Math 305 is not required for a major or minor in mathematics, and students who are confident in their proof-reading and -writing skills may choose to move directly to Math 307 and Math 321. If you're not sure which is the right course for you, try taking the Math 305 self-test. If you can do all the problems on the self-test then you can probably move on to other proof-oriented math classes. If you don't understand what the problems are asking, then Math 305 may be for you. If you're anywhere in between, then please discuss it with me.
We will cover all of the first five chapters of the textbook, and selected topics from chapters 6–8, as time permits. By the end of the semester, you should be able to:
Each class will consist of a lecture followed by group work. You are expected to attend and take notes. Taking notes and listening actively to the lecture at the same time are important skills to learn for success in future math classes. For many people, taking notes helps keep them engaged in the lecture, and being able to look at one's own notes later is a helpful additional association for retaining the material. Furthermore, some advanced courses do not have a textbook (or have one but don't follow it), so you will need to take notes in order to have a reference for the course — now is the time to learn to do that well! After the lecture, the remainder of each class will be devoted to group work. (I will assign new groups periodically during the semester.) You will be given a problem to work on with your group. Once you have solved it, you will write out a careful solution to be turned in. If you can't solve it, you will write out a detailed explanation of what you tried and why it didn't work. One group will be chosen at random to present their work to the class.
There will be homework problems based on the material from each lecture, normally due on Friday. All homework assignments are due by 2 p.m. on the listed date, in class or at my office. Late homework will not be accepted. If unusual circumstances arise and you contact me in a timely manner, then we can discuss alternative arrangements.
Throughout this class, you need to explain your answers even when the problem doesn't explicitly ask for a proof; this typically means writing in complete English sentences. When deciding how much detail to include, here's the standard to keep in mind: your solution to a problem should be complete and clear enough that one of your classmates, who has paid attention in class but hasn't thought about that specific problem yet, could read your solution and understand exactly how it works. If you only try to convince the grader that you understand the solution, then you almost certainly won't write enough.
Students may work together on homework. However, each student must figure out how to write up his or her own solution to be turned in. That means for example that you and a friend may figure out together how to prove a statement, but the written-out proofs you turn in should not be verbatim copies of each other.
Reading and homework problems will be posted on this page.