- Instructor: Lee Troupe (I go by "Lee" or "Dr. Troupe")
- e-mail: ltroupe at math dot ubc dot ca
- Lectures: MWF 9:00 - 9:50 in Geography 212
- Office Hours:
- Monday 10:30 - 11:30am
- Wednesday 12:00 - 1:00pm
- Thursday 1:00 - 2:00pm
- or by appointment.
- All scheduled office hours are held in LSK 300.
- We will more or less follow these course notes, written by Nuno Freitas and Adela Gherga. These course notes contain exercises at the end of each section, which will form some component of your homework grade. See the Homework page for more info.
- Check back for more info and resources throughout the semester.
This course serves as an introduction to basic number-theoretic concepts, such as divisibility, prime numbers, congruences, arithmetic functions, and other topics. We'll also discuss certain applications of number theory, such as cryptography. Emphasis will be placed on building proof-writing skills and developing mathematical intuition.
- Wednesday, January 17: Last day to withdraw without receiving a "W"
- Friday, February 9: Last day to withdraw (with a "W")
- Monday, February 12: Family Day, university closed
- February 19 - February 23: mid-term break, no class
- Friday, March 30: Good Friday, university closed
- Monday, April 2: Easter Monday, university closed
General advice for success
All of these tips and strategies are discussed in more detail on the UBC math study skills wiki page
Effort pays off! It is simply untrue that people have a fixed amount of math ability that determines how well they do. Just like any other skill, doing mathematics becomes easier with hard work, practice, and willingness to challenge yourself.
Stay caught up! Mathematics is a very cumulative subject: what we learn one week depends crucially on understanding what we learned the week before. Students who fall behind early struggle to catch up for the rest of the course. This is especially true in summer courses, in which the same amount of material is presented in roughly half the time.
Put in the hours! Remember the 2-to-1 rule for university courses: expect to spend an average of 2 hours outside of class for every 1 hour spent in class. In our course, that means 14 hours per week, in addition to coming to lectures, is quite reasonable (and some students will spend more than that). That seems like a lot, and it is, but I strongly encourage you to make the effort. Jump right in and start spending that time; don't wait until later in the course.
Work on the homework problems! Solving homework problems is the most direct way to practice for the exams. It's tempting to try to find some short cut to obtaining the answers, such as taking dictation from a fellow student, searching the internet, or using a friend's work from a previous term. Besides the fact that cheating in this way violates UBC's academic misconduct policies, it's important to realize that working on the homework is the primary way for you to learn the course material. Learning to do mathematics is like learning to do anything else: you can't learn how just by watching someone else do it. Take it from someone with years of experience teaching university courses: people who work through the homework problems do better on the exams. It's that simple.
Don't give up! In earlier math courses, everything we needed to be able to do might have been conveniently written in boxed formulas that we can instantly apply. In more advanced mathematics courses, however, we don't always immediately know the correct way to proceed; sometimes trial and error is necessary, and there's nothing at all wrong with this. Trying, struggling, going back to another idea, making mistakes, fixing them—these are all part of the learning process.
Use available resources! If you are stuck in the middle of a homework problem or a concept from the course, you are on the cusp of a great learning moment. Your fellow students (I imagine) and I are very happy to help you see the way past that obstacle. Additional resources, such as practice problems, will be posted here throughout the semester.
Consciously address what you find hard! Why do some people get better quickly when they work hard, while others don't seem to progress as fast? One answer is that deliberate practice is much more effective than going through the work just for the sake of finishing it. From a Freakonomics blog post (boldface is my emphasis): “For example, in school and college, to develop mathematics and science expertise, we must somehow think deeply about the problems and reflect on what did and did not work. One method comes from the physicist John Wheeler (the PhD advisor of Richard Feynman). Wheeler recommended that, after we solve any problem, we think of one sentence that we could tell our earlier self that would have ‘cracked’ the problem. This kind of thinking turns each problem and its solution into an opportunity for reflection and for developing transferable reasoning tools.” Stephen Chew lists several ways to develop and improve your study skills, summarized by “unplug and think hard about the meaning of the concepts you're studying”.