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

• How to Prove It by Daniel Velleman.
• How to Think Like a Mathematician by Kevin Houston.
• 100% Mathematical Proof by Rowan Garnier and John Taylor.

Homework assignments will be due every other class period 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! All homework assignments consisting of more than one page must be stapled. Your lowest two homework scores will be dropped.

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 write convincing detailed proofs. Do not be alarmed if your homework has many comments about how to improve (nobody starts out as an expert).

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 two homework scores are dropped to skip writing up a homework assignment if you have more pressing demands on your time.

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

In class exams dates: February 17, March 16, and April 30.

Final exam date: Friday, May 18 at 9:00am.

• Very few homework problems can be solved by looking up a similar problem in the book/notes and making small adjustments. Relying on pattern matching and mimicry of past solutions will not lead to success. Spend your time trying to internalize rather than memorize. Work to engage with and deeply understand the material. This requires a lot of contemplative thought and individual focus, so you should start working on the homework very early.

• Only a small number of the particular theorems we cover will appear in later mathematics, computer science, or economics courses. The fundamental goals of the course include learning to abstract away essential ideas, to argue inductively/recursively, to model a situation with graphs/data structures, and to write clear and correct proofs. These techniques are vital to success in later mathematics courses and they are essential skills to have when writing correct, elegant, and powerful computer programs.

• Most of your learning will happen outside of class. Many students should anticipate spending about 12 hours a week devoted to the course. In other words, you should schedule at least 9 hours outside of class for homework and independent reading/working. Learning math requires practice, patience, and endurance.

• There is no strict attendance policy. However, if you miss class, you are responsible for the material that was covered. You should obtain notes from somebody else in the course and work through them. I will certainly help you with any questions you have about material you missed, but you must have worked through the ideas on your own first. Also, I do notice when students often miss class and/or show up late. It speaks to your dedication when these are regular occurrences (excepting illnesses and emergencies of course), and will make it less likely that I will be lenient and flexible for you.

• If you are stuck on a problem, begin by working on simple examples and special cases. Don't be afraid to "play" and "experiment". Although I encourage doing this in all of your math courses, Combinatorics is a subject where this approach is especially helpful and often leads to key insights. The process of abstracting from special cases to general patterns is difficult at first, but the only way to improve is not to be afraid to try.

• I really enjoy interacting with students. Please come to my office hours. But please come after you have grappled with the ideas and you have some scratch work. One of the most difficult parts of your mathematical education is learning how to transition from having no idea, to obtaining vague hunches, to seizing on key ideas, to writing correct proofs. If you bring your ideas and scratch work, we can focus on how to help you manage these transitions.

• When graded homework is returned, spend time reading the comments and reflecting on how you can improve your writing. Also, read the posted solutions and compare them to your own. Examine and learn from how the solutions differ from yours in ideas, language, and organization.

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.

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.