How do I go about self-studying Maths? Do I create a routine? Answer a bunch of Q's?

Question

Im 19F & I'm starting my Computer Science course this year. Before starting it, I wanted to make sure I had good GCSE & A level Maths knowledge.

The problem is I don't know how to go about self-studying Maths. Do I answer textbook questions section per section? Do I watch videos? How do I know when I'm comfortable enough with a topic to move on to the next? Do I do 1 section a day? How do I organise it all?

To add: I have plenty of time in my day to dedicate to self-studying. I have no commitments. Apart from Maths, I'm also learning Java which is going well!

Please be kind, I'm new here :)

Answer 1

Each one learns differently, find a method that works for you.

Narrow down, "mathematics" is huge. For Computer Science, you'd need some logic/proof techniques (check out some texts/lecture notes on "bridge" courses, I happen to like Hammack's "Book of Proof"). Combinatorics, some graph theory are a must. Perhaps go for Sedgewick's "Introduction to the Analysis of Algorithms", it has very polished slides/videos. I'd also look e.g. at Erickson's "Algorithms". Not mathematics per se, but much of the material on algorithms is applied mathematics, it will at least give you an idea where it much of it is going. Also to consider is Lehman, Leighton and Meyer's "Mathematics for Computer Science"(look around, there might be a newer version available). Note that the cited texts are not easy, perhaps you'd need some more introductory material to get started.

I'd also take a peek at Downey's "Think Python" (make sure you get the second edition, the first one concentrated on --now discontinued-- Python 2), it will teach you much about what computer science/programming is all about.

Check out syllabi of schools that interest you, perhaps the lecture notes or texts cited are a better bet for material, or give you an idea what they deem important to start out. Or make a good complement to the above.

Answer 2

Well, first of all, I guess it helps to be more specific about your goals and tasks. Students tend to wander around with their thoughts, being romantic about the idea of studying any subject and thinking about how they ideally could study.

But the simple truth is: You have to work on what you have to work on. And your goal probably will simply be "Understand every detail of the course." Eventually "learning and understanding math" will take care of its own.

A lot of this work includes work, that appears as "unnecessary" or "uncomfortable" for the student. But this work is actually crucial to learn for a student. For example, contacting your lecturer, asking questions about details and willing to work on details for a longer period of time. Also willing to ask a second time about the detail you have not understood, when he/she explained it the first time.

If you think about it twice, you will realise, that the best way to prepare for your course, would be to find out, who your lecturer is and what this course is about in more detail. A lot of professors taught the same course some time ago and have scripts and textbooks available on their homepage for this specific course. Find out about that and study this textbook. If you cannot find this textbook, ask yourself again, what obvious task has to be done otherwise and how you can solve it. Probably: Ask your lecturer, if he has already a script for the course or a textbook, he can recommend. And actually write this mail. Tasks that feel uncomfortable to be done, sometimes can have the most impact on solving an issue. This does not mean that you should not use any other books. It only means you should use books in order to understand the topics and contents of the course.

Otherwise this can lead to a typical frustation a lot of math students experience: They will try to work around the "uncomfortable tasks" by spending a lot of time on "somehow understand", but will have an even harder time studying for the actual course. They spend too much time on trying to learn from books or thinking about how things should be, instead of facing and attack the next step, they should be actually working on. Courses are designed to teach you the steps that are necessary to be done. Instead of thinking about, if the course is done right way, you should rather try to think about, how you can deal with it the right way.

And lately about studying a math text for a course. It is again quite simple. Read it from beginning to the end. If there appear details, you do not understand: Spend time to make a good request for that, for example here on stackexchange: Write down the problem properly, write down what you already have tried to solve the problem, write down your question properly. Often, just by figuring out, what you want to ask, you might find an answer to your question yourself, because you specify about what you want to find out.

Answer 3

I'm copying the comments I posted under your question, so that they are more cohesive and easier to read.

I'm doing Computer Science too (starting 2nd year). I think every person should develop their own, unique way of studying, because all people are different, and you can't really create a perfect solution for all of them. Personally, I usually find the topic I want to learn, then search forums etc. for the best books on that topic, and pick one them. Then I go through of all of the theory and make sure I understand it, and only then I proceed to solve some exercises related to that topic.

As for the organisation, it depends on my mood. Sometimes I can go for hours without getting tired, but sometimes I give up doing almost no work. I think it's pointless to force yourself to do fixed amount of work every day, because to learn maths you need the right mood. Without it you might do hours of work with little to no effect, so it's more efficient to wait for the good disposition. It all depends on the type of topic you learn too. You should consider diffrent approaches if the topic is more theoretical or if it's more practical.

Another advice I can give you, that I think is very useful is to make breaks, especially when learning theoretical topic. You can walk away from your desk, do some coffee or sth and in the meantime try to sort the infomations you have learnt and put them in order, and generally think about them, their uses, connections to other topics you already know etc. I think doing this is very important to thoroughly understand topic, and I usually do such breaks every 30min when learning theory and every hour when doing exercises. Such breaks allow me to remember and understand the topic way faster.

Also, many people agree that teaching a topic is the best way to learn it as well. While you obviously may not have someone to teach if you are learning alone, but you can imagine that you are teaching someone given topic, and think of ways you could present it to him/her. I usually do that during these "breaks" I mentioned above, and I find this method really helpful.

If you have any further questions, feel free to ask.