I’ve been emailed by some of my former students who are considering second year courses in mathematics. They wanted to know which courses would be best to take. Also, a few students who were just entering UWO in the fall emailed me about my thoughts about taking mathematics as a module. I only have experience with Pure Mathematics (which is mostly about theory - in contrast to Applied Mathematics and Statistics). But, here are my thoughts.

Professors

While first year math courses generally don’t change from year to year (with a few exceptions), higher level math courses are a bit different. The professor has a bit more say in what gets taught. So, to start, here’s a list of professors whose classes I enjoyed the most (because of their teaching style) or who my students enjoyed the most:

• Dr. Bryan
• Dr. Renner
• Dr. Dawes
• Dr. Minac
• Dr. Ditor
• Dr. Rankin
• Dr. Boivin

These people were good at giving a good picture of what was going on, why theorems were important, etc. If you have a chance to be in their class, you should try and do that. You’ll still have to put in a lot of work outside of class, but it’ll be less painful with one of these people as your prof. I’ve tutored students who didn’t like some of these professors. But, my personal opinion is that, given the course material, it’s impossible to make it really interesting. I think that those students wouldn’t have liked any of the professors. All I can say is that if you take a class by one of these professors and don’t like it, try one of the other sections and see if it’s any better for you.

If you’re considering taking a module in Pure Mathematics, keep in mind that university mathematics is a lot different than high school math (or even first year math). Until I came to university my experience in math went something like this:

1. First the teacher would go through a lesson and we’d learn some new formula.
2. We’d do many examples with the new formula or idea.
3. Homework would be assigned asking us to apply the new formula
4. etc

Even in first year courses, there’s a set number of theorems and ideas where if you memorize them all, you’re nearly guaranteed to do decently in the course. You may not get 100%, but you shouldn’t fail the course.

In most second year and higher courses, you may go through several theorems in class (some might even already be familiar), and the emphasis shifts to proving that the theorem is true. Now, instead of regurgitating formulas on the homework, you’ll be asked to come up with a proof of some theorem. At first, this new way of looking at math can be a big leap from the way that math has been taught for so long, but after a while it’ll “click” and your mind will shift gears and it won’t seem as hard. But, it may take a while because it clicks. Just be forewarned that if you sign up to do a math module expecting the same type of math as high school, you’ll be disappointed. Higher level university math requires a lot of creativity and cleverness. When you have an essay course in some other area, you can be sure that, if you research it enough, you’ll have enough information to crank out some kind of decent essay. In math, the assignments and homework, you may just not see how the pieces of the puzzle fit together no matter how much time you put into it. If you enjoy puzzles and working with others (if you don’t work with others in your class, you’ve just made the course that much harder), then a math module might be a good idea.

The Courses

I’ve separated the courses below by topic - Calculus, Linear Algebra, etc. I haven’t taken all of these courses, but I’ll mention when the course is one that I have. When I was an undergraduate, nearly all of my electives came from the Department of Mathematics. Part of the reason is that there’s sometimes a bit of overlap between courses. So, taking two courses where a particular topic is taught in both is easier than taking two completely different courses (since the two similar courses will complement each other). If you’re undecided between one or many courses, try looking for the previous years’ course webpage. It may give you a glimpse into the course content and give you a better idea if you’d like it or not.

Courses to consider if you liked Calculus

As an undergraduate, I took the former Calculus 250 and 251 (now Calculus 2502 and 2503)

Calculus 2302 and 2502 are comparable in the same way the 1301 and 1501 are. 2302 is an easier version of 2502. The topics are very similar between the two, but 2502 is intended for math majors. If you have a choice between the two, take 2302.

Likewise, the second semester continuation of these courses - 2303 and 2503 - are related the same way. 2503 is by far more difficult. Take 2303 if you’re choosing between the two.

Unfortunately, I don’t know enough about Calculus 2402 to say anything about it.

In order, from easiest to hardest, I’d say:

Easiest
2302
2303, 2502
2503
Hardest

Courses to consider if you like Linear Algebra

2120 is a linear algebra course involving proving (from basic principles) facts about vectors and matrices. 2211 is a similar course, but is intended for people who are not in an honours mathematics program. If the option of taking 2211 is available, I’d pick that over 2120. 2211 would be the
less intensive of the two.

2121 is a continuation of 2120. I hated this course more than any other course I took. Part of the reason was the professor (I don’t know if she still teaches this particular course). The course deals with linear algebra and is very abstract. When I took it there were about 12 assignments we had to do during the semester that were incredibly difficult and time consuming. I’d personally avoid this course if you could.

