MATH 461 - Affine and Projective Geometry

The class meets TuTh 1:00 - 2:15pm in LGRT 141.

Professor: Jenia Tevelev

Office: LGRT 1235E. Office hours are TuW 2:30-4:00

E-mail: tevelev(at)math.umass.edu

Textbook: The four pillars of geometry by John Stillwell. We will cover pretty much the whole book except for the last section. Take lecture notes because I will often give examples and proofs that are not contained in the book.

As in any math class, it is very important to understand everything written in the textbook and covered in lectures. Read slowly and take your time understanding all definitions, examples, and proofs. Don't take anything on faith. Use as a motto a famous phrase of Alexandre Grothendieck: "I never once doubted that I would eventually succeed in getting to the bottom of things." Every time you read a statement of a theorem or lemma, pause and think about it before reading the proof. Do you know definitions of all concepts mentioned in the statement? What makes this statement non-trivial? Have you seen similar statements before? How would you prove it? When you read the proof, try to isolate its main idea. Remember that each problem is unique but there aren't that many different proof techniques. A trick used in the proof of a theorem can often be re-used in the proof of a homework problem. Reading a mathematical textbook is not always easy. Sometimes you will be under impression that two consecutive sentences are not logically connected. If this happens, the author probably wants you to make this logical connection yourself.

The homework will be posted on the class website. It will be collected each week on Thursday. Most of the problems will require writing proofs. Write them in an essay style (like proofs in the book) using complete English sentences. Check that everything you are saying is rigorously justified. You will make the grader's life easier by providing as many details as possible.

There will be two in-class midterms (October 5 and November 9) and occasional 15-minute quizzes (I will e-mail the class before every quiz).

The final grade will be 20% midterm 1, 20% midterm 2, 20% final exam, 30% HW, 10% quizzes. Two worst HW grades will be dropped. All grades will be posted on Moodle.

HW assignments: