Professor: Scott Ahlgren
Email: ahlgren@math.uiuc.edu
Phone: 244-1738
Office: 302 Altgeld Hall

This course gives an introduction to abstract mathematical thinking, problem solving, and exposition through the study of some interesting and beautiful topics in pure mathematics. Some of the goals of the course are

• To become familiar with various abstract objects and problem solving techniques in higher mathematics.
• To learn how to correctly form mathematical arguments. The goal is not just to get the right answer to a problem, but to construct a logical argument which proves that a statement is correct.
• To learn to communicate your work in a way which others can understand.

This course may differ from earlier mathematics courses which you have taken. Most of the problems require creative input. You will spend a lot of time thinking about how to present your work so that it is understandable to others. You may also have to struggle with concepts which at first are unfamiliar. As a payoff, you will have the opportunity to think about lots of interesting and beautiful things.........

Text. Mathematical Thinking: Problem Solving and Proofs, 2nd Edition. by D'Angelo and West.

Webpage. This syllabus and other course material can be found on the course webpage:  http://www.math.uiuc.edu/~ahlgren/math347/math347.html

Classes.
Section C1 meets MWF at 10 am in 143 Henry.
Section D1 meets MWF at 11 am in 143 Henry.
You should be present at each class meeting.

Grading. Your course grade will be computed using the following system.

• Three midterm exams in class. Each exam is 15% of the final grade.
• Final Exam: 25% of the final grade.
• Homework: 30% of the final grade.

Exams. The three midterm exams will be held during the normal class hour. The approximate dates are Friday, February 15, Wednesday, March 12, and Friday, April 18.

The final exam will be held in the normal classroom at the following times:
Section C1: 8-11 am on Tuesday, May 6.
Section D1: 8-11 am on Saturday, May 3.

Written Homework. Written homework problems will be assigned weekly, and will be collected at the start of class each Friday. You are welcome to discuss homework problems with other students in the class. However, you must write up solutions on your own. Your solutions should be written legibly, in complete mathematical sentences, and should be stapled. Part of the homework grade is based on the quality of your exposition, and standards for exposition will increase as the semester goes along. Problems will be graded and returned promptly. The lowest homework score will be dropped.

Plus Problems. "Plus problems" will be distributed with every homework assignment. These may be slightly harder then the usual homework problems. They will be assigned weekly and can be turned in at any time before April 25. Once turned in, will be graded as correct or incorrect, and returned promptly. If incorrect, they can be resubmitted anytime before April 25. They are intended for students who are fairly comfortable with the standard course material and who are aiming for a high grade in the course. Students who wish to obtain some sort of an "A" must turn in at least ten correct solutions over the course of the semester. Students who wish to obtain some sort of a "B" must turn in at least five. Obviously, if you plan to do these then it is advisable to turn them in as early as possible.

Office hours. I will have several office hours per week. The times may vary from week to week. Please check the main course page for a list of office hours. I am also available by appointment (talk to me during class or email me). Or, if you are nearby, you can stop by and I'll talk with you then or tell you when I can.

Material to be covered. This gives an idea of what we will be studying this semester, and the number of days which we will spend on each topic. This is a rough outline, and the schedule may be modified (and topics added or deleted) as appropriate.