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

• Learn how to communicate abstract mathematical ideas efficiently and elegantly.
• Learn how to think axiomatically and how to abstract specific instances to wider generalizations.
• Learn some fundamental concepts of algebra, including the fundamental properties of groups, rings, and fields.

Homework assignments will be due every other class period and will be posted to the course webpage. Your solutions must be turned in at the beginning of class, and must be stapled. Please take the time to write up your solutions neatly and carefully! Your lowest homework score will be dropped.

Solutions to the homework will also be posted to the course webpage.

Although there will certainly be some "computational" problems in the course, most of the homework involves writing proofs and/or detailed explanations. This means that there are often 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. A major goal of this course is to learn how to express your mathematical ideas correctly and to write convincing detailed proofs. Do not be alarmed if your homework has many comments about how to improve (nobody starts out as an expert).

I strongly recommend that you learn to type your solutions. LaTeX is a wonderful free typesetting system which produces high-quality documents at the cost of only a small amount of additional work. If you plan to do any kind of scientific writing in the future, you will most likely use LaTeX, so taking the time right now to familiarize yourself with it will pay off.

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 one homework score is dropped to skip writing up a homework assignment if you have more pressing demands on your time.

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

In class exams dates: February 28 and April 23.

Final exam date: Wednesday, May 14 at 9:00am.

Homework: If you enjoy working in groups, I strongly encourage you to work with others in the class to solve the homework problems. If you do collaborative work or receive help form somebody in the course, you must acknowledge this on the corresponding problem(s). Saying "I worked with Sam on this problem" or "Mary helped me with this problem" suffices. Failing to acknowledge such collaboration or assistance is a violation of academic honesty.

If you work with others, your homework must be written up independently in your own words. You can not write a communal solution and all copy it down. You can not read one person's solution and alter it slightly in notation/exposition. Discussing ideas and/or writing parts of computations together on whiteboards or scratch paper is perfectly fine, but you need to take those ideas and write the problem up on your own. Under no circumstances can you look at another student's completed written work.

You must cite other books or online sources if you use them to help solve a problem. If you get ideas from such sources, you must cite them. However, you may not specifically look for solutions to homework problems online and you may not solicit help for homework problems from online forums. Also, you may not look at past students' completed solutions. You may ask students outside the course for help, but you need to make sure they understand the academic honesty policies for the course and you need to cite their assistance as well.

Exams and final: You may neither give nor receive help. Books, written notes, computers, and calculators are not permitted.

• 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.

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 on the third floor of the JRC (x3702).

I encourage students who plan to observe holy days that coincide with class meetings or assignment due dates to consult with me as soon as possible so that we may reach a mutual understanding of how you can meet the terms of your religious observance and also the requirements for this course.