- Friday 5/25/12: The LaTeX tutorial will be Tuesday May 29 at 5-6:30ish pm in Wean 5207
- Sunday 5/20/12: Course calendar is settled (as far as I know!). Homework 1 is up as well, and notes for the first day. Notes for the second and third day should be done before class tomorrow.
- Thursday 5/17/12: Syllabus is finalized. I am still messing with the course calendar though. It will be settled as far as I know by the beginning of the course
Welcome to Concepts of Mathematics. This course is a prerequisite for any theoretical course here at CMU. It will train you how to reason and think about mathematical problems, as well as give you a base of knowledge and concepts that will aid in your understanding of more advanced mathematics. This course will have three parts, which should transition fairly well to one another.
The first part of the course will be on logic and proof techniques. Here we will introduce logical notation and talk about how to prove different statement. We will pay particular interest to quantifiers. We will also talk about the algebra of logic. The first part will conclude with some basics of set theory, which make our logic much more expressive.
The second part of the course will cover structures on sets. We talk about relations. Using relations, we will define orderings and equivalence relations. From equivalence relations, we will make a quick detour into the world of number theory. After this detour we will define maybe the most important type of relation: the function. We will discuss properties of functions, and cardinality, ending with Cantor's Theorem.
The third part of the course will be on discete math. Ostensibly, this is a complete diversion, but when we begin with counting; here we borrow from the notions of injections and surjections from the previous part to ensure that we neither over or under count. After learning to count we look at graph theory, which relates to our study of combinatorics and our prior study of relations.
This course, especially over the summer when the time to teach is cut in more than half, is very intense. As you can see, I have scheduled many office hours. The homeworks are designed to be very challenging, yet incrementally more challenging to allow you to ease into a topic and do the homework as we learn.