I will not closely follow any particular book. However, much of the mathematical material that we will cover can be found in book Mathematics for Computer Science by Eric Lehman, F. Thomson Leighton, and Albert R. Meyer.

For an eye-opening introduction to computer science (and some of the mathematics behind it) using Scheme, I highly recommend Structure and Interpreation of Computer Programs by Harold Ableson and Gerald Jay Sussman, with Julie Sussman. You can also find this book on the official site at MIT, or find other versions at the ebook site.

For a book that focuses on teaching the fundamentals of reading and writing mathematical proofs, I recommend Mathematical Reasoning: Writing and Proof by Ted Sundstrom.

I also recommend looking at the materials from John Stone's Discrete Structures course in Spring 2014.

Finally, I will distribute notes on a few of the topics that we will study.

• Learn how to interpret mathematical language and symbols properly, and how to communicate mathematical ideas effectively.
• Learn the logic of mathematical arguments, different ways to prove a statement, and how to construct your own proofs.
• Develop your ability to think recursively, and how to justify recursive procedures using mathematical induction.
• Develop your functional programming abilities in Scheme.
• Understand the relationship between programs and proofs.
• Learn new ways to justify the correctness of a program, as well as conceptual techniques to help understand the run time of a program.
• Learn some fundamental combinatorial concepts: sets, propositional logic, relations, counting, bijections, permutations, graphs, and trees.
• Learn how to abstract away essential ideas and to represent data using sequences, graphs, trees and other combinatorial models.

Homework assignments will be due every other class period. Homework will be posted to the course webpage, and will include a mixture of computations, explanations, proofs, and programming.

• Please take the time to write your solutions neatly and carefully! All homework assignments consisting of more than one page must be stapled.
• In addition to your written work, you should email me the text of all Scheme programs that you write for a given assignment. Please just copy and paste the text into the body your email.
• Homework is due at the beginning of class (i.e. at 11:00am). You will receive a 10% penalty if you turn the homework in during class time but after 11:00am.
• Unless you have a serious emergency that you bring to my attention before a homework assignment is due, late homework will not be accepted after the class in which it is due.
• Solutions to the homework will be posted to the course webpage.
• Your lowest homework score will be dropped.

Unlike some of your past experiences in mathematics, there are often many correct answers to a given problem. 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 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 keep digital records of your work, 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 to use it). If you plan to do any kind of mathematical or scientific writing in the future, you will likely use LaTeX, so taking the time now to familiarize yourself with it will greatly pay off in the long run.

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

In class exams dates: February 20, April 1, and April 29.

Final exam date: Friday, May 15 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). 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. You can not write a communal solution and all copy it down. 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 or code.

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

• Very few homework problems can be solved by looking up a similar problem from class 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.

• Much 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.

• 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 and computer science courses, Discrete Mathematics 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 when you want assistance! To use our time together most effectively, it helps if you have grappled with the ideas and you bring some of your scratch work and attempts. 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.

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.