2290 is a full year course on some advanced algebra topics. The course isn’t intended for students in honors math (that usually means it’s less intensive). So, if you ended up taking 2120 and enjoying it, then this is the course that would follow from it. Personally, I really didn’t enjoy the topics taught in this course (I didn’t take this particular course, but a similar one intended for math majors). If you like linear algebra and matrices, this might be a good choice. But, it’ll be getting a bit more abstract.

Easiest
2211
2290
2120
2121
Hardest

Analysis

Analysis isn’t related to anything taught during first year or high school. It could be considered a distant relative of calculus, but it’s still quite a bit different. Analysis involves proving calculus concepts from basic principles in a way that will be quite foreign at first. After you wrap your head around things, it’s not so bad. Things started to “click” with me about a month into the course. But, by the end of it, there were still a lot of people who were struggling. 2123 is a continuation of 2122. To give an idea, there were about 28 people when I took 2122 (actually I took the former Math 207). Only 5 people took the continuation 2123 (I took the former Math 217).

2122 and the second semester continuation 2123 are introductory analysis courses. Most of the class involves going through all the theorems from Calculus 1000 and 1301/1501 and proving them from first principles. As I mentioned above, the type of math in this course is very new and unlike other maths that you have taken before. So, at first, everyone feels very lost when they take this class. But, after you get past the initial learning curve, it’s not an overly hard class. It involves some creativity in coming up with proofs for the theorems and an ability to visualize what’s really going on is helpful. If 1000 and 1301/1501 go really well, then this might be a good option.

2212 is a little bit like 2122 except that it also involves complex numbers. If you take 2122 and like it, then this might be a good course to ake. I found it interesting but, at the same time it was very hard to
wrap my head around some of the ideas. Some of the theorems are bizarre and counter intuitive. And that loss of intuition makes the course even more challenging. I didn’t take this particular course, but a version of it intended for math majors. I’d probably suggest sticking with some of the other, safer courses. Although, if you enjoy the other analysis courses, this might be a good pick.

Easiest
2122
2123
2212
Hardest

Courses to consider if you like Data Management

2124 is sort of a mishmash of miscellaneous topics from a variety of areas of math. It’s basically a course on problem solving. It definitely involves some creative thinking, but I found that part kind of fun. When I took the course, the exams were set up with about 15 question and you could pick any 8 of them to solve. There were biweekly assignments. Since there’s a variety of topics covered, probably a few might be familiar from high school and won’t be as difficult as the newer topics. Anyways, basically, if you enjoy puzzles then this would be a good course to take.

2155 and it’s continuation 2156 are the courses that follow Data Management from high school (even moreso than 2124 might). The course begin with set theory and goes in to probability and counting and mathematical induction (I think those are all topics still taught in high school). I enjoyed these courses. These courses are geared towards people in Computer Science. In fact, out of about 40 people in the class, I was the only person who wasn’t majoring in Computer Science. Dr. Rankin usually teaches these courses. The course has multiple choice exams and past exams are available to study from.

2251 is an essay course jointly offered by the Departments of Math and Philosophy. It basically covers some of the history of math. There’s a lot about the ancient Greeks. The prof who teaches this is very passionate about what he talks about - and that’s what really made the course interesting for me. The course isn’t offered every year though. Much of the material reminded me a lot of a book I read. So, if you’re not sure if this would be a good course to take, you could check out this book “Journey Through Genius” (http://www.amazon.ca/Journey-Through-Genius-William-Dunham/dp/014014739X/ref=sr_1_1?ie=UTF8&s=books&qid=1243538444&sr=8-1) The course follows a lot of the major ideas discussed in the book.

2291 overlaps a little bit with 2155. So, if you were taking 2155, it might be good taking this course too since the same material would be taught in both courses and it’d be a bit of a free ride at the beginning. I took a course in third year that was similar in content to 2291 that I enjoyed. The course basically just focuses on an area of math that involves only whole numbers (as opposed to fractions or decimals). It’s interesting and not overly difficult.

2292 is a geometry course. I took a similar third year course that I found a little confusing and difficult. I’d probably avoid this course unless you really really love geometry. The theorems are difficult to understand without a drawing nearby - and proving them is usually even more difficult.

2293 is a course that is (I think) intended more for Computer Science students. In any case, it’s definitely intended for non-honours mathematics students. It’s focused on learning math that is applicable in the real world. The assignments involve various applications. I didn’t personally take the course, so I don’t know a lot about it.

Easiest
2155
2291
2251
2124
2156
2292
Hardest

I hope that helps - if you have questions, feel free to email me at jeff@londonmathtutor.com