We will not follow an official textbook. Instead, I will write course notes that I will post here: Current Notes.

A major goal of the course is the development strong proof writing skills. For additional references about mathematical notation and proofs, I recommend the following:

• Book of Proof by Richard Hammack. Available online.
• Mathematical Reasoning: Writing and Proof by Ted Sundstrom. Available online.
• How to Prove It by Daniel Velleman.

For general advice on making the transition from a computational perspective of mathematics to a more conceptual understanding (including how to think logically and how to write mathematics), consider reading the following:

• How to Think Like a Mathematician by Kevin Houston.
• How to Study as a Mathematics Major by Lara Alcock.

• Develop technical writing skills, including the ability to communicate abstract mathematical ideas correctly and clearly.
• Learn how to approach new and challenging problems by developing creative problem-solving strategies and techniques.
• Learn how to abstract away essential ideas, to argue inductively/recursively, and to model applied situations using graphs and other combinatorial tools.
• Develop an appreciation for how penetrating theoretical insights can lead to significantly faster computational tools.
• Learn some of the fundamental concepts from combinatorics and graph theory: set operations, equivalence relations, counting, bijections, binomial coefficients, permutations, trees, matchings, colorings.

Homework assignments will be due on Tuesdays and Fridays, and will be posted to the course webpage.

• Homework is due at 5:00pm Grinnell time.
• You should submit you solutions as one pdf file to the corresponding homework folder within your course OneDrive folder (that I will share with you).
• Your lowest homework score will be dropped.
• Solutions to the homework will be posted to the course webpage.
• Throughout the semester, you may extend the deadline of at most two homework assignments by (up to) two days. If you choose to extend the deadline of an assignment, you should send me an email by the usual due date. Beyond these two extensions, late homework will not be accepted for credit, unless there is an emergency that you bring to my attention before the due date.

Although there will certainly be some "computational" problems in the course, most of the homework involves writing proofs and/or detailed explanations. As a result, 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).

If you want to learn how to present your work professionally, as well as keep digital records, I recommend learning how 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 effort (beyond the nontrivial start-up cost of learning the fundamentals). If you plan to do any kind of mathematical or scientific writing in the future, you will likely use LaTeX, so it is worth your time to familiarize yourself with it. See Jim Hefferon's LaTeX for Undergraduates and his LaTeX Cheat Sheet for the basics. Also, feel free to ask me questions about how to use LaTeX, and/or to send you the LaTeX file for homework assignments.

There will be two exams and a final, each of which will be open book and open notes, and which will focus on conceptual problems and proofs.

Exam dates: Friday, February 19 and Tuesday, March 9. The final will be taken during the 2-day final exam period (March 23-24).

In order to learn mathematics effectively, it is essential to constantly ask questions, to isolate which aspects of the material are unclear, and to make conjectures. To help develop these skills, please participate in class, post questions to the Piazza discussion board, and bring questions to office hours. Any kind of question is welcome! For example, you can ask whether a conjecture you have is true, how to overcome an obstacle in a proof, or why a definition takes the form it does.

Consult the general Grinnell College policy on Academic Honesty and the associated booklet for general information.

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). Writing "I worked with Sam on this problem" or "Mary helped me with this problem" suffices. 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. 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 cannot write a communal solution and all copy it down. You cannot read one person's solution and alter it slightly in notation/exposition. Discussing ideas and/or writing parts of computations together on a shared document 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 may look at other sources, but you must cite other books or online sources if they provide you with an idea that helps you solve a problem. However, you may not specifically look for solutions to homework problems, and you may not solicit help for homework problems from online forums.

Exams and Final: You will be able to use the Course Notes, the homework solutions, and your own written notes and solutions. You can not use any other sources (books, online sites, other people) during the exam period.

I encourage students with documented disabilities to discuss appropriate accommodations with me. You will also need to have a conversation with, and provide documentation of your disability to, the Coordinator of Disability Resources, John Hirschman, located on the third floor of Goodnow Hall (x3089).

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.