Two Different Approaches to Self-learn Calculus

Question

Here's my situation: I'm a computer science student who has taken Calculus I twice. Not less than a week ago, I finished a second semester of the class and felt entirely defeated finishing the final. I've never felt a proficiency in Algebra, Geometry and Trig, and my professors have always said that a successful Calculus student needs to master those subjects before trying to take on Calculus. Therefore, after reading many of the questions on MSE, I've noticed two different approaches. (1) My initial approach, I would pick up textbooks on Algebra, Geometry and Trig. so that I can be prepared for Calculus or (2) I can pickup a Calculus textbook (I don't really like the one we used last semester by Stewart) and actively study from that and ask questions when I can't figure something out. My question is, being that some or many of you have gone through this, what would be the best approach to be prepared for and eventually master Calculus? I don't want to continue making the same mistakes and seeing as I have relatively long Summer, I would like to take the time to fix them.

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Also, I do apologize if this is too general of a question, or is not specific enough. I know that similar questions have been asked consistently but I don't believe that this specific question has been, feel free to tell me otherwise though.

Conclusion

I didn't expect such a quick response! Thank you all for answering my question. So far the consensus is mixed. Therefore, I've decided that I will try to review Pre-Calculus (Algebra, Geometry, Trig.) in more or less a month's time frame before tackling Calculus. Then, I'll use resources such as Khan Academy, MIT Open Course Ware, PatricJMT and definitely MSE while studying Calc. I can finally start studying, haha.

Answer 1

I feel the thing that helped me the most was to read the material before lecture and then do the questions in the book. Once I could do a type of problem with ease, I'd move on to the next type of problem. So I would recommend your second option: pick up a good Calculus book and read and work on the problems.

Edit: As Armin has suggested, I also recommend supplementing your knowledge with videos as well. Sometimes when the book seems to be unclear a video can be very helpful. Armin has suggested the MIT videos, and Khan Academy. I would like to also add PatrickJMT to that list. Since they are videos you are free to go at your own pace and can pause them if you didn't understand a concept they were discussing.

Answer 2

There are also quite a lot of excellent calculus lecture videos on youtube, from short khanacademy videos to a lecture series by open course ware from MIT. So, my suggestion would be to use a calculus book, and look at the videos as supporting material. The videos from khanacademy cover also more basic stuff than calculus.

Answer 3

Purchase and work through a Pre-Calculus book. Usually it will include refreshers/reinforcement of the most useful topics in Algebra, Geometry and Trig.

Answer 4

Having worked with students for years on courses from algebra through calculus and further, I would say that starting from a calculus textbook will not be helpful to you (and if you didn't like Stewart's book, you won't like too many others...).

At a minimum, I'd say you need to have high-school algebra and geometry in hand (which includes being comfortable with even just basic arithmetic -- I've seen many students in trouble because they didn't yet understand how to add and subtract fractions). A lot of the work involved in developing the methods of calculus are built on those of algebra and geometry (including analytic geometry and graphing). If you don't think you are going to be involved with work that uses trigonometry, you can put that off for the time being (there are courses in calculus offered -- where I work, for instance -- that do not touch on trigonometric functions).

Proficiency in those subjects is important because you will encounter many discussions (and worked-out problem solutions) which will assume that you are familiar with various topics in algebra, geometry, and sometimes even things like basic number theory (what are prime numbers? how do you factor a number? and so forth).

It will also be important to become comfortable with applications problems (what folks usually call "word problems"). A major problem for many students is that they do not get enough experience with how to turn the language of a stated situational problem into the language of a mathematical equation or a stretch of analytical calculation, so that they can then use the techniques of the math they've been learning. (This seems to be something that U.S. schools, at least, have become rather slack about...)

You should also be prepared to spend a good amount of time practicing a variety of problems. I tell students that learning to work successfully with mathematics is similar to learning to become fluent in another language, and requires comparable amounts of time. As you come across even "worked-out" problems, you should make sure that you can follow the discussion of the solution and fill in any details that are omitted (these will usually be "obvious" details, but not always).

It will also be important for you to be able to be in contact (face-to-face, online, or however) with people who already know the subject well and have good communications skills. [I think any number of us have had to deal with those who "know their stuff" but can't get it across to anyone else...] You should of course make as much of an effort on your own to solve problems, but when you get stuck after a few tries, it is generally a good idea to get someone else to look at what you've been doing. Bogging down on one stubborn problem often leads students to start down the road to procrastination, since gratification can usually be found doing something else, instead of "that stupid math stuff". (As I've put it, it is not your life's work just to master Problem 37...)

I guess this ran a bit long, but I think this covers most of what I tell students and tutors concerning how to get better at math, or helping others with that. Like any number of other human skills, practically anyone can master quite a lot of it, but it is a lot of work and by no means a short road (there are quite a few people on this site who have spent a huge piece of their lives at it!).

P.S. Online videos and such can also be quite helpful, but no one learns much just by watching -- there is no easy substitute for your own practice (sorry!).