If you would like a book which teaches the fundamentals of reading and writing proofs, I suggest the following:

Homework assignments will be due for most class periods and will be posted to the course webpage. They must be turned in at the beginning of class. Solutions to the homework will also be posted to the course webpage. Please take the time to write up your solutions neatly and carefully! Your lowest three homework scores will be dropped.

Although there will certainly be some "computational" problems in the course, most of the homework involves writing proofs. This often means that there there are many correct answers. This also means that the clarity of exposition and the proper use of mathematical terminology are as vital to your solutions as having the correct idea. I understand that you may not be entirely comfortable with writing mathematical proofs (especially early in the course), but learning the standards of such proofs is as important a goal of this course as is learning the technical material. Do not be alarmed if your homework has many comments about how to tighten your mathematical prose.

Unless you have a serious emergency which you bring to my attention before a homework assignment is due, late homework will not be accepted. However, please feel free to take advantage of the fact that several homework scores are dropped to skip writing up a homework assignment if you have more pressing demands on your time.

There will be two in class exams, a take home exam, and a scheduled three hour final exam.

In class exams dates: September 22 and December 1.

Take-Home Exam: November 3 - November 5.

Final exam date: Tuesday, December 14 at 9:00am.

• Spend time reading the course notes, your notes, and any other sources you choose. And by "time" I mean a lot of time. I read one chapter of my algebra book nine times during the course of the semester (not counting reading portions of it to help with homework problems). This is normal, as you should not expect to master a section from going to class and reading it once.
• When reading a book or the course notes, do not sit down and read through it like you would a novel. While reading, have a pencil and paper at your side to work through steps on your own. After reading a proof, stop to process it in your own way and then work through it again in your own words. When you see an example illustrating a result, go back through the proof in the context of that one example.
• There will be many new abstract concepts and definitions introduced throughout the course. In my experience, attempting to memorize them directly is not helpful, and the way to master these ideas is to work with them (both on the homework and on your own) until you are so comfortable that it becomes natural.
• The material is challenging at both a high abstract level and a detail-oriented technical level. In my opinion, the best way to understand both is to switch back and forth between the two often. When trying to understand a difficult theorem, think about what it says in terms of examples you know in addition to reading the proof many times. When working through an example, picture it in the context high level theory we are developing.

Homework: You must cite other books or online sources if you use them to help solve a problem. If you enjoy working in groups, I encourage you to work with others in the class to solve the homework problems, but you must write on your homework the names of those with whom you worked. In all cases, your homework is to be written up independently in your own words. This means you can not write a communal solution and all copy it down, and you can not copy and paste a solution from somewhere else. In general, getting ideas from other people or sources is fine (so long as you do not read another solution), but you need to cite such assistance and then take those ideas and write the problem up on your own.

In class exams and final: You may neither give nor receive help. Written notes and computers are not permitted.

Take-home exam: You may consult the course notes, your own notes from class, old homework and their solutions. You man not consult any outside sources (books, online materials, etc.) and you may not discuss the problems with anyone.

Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment with me in first few weeks of class. You will need to provide documentation of your disability to the Associate Dean and Director of Academic Advising, Joyce Stern, located in the lower level of the Forum (x3702).

If you have a religious observance that conflicts with your participation in the course, please come speak with me as soon as possible to discuss appropriate accommodations.