How to do well in your Mathematics and Computer Science courses

During my second year at university I wrote a post about my studying process. A lot has changed since then, and I wanted to update it and make it a bit more mature. In this post I try to give an idea of what worked for me, both in terms of learning and of getting good grades. Unfortunately, these two things are at times uncorrelated.

I acknowledge that some of the things I advice here may take a lot of time, and time can be scarce, specially in a joint bachelor program where you take 1.2-1.4x the workload. You may take what works best for you given the time you have. It is also important to be focused during the time you put in. In this regard, I have two pieces of advice. The first one is to be consistent with your schedule, as building the stamina to study for hours without distractions takes time. The second is minimizing the time in very stimulant activities such as social media.

The post has three sections. In the first one, I talk about the main general principles that guided my studying process and projects, helping me prioritize what’s important. The second one describes a general overview of a full semester for me. Finally, I discuss some other topics that typically come out when talking about studying, but that do not make, in my opinion, a big difference.

General principles and techniques

Solving problems

The post could probably end right here. The single most importance thing you can do for yourself is solving problems, specially in mathematics, where you need to grasp complex concepts and apply them to solve non-algorithmic exercises. I have seen a lot of colleagues spending large amounts of time trying to get a deep understanding on the theory before getting to the problem sheets, leaving very little time for the latter.

I prefer doing the opposite: I first get a very broad overview of the topic, and then start solving problems. This will force me to go back to the theory, search for what I need, and organize and connect ideas together. When the exam is close, I go back and study the theory thoroughly, but by this time I already knew most of it.

This way, you are actively engaging with the information, because you need it for a specific goal. You need to understand, filter, connect and organize the information in order to solve your problem. This is much more entertaining than passively going through the text without any purpose or emotional attachment, and I find that information sticks in my mind much better when practicing these higher order thinking skills (organizing and connecting concepts to form arguments vs. understanding other’s arguments).

Another reason to prioritize problems is that this is the skill you will actually get paid for in the future. If you are a master of consuming and understanding information but not of reusing it for a particular problem or situation, you will provide little value for others.

One practical consideration is deciding how much time you spend on any given problem if you are not able to solve it. This again will depend on how much time you have. I prefer spending at least 10-30 minutes on each problem, and trying again for several days. I find that the more effort I put into a problem, the better that particular pattern is encoded in my brain. Of course, if you are pressed for time, you will want to look at solutions much sooner. If solutions aren’t provided in your class, you can always share solutions with your classmates.

Sometimes you want to learn something relatively complex but your professor doesn’t provide exercises or other ways to practice. In these cases you can find your own ways. You may find exercises in books, try to implement algorithms, create detailed concept mindmaps…

Finally, sometimes you have to complete algorithmic exercises, where you always have to do the same steps, and the difficulty lies in not making stupid mistakes. I try not to lose a lot of time on these, as you don’t get a lot of learning from them. I often do two or three of these exercises each day before the exam, so I am used to them and minimize the chances of dumb errors reducing the grade.

Flashcards for rote memorization

While mathematics and computer science are two fields where you can mostly get away with understanding everything, you may still need to memorize things from time to time. This is the case of proofs that you may get asked during the exam, or questions about an IEEE standard if your professor wants to make everyone’s life miserable.

In this case, flashcard apps like Anki are the way to go. They force you to actively recall the information and automatically space out the flashcards so you don’t over study (search active recall and spaced repetition if you are not familiar with these concepts). Mathematical proofs are a bit tricky because they can be quite large. You can divide them in parts if you prefer to, and write them out when you get the flashcards.

Spacing

I try to space both my flashcard reviews and my practice sessions with exercises. While I recommend a decent block of time (at least 1-2 hours) for a practice session on a subject, I also like to interleave subjects and touch each subject in different days, allowing the information to rest in my mind during the night. As an example, if I have to do exercises for two classes and I have two days, I prefer doing one half of the exercises for each class both days. This also allows me to try unsolved exercises again.

