This course will introduce common structures and tools found in discrete math and computer science. Examples include enumeration, graphs, algorithms, recurrence relations, optimization, strategies, existence proofs, and basic number theory. Problems will be inspired by applications in a wide variety of topics including game theory, combinatorics, discrete geometry, voting theory, finite automata, complexity theory, cryptography, mathematical biology, and origami.
This class is intended for students who are new to discrete math. The only formal required background is some experience with writing proofs and a bit of linear algebra. Proofs should be carefully and concisely written, but not too terse. Lots of examples are in the textbooks, and we will discuss the style of proof in this field of math along the way.
The course will be somewhat experimental in nature. Be prepared to be scientist as well as a mathematician. There will be in class activities as well as more traditional homework. A big goal of the class is to get you exploring new concepts. We hope you can contribute to the class with your creativity, engagement, intellect and feedback.
Grading: There will be regularly assigned homework worth 30% of the final grade, two quizzes worth 15% each, and a final exam worth 30%. To encourage participation in class discussions, attendance and class contributions will be worth 10%, to be determined by the instructor.
Tests: Discrete math is fun and exciting, but it takes hard work to become a master at it. Listening to someone else explain a solution is not the same as coming up with it yourself. We will have two quizzes and a final exam in this class so you can show what you know as an individual. The tests will be based on material covered in the lectures, plus the recommended reading assignments. Anything covered in class is fair game whether it appears in the textbook or not. You are responsible for taking notes so you have a complete record of what we discuss. Also, be sure to fill in the gaps if you don't fully understand something. I am always happy to clarify questions before or after class. The dates to remember are:
Homework: Problems will be assigned almost every week. You are encouraged to do the homework with a group of 4-5 students and submit one assignment with all names on it. Homework should be typed in latex. Resources on learning latex are listed below. We will fix the groups in the first 2 weeks of class. Each person will have a specified role. You will be expected to rotate positions among everyone in the group. More info on group work is posted on Canvas.
Late Homework: Please do your best to turn in the homework on time and communicate with your group when it is uploaded so they can all check it! We do understand that sometime homework has to be turned in late. No worries! But, there is a 10\% deduction for each day late for up to 4 days. Homework turned in on Monday cannot be turned in after the following Friday.
In-class Assignments: From time to time we will use in-class assignments to motivate a topic or collect data. These assignments are due at the end of class. They will be graded like homework problems. If you are not present, you will not be allowed to turn in the assignment for credit, but you are always welcome to complete it the experience.
Discussion Time: We have reserved MGH 044 every Friday 3:30-4:30. This space is open to everyone in the class to get together with your groups and/or continue on activities from class. Please hold that time open in your schedule if possible. I will hold office hours in that room at that time as well.
Computing: Use of computers to verify solutions, produce examples, implement algorithms, and prove theorems is highly valuable in this subject. If you don't already know a mathematical computing platform, then try Python, Sage, Maple, Matlab, or Mathematica. We will work with Sage/Cocalc in class.
Laptop Computers in Class: Please bring a laptop computer to class on Friday April 12 and Friday April 19 for the introduction to Cocalc/Sage. Otherwise, please don't open your laptop in class so you can focus on the discussion and to avoid distracting the other students around you.