Unique number: 59995

Lecturer: Henry Segerman
Email: henrys@REMOVETHISmath.utexas.edu (preferred method of contact)
Office Phone: (512) 471-8143
Office: RLM 10.140
Office Hours: M 11am - 12 noon, 4pm - 5pm, W 11am - 1pm, 4pm - 5pm. Outside of these times, please feel free to email me with questions or for hints.

Website: http://math.utexas.edu/users/henrys/m325k.html

Meeting place and time: GEO 2.102, MWF 10-11.

Text: Extending the Frontiers of Mathematics, Inquiries into proof and argumentation by Edward B. Burger.
We will cover chapters 1 - 7, 11, 12, and if there is time, 13, 9, and 10.

This is an inquiry style course (also known as "guided discovery", "modified Moore method" or "inquiry based learning"), which may be very different from any courses you may have taken in the past. We will follow the text closely. The book consists mostly of statements that we (or rather you) will be proving (or disproving if the statement is false!) throughout the semester. There are very few proofs in the book, and going to sources outside of others in the class, the book or myself is verboten. The point of all of this is that you will be creating the proofs as we go. Mathematics is an intensely creative endeavour, and this course aims to introduce the student to that creative process, and the language and style of precise communication and thinking used in mathematics.

The standing homework assignment is for each student to read ahead and prove the next theorems or settle the next questions in the book. In class I will do very little lecturing. Instead I will ask students to present their proofs to the class. The job of the other students is to try to understand the proof presented and ask questions. I may ask other students to rephrase parts of the proof presented, or explain why parts of it are true.

Prerequisites: Mathematics 408D or 408L with a grade of at least C, or consent of instructor.

Homework: There are theorems in the book which you are to write up proofs of, and indicate ways to extend if possible. There are also statements for which you are not told if they are true or false. For these either prove and extend or disprove and salvage (i.e. can you prove some variant of the statement?). You should write these up neatly ahead of the class in which we will cover that statement, and I will collect them at the start of that class (you can get them back from me if you want to refer to them when presenting). Some fraction of the proofs will be graded. I will let you know how far ahead we will present in the next class, and so how far ahead you will need to be working. Of course working further ahead may be wise in order to be able to take advantage of office hours. In addition you should maintain a notebook of correct proofs of all of the statements that you can update after we have covered those results in class. This is part of the homework requirement, and I will ask you to bring your notebooks to class with you when we have an exam so that I can look over them.

The lowest n proof scores will be dropped, where n will be determined later in the semester. This is to accomodate occasions when for whatever reason you are unable to hand in homework before the deadline. I'll talk about n later on, the aim being to allow missed homework from about 2 or 3 classes. You should still write up proofs from hand-ins you miss in your notebook, so that you have the proofs of the results. One of the points of the homework is that in your notebook you will be writing your own version of the text book, with the proofs included.

Exams: There will be three in-class midterms and a comprehensive final. The exams will be of a more traditional format than class, in that they will cover working out of exercises in the material we will cover, as well as proofs, both of results we (you) will prove in class and some closely related results you won't have seen.

No books, notes or calculators will be allowed in any of the exams (not that calculators will be of much use anyway). There will be no makeup exams. If you must miss a midterm (at most one allowed) then you must let me know one week in advance of the midterm with a documented excuse. The lowest (or missed) midterm score will be replaced by that of the final if it improves the total. Exam dates are:

• Midterm 1: Friday Sept 21 (in class)

• Midterm 2: Monday Oct 15 (in class)

• Midterm 3: Monday Nov 12 (in class)

• Final: Monday 17 Dec, 2pm to 5pm

Grading: Homework will count towards 15% of your grade. Each midterm will count 15% and the final will count 30%. There is a further 10% for participation in class, for which I will be very generous with. If you put in the effort and turn up to class then you will score highly in participation. I will release approximate letter grade boundaries based on performance in the midterms.

Students with Disabilities: At the beginning of the semester, students with disabilities who need special accomodations should notify the instructor by presenting a letter prepared by the Service for Students with Disabilities (SSD) Office. To ensure that the most appropriate accomodations can be provided, students should contant the SSD Office at 471-6259 or 471-4641 TTY.

Some Philosophy:

• Students are encouraged to talk over the homework with each other and then do the homework on their own. Copying down someone else's proof defeats the point of figuring things out for yourself. Even better if you have a go at the problems on your own before talking to someone else.

• It is a good idea to work out and write down the ideas involved in a proof in a rough form before attempting to write a more formal proof. In particular, presenting your proof to the class will be easier if it is written up neatly.

• Take advantage of office hours! Seek out help before problems get too large to tackle. You will find that I have a lot of patience with people who are genuinely interested in learning, and decreasingly less for those who regularly skip class/homework/etc. Don't hesistate to ask me or others in the class if you have questions or are having trouble.