Going the extra mile in projects

In computer science you typically have to complete practical assignments. While sometimes useless, they often serve as a way to learn the topics for the class. I try, specially when I like the topic, to do something extra, something that I find motivating. This will make you learn more, have better projects for an initial portfolio, and help you lock in the highest grade. Some professors grade the assignments comparatively, so if other students do something extra and you don’t, you may get penalized.

An overview of a semester

After seeing the general principles you may want to know how they look like during a full semester. In Spain most people do 5 courses simultaneously spread over a 5 month period. How you structure your studying will obviously depend on the structure of your program.

During the semester

The semester could be a bit chaotic. The only plan was to keep up with the exercises, specially for math courses, while also completing the assignments for computer science. Ideally I would also create theory flashcards along the way, but I almost never managed to.

In the middle of the semester we would usually have midterms. I approached them exactly the same way as finals, with the process described in the next section. Since we still had classes I would apply the process during the previous weekend, and whenever I could during weekdays, although they were busy with classes. During these periods you will have to prioritize a lot, and catch up with the work you leave behind later on, often during holidays.

During final exams

Finals usually take one full month, with 2-6 days between each exam. When finals start, it would be ideal to have finished almost all practice problems already, except perhaps algorithmic ones. This often requires spending the previous holiday (Christmas and Easter) completing them.

In the days between exams I often only study for the next exam, except if some other exam is particularly difficult or the exam calendar is very imbalanced. I dedicate each day to perform one full review of the theory, one pass over each type of algorithmic exercise and some exams from previous years, if available. If I didn’t manage to complete all problems before this period, I’ll start with that while also studying the theory.

The first day I almost always had to create flashcards from scratch, which was a bit painful. I swear revising becomes easier afterwards. Although I often ended up not spacing but cramming my flashcards, I already have a good idea of the theory from other activities. If we had a high theory load I would split revisions across days, but I always tried to do a minimum of two full revisions before the exam.

Exam days were off days, I tried not to study before the exam. I would just get more nervous, and I don’t think it pays off a lot if you studied before this point.

Other topics

In this section I will go over some disconnected topics that are often discussed in the online study community. I leave them here because most of them aren’t really critical, and doing what works best for you or makes your life more enjoyable is probably the right choice.

Note taking

Many people take notes during classes. Of course, if your professor doesn’t provide any material, you are basically forced to. In other cases, I prefer not taking notes and focusing on understanding everything. If taking notes helps you keep your focus that’s okay, but I wouldn’t sacrifice understanding what is being said to take my own notes. If you are able to keep up with the class and still take notes, you could try creating a concept map during class, trying to connect ideas and getting some higher order thinking done.

Cleaning up notes is more often than not very useless. It is very passive. It might make people feel productive but it is not forcing them to think about the topic. Summarizing can be a bit more active, since you need to evaluate and rank the information in terms of importance. If you can add mindmapping to connect ideas and get a high level picture of the topics it’s probably even better. In any case, I think it is better to spend your time solving problems, and would only do these if I have spare time.

Study block sizes

How long do you study and rest for will depend on your preferences. I like using the Pomodoro method (with 25 minute sessions and 5 minute rests) for activities that are not very engaging, such us studying theory, or when I am having trouble focusing. For problem solving or coding I like going with the flow and taking rests whenever I feel very tired, typically every hour and a half or two hours.

Scheduling study sessions

When scheduling my sessions and activities, I try to get the least engaging or most boring things out of the way first, when I am not tired. Even though these things are often less important, I have no trouble keeping my focus for long hours on engaging activities like problem solving or coding. I also try to keep the study time (without breaks) below 7-8 hours each day, and I will almost never study after dinner. That’s very personal, some people might prefer studying fewer days a week and more hours, or studying during the night.

Conclusions

That’s it for my studying advice. Not many novel ideas, just focusing on what’s important and allocating a lot of time. Of course, you will need some balance to make studying sustainable. I did all of this while going to the gym and spending time with friends regularly. I wish you good luck with your studies and a good time during your university years :)