative methods and development of skills in problem solving, mathematical writing, and mathematical discussion.
Textbook:
R. Brualdi, Introductory Combinatorics, 4th edition, Prentice Hall, 2004.
Course plan:
We will cover chapters 1-8 and 13 of the text, possibly with some supplementary material provided in lecture. There will be a great deal of emphasis on problem solving, and we will spend a lot of class time discussing exercises.
The material of this course ideal for learning about mathematics as practiced by mathematicians - which is not a system of rules to be followed but a field of questions to be explored. The material is accessible to investigation by experiments and examples, and students are encouraged to proceed from experiment to conjecture to final explanation.
The theory in the course is for the most part rather straighforward, and does not entail long and complicated chains of reasoning. The statement of problems are usually easy to understand, but the problems can require a great deal of ingenuity and persistence to solve.
This course is appropriate and useful for both undergraduate and graduate students in mathematics, mathematics education, computer science, science and engineering. Graduate students in mathematics will be expected to do some some more challenging exercises.
Homework:
There will be eight to twelve homework assignments which may require lots of time.
You may collaborate on homework (discussing mathematics with your peers is an important skill), but you must write your own solutions. In general your homework solutions should be literate; the point is to explain your method, not just to obtain an answer.
Exams and grading:
There will be one or two midterm exams on dates to be arranged. There will be a comprehensive final exam.
Grades will take into account both homework and exams. I will weigh most
heavily what you do best, but the homework will recieve substantial weight.
Other resources:
We may find some opportunity to do computer exercises or experiments, using a computer language of your choice. It will be possible to do this work on the department unix system, or on Macs or PC's.
Attendance and absences:
Regular attendance will be expected. However, if you must miss class, you will still be responsible for the material discussed in class. You are responsible for announcements made in class, which may concern changes in the assignments, syllabus, exams, etc. Absence from exams will require a compelling reason, and must be arranged in advance.
Complaint procedure:
I hope and expect that you will have a good time, work a lot and learn a lot in this course. If you have concerns or complaints about any aspect of the course, please discuss these with me. If we are not able to resolve the difficulty, please contact the Chair of the Department of Mathematics, room 14 Maclean Hall.
Required information from the College of Liberal Arts:
The College of Liberal Arts requires certain information to be available on every course syllabus. Follow this link to obtain this information.
Fred Goodman