Here’s a similar page from the Department of Mathematics at the University of Western Ontario.

Many students have asked me my opinions on which first year math courses are the easiest. So, I made a list ranking the courses from easiest to hardest based on my own personal experience (with the courses I took as an undergraduate) and based on how difficult they were for students I’ve tutored. This is just a general guide - different people will have different strengths and weaknesses. A course that’s hard for one person may be easy for another.

I’ve personally taken Calculus 50 (now Calculus 1000), Calculus 51 (now Calculus 1501), Linear Algebra 40 (now Linear Algebra 1600) and Math 31 (now split into Math 1229 and Math 1228)

Easiest

Math 1229a/b
Math 1228a/b
Math 1225a/b
Math 0110a/b
Calculus 1000a, Calculus 1100a
Calculus 1201b, Calculus 1301b
Linear Algebra 1600a/b, Calculus 1501b

Hardest

The courses

Calculus 1100 was first introduced in September 2008. At the time, I wasn’t sure how the difficulty would compare to other courses. I emailed Dr. Jones (one of the professors for Calculus 1100 at the time) and this was her reply:

It is for students who did not take calculus in high school. We teach them what they missed from not taking Grade 12 calculus and get them up to the level of cal1000 to write a common exam at Christmas with cal1000.

Calculus 1100 covers a few sections that are omitted in Calculus 1000. 1100 is intended for students who have never taken a Calculus course before (in high school or otherwise). Because of this, the course offers tutorials to complement the lectures and the pacing is slightly different. Calculus 1100 moves more slowly at first (in September and October and the first part of November) in order to solidify the basic concepts. Calculus 1100 and 1000 write different midterm exams, but they write the same final exam. At the end of the semester, a student in 1000 and 1100 will have learned the same amount of material. The main difference is the pacing.

The problem I found is that by moving more slowly in the start of the course, the topics that come later (which end up being more challenging) need to be covered in less time. This didn’t go so well with the students I was tutoring in 1100.

Calculus 1000 is a requirement for many, many degrees. The course is based on the former Calculus 50. Depending on your professor, you may have either quizzes or assignments. The class has a midterm and a final exam. Regardless of your professor, everyone writes the same midterm and the same final exam. On each exam, half of the marks are allocated for multiple choice questions (25 multiple choice, 2 marks each). There are no part marks on multiple choice. The remaining 50 marks are given for the “show your own work questions”. Usually, there are about 8-10 show your own work questions. Part marks are given here. Often the same types of questions are asked each year, so looking at old exams can give you a pretty good idea of what to expect. However, the very last question on the exam is always “extra tricky” and may require the student to go beyond what may have been taught in the course. Calculus 1000 is typically a first semester course, but it’s also offered during the second semester. Usually there’s 8 - 10 different sections during semester one and 1 - 2 during semester two. It’s usually a good idea to take it during the first semester if you can because:

1. If you don’t like your professor, it’s a lot easier to find a different section to switch into.
2. When the course is offered during the second semester, the exams tend to be less predictable. By looking at the past exams (which are offered at the UWO Bookstore), you can get a strong sense of what will be asked. Many years, the exact questions are asked with only the numbers changing. In the second semester, the exams tend not to be as close to past exams.

Calculus 1000 and 1100 both lead into the second semester courses with Calculus 1201 (the former Calculus 91) or Calculus 1301 (the former Calculus 81) or Calculus 1501 (the former Calculus 51). Calculus 1301 and Calculus 1501 are very similar topic-wise. However, there are a few things taught in 1501 and not 1301. Both courses have either quizzes or assignments. The format of the midterm and final in 1301 is the same as in Calculus 1000 - half multiple choice and half show your work. The midterm and final for 1501 are entirely show your work. Also, the questions given on exams and assignments/quizzes in 1501 are much harder than those in 1301. 1301 is the undoubtedly the easier course. 1501 is usually a requirement for math intensive degrees.

Calculus 1201 is directed at students in biology programs. It focuses on applications of Calculus to biology and the topics covered are very different than those in 1301/1501 with almost no overlap. My experience has been that the topics taught in 1201 are largely dependent on the professor teaching the course - something that may change from year to year.

Math 0110 (the former Math 12) is the equivalent of high school Calculus. The structure of the course (in terms of exams, tests, assignments) changes depending on who is teaching. But, typically, there are either one or two midterms and a final exam. The marks are usually equally divided between a multiple choice section and a show all work section.

Students usually struggle a bit with this course as it’s usually their first encounter with Calculus.

Linear Algebra 1600 (the former Linear Algebra 40) is a very difficult course. The course used to involve weekly labs which entail solving a set of questions using a computer program (Matlab). However, these seem to have been discontinued. It can be difficult for students to learn both the mathematics involved as well as the commands to solve the problems in Matlab. The material gets very abstract near the end. Calculus courses usually deal with graphs and functions - things that are easy to visualize. Linear algebra, on the other hand, considers things like lines and planes (easy to visualize) and later on moves into things like hyperplanes and objects with more than 3 dimensions (very hard to visualize). To give a comparison between Linear Algebra 1600 and Math 1229 (both linear algebra courses) - the entire set of topics taught in 1229 are covered within the first month of 1600.

