Unique number: 58805

Lecturer: Henry Segerman

• Email: henrys@REMOVETHISmath.utexas.edu (preferred method of contact)
• Office Phone: (512) 471-8143
• Office: RLM 10.140

Teaching Assistant: Cyntreva Paige

• Email: cyntreva(at)hotmail(dot)com
• Office Phone: (512) 232-6191 (usually answered only during office hours)
• Office: RLM 13.152

Website: http://math.utexas.edu/users/henrys/m328k.html

Meeting place and time: RLM 7.124, Tu-Th 11-12:15.

Text: Number Theory through Inquiry by David C. Marshall, Edward Odell and Michael Starbird. We will most likely cover chapters 1 - 5. 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 throughout the semester, then presenting in class. There are very few proofs in the book, and going to sources outside of others in the class, the book, or us 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 make sure they 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. If you don't follow an argument, it is your responsibility to ask a question of the student presenting.

I will be coordinating with Elizabeth Stepp, who is teaching one of the other sections of M328K, unique number 58800, which meets MWF 11-11:50 in RLM 6.114. You are welcome to attend office hours of either of us and/or Cyntreva Paige, who is the TA for both sections. If you want, you may also attend classes of the other section, to see a topic covered again etc. Throughout the semester, each student will be required to attend one 20 minute session of office hours with Cyntreva during each two week period. Sign up sheets will be made available, and students may attend in groups of three or four. Attending these office hours will influence the homework/presentation portion of the grade.

Prerequisites: M341, with a grade of at least C.

Homework: There are theorem statements, questions and exercises in the book, which you are to write proofs of, settle or work out the calculations for. You should write your solutions up neatly ahead of the class in which we will cover that statement, and we will collect them at the start of that class (you can get them back to use when presenting). Some fraction of the proofs will be graded. I will let you know roughly how far ahead we will present in the next class. 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 (as well as being very useful for studying for exams). 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 homework 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. 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 doing 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: Thursday February 7th (in class)

• Midterm 2: Thursday March 6th (in class)

• Midterm 3: Tuesday April 8th (in class)

• Final: Saturday May 10th, 2:00-5:00 pm, RLM 5.118

Grading: Each midterm will count 15% and the final will count 30%. The remaining 25% is for homework and participation in class. 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. If you would like to, this course is an excellent opportunity to learn the technical typesetting language L^ATEX.

• 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.