The former full credit courses Math 30 and Math 31 have been restructured and broken down into the half credit Math 1225, Math 1228 and Math 1229. Each of these courses have predominantly multiple-choice exams and tests with no assignments. Occasionally the tests have a few “short answer” problems at the end (as far as I know, only Math 1228 does this). These courses are usually intended for students in Social Science and Business programs. They are relatively easier than the Calculus and Linear Algebra courses mentioned above, for that reason. However, by taking these courses instead of more difficult math courses, several modules will be closed off to you. If you are unsure about what degrees/modules you want to pursue, make sure that the course you take can be used as a prerequisite.

I would say that the easiest course to take is Math 1229. Between 1225 and 1228, 1225 might be a touch easier. 1225 contains a lot of formulas, but once you memorize it all -there’s not a lot of thought or deep understanding involved. Just plug into the formula and you’re done. 1228 is more conceptual and “word problem” and thinking about the question. This is what gets most people - in 1228 nearly every question is different and changing a single word in a question can charge the solution dramatically. Also, there’s usually a “show you work” component on 1228 tests whereas 1225 tests are completely multiple choice.Strangely, in 1228 the most difficult material appears at the beginning of the course. So, by the end of the semester, the material becomes very easy.

The way I think of it is that 1225, 1228 and 1229 cover a lot of material, but not incredibly in depth. So, you’ll need to know how to do a lot of different things, but the questions will all be straightforward “does the student know how to do this”-type questions. In 1000, 1301, 1501, 1600, etc, students need to know the concepts considerably better. There might potentially be 8 different approaches to a particular question and the student needs to be able to evaluate which is more appropriate to use. Additionally, 1000, 1301, 1501, 1600, require a higher understanding of what’s really going on. A student in 1225, 1228 and 1229 doesn’t necessarily need that deeper understanding.

Areas of Math

First year math courses fall into one of three topic areas - Calculus, Linear Algebra and Probability. Each topic has it’s own difficulties.

Calculus courses can be difficult due to the large amount of material covered. Calculus courses usually involve the memorization of several formulas. However, each concept only involves learning a specific set of steps for solving the problem. So, even though there are many topics to learn, once you master the steps, there won’t be a lot of variation between the problems in that area.

Linear Algebra courses usually start out with relatively simple material that students don’t find too hard. Somewhere in the middle of the course, the material shifts towards more abstraction. If you find it easy to picture abstract ideas in your head, then you might not have a lot of trouble. Also, a big part of the course is how each new concept fits in and relates to the others. And this can lead to more difficult exams. (You may be given one piece of information and to solve the problem you need to realize that this information implies that another piece of information must be true. This second piece of information may lead to yet another piece of information which you need to solve the problem.) The topics in linear algebra are all connected much more strongly than in calculus or probability.

In probability, the difficulties are usually in breaking down what the question is really asking. It can be hard to see how to break down a question. A single word can completely change the approach you’d take. Also, in probability courses, it’s usually harder to double check your answers. One reason I did well in mathematics was that I double checked everything I did. On the upside, probability courses usually have the fewest number of formulas to memorize. (I made a formula sheet for a probability courses and I could only come up with 2 pages worth - compared with about 8 pages each an algebra course and a calculus course)

More Stuff

I personally found linear algebra to be the most difficult. Calculus and probability were about equally hard for me.

Courses offered in the summer are sometimes (though not always) easier than the same course offered during the regular Fall or Winter semester. Topics may be cut from the curriculum during the summer due to time constraints. Also, the regular instructors (the ones that usually teach the course year after year during the regular Fall and Winter semesters) may be replaced in the summer months by less experienced instructors. On the other hand, sometimes courses end up being harder in the summer. Professors might make more challenging assignments and exams. It’s a bit of a gamble taking a course during the summer that may go one way or the other.

You can look at what students in previous years thought of their professors and classes by reading their evaluations here (you’ll need to log in with your UWO username and password - the same one you use to read your UWO email)

Or you can look at RateMyProfessors.com for more students’ opinions.

I’ve taken courses from many of the professors currently teaching at UWO and I’ve constantly heard from my students about which professors are better at explaining the material than others. If you want my advice about specific professors or you have any further questions about specific courses, feel free to email me - jeff@londonmathtutor.com

Still Not Sure?

Did you take math in high school? Think about the topics you did the best on or the topics you enjoyed the most (if there were any). Your own personal experience is the best judge of what course you should take in university. If you’re still stuck,

1. Take a probability course if you don’t mind word problems.
2. Take a calculus course if you don’t mind memorizing a lot of formulas and are good with graphs.
3. Take a linear algebra course if you are better understanding a set of steps (or an algorithm) to solve a problem than you are with memorizing formulas.

Of course, linear algebra also involves formulas and some calculus problems involve knowing a set of steps. Probability courses involve formulas, too. But word problems are central in probability courses. Formulas are central to calculus courses. And algorithms and learning steps are central to linear algebra courses.