Mathematics for Computer Science Students
July 24th, 2008Those that read my Blog now and again will know of my achilles heel. For those that are new and have just read this post the main thing holding me back from being great with programming and Computer Science is my lack of Mathematical ability. I am very passionate about Computer Science, but my lack of formal education in Mathematics holds me back from really pushing myself in certain areas that I enjoy.
The other day I decided to read through a couple of research papers I had found lying around on my university intranet when I met some equations, probably simple ones, and my lack of Math knowledge forced me to stay on that page for about an hour to find out exactly what one equation meant. I then moved to the next page and discovered seven more!
Finally, I snapped. No longer will Mathematics be my downfall. I will spend as much free time as possible going over every necessary subset of Maths that I need to be a capable Computer Science student!
With newly-found enthusiasm I crawled the Internet looking for advice and eventually found out what I needed to learn. Being from the UK I left school at 16, the time when I stopping taking Maths as a subject. Thanks to this I would need some heavy training to get back to where I was at when I was 16 and onwards to actually knowing the stuff that the majority of CS students at top universities know. After a few days I formulated my plan of action, consisting of the following in video lecture format:
- Linear Algebra
- Differential Equations
- Probability & Statistics
- Algebra & Pre-calculus
- Calculus
- Discrete Mathematics
- Anything else that is apparently basic that I cannot do in my head
It’s definitely going to take me a long time to become capable in all of these subjects, but I have a long summer ahead of me and I am making decent progress. I am now edging closer to the halfway mark with Linear Algebra and with luck will have it all finished within two weeks, when I can move onto two at a time, probably Algebra and Pre-calculus, and Differential Equations. I’ve done so much writing that I’ve even purchased two gigantic notepads and two pots of Tipp-Ex to correct the several mistakes per page that I am currently making. By the time I get to university in October I want to be capable of handling any algorithmic problems that can be thrown at me.
If you’re looking to study Computer Science, or are studying CS now and don’t know this stuff, hurry up and watch these lectures! Trust me when I say that knowing this will make your lives a lot easier.
July 28th, 2008 at 1:30 am
It is really great that MIT and others are providing these lectures for free. I am curious about why you have decided that it is appropriate to study Differential Equations before studying Calculus. At my college, we cannot take Differential Equations until we’ve taken Calculus I and II. I know that I could not possibly have made it through Differential Equations otherwise, since it requires knowledge and skill in both derivatives and integrals. Also worth noting is that MIT’s syllabus for Differential Equations lists Calculus as prerequisite.
My own order for those subjects is this:
Probability and Statistics; and Discrete Mathematics
1) Algebra
2) Trigonometry and pre-calculus
3) Calculus I
4) Calculus II
5) Calculus III
6) Differential Equations
7) Linear Algebra
Probability and statistics also relies pretty heavily on calculus from what I’ve seen (will take this Fall). It also surprises me that you are managing to understand Linear Algebra before algebra and pre-calc. In fact, Discrete Mathematics and even Calculus (again, see MIT syllabus) should probably come before Linear Algebra as well. I don’t mean to be a jerk here, and I would hope that you know what you’re doing.
July 28th, 2008 at 1:32 am
well, that sunglasses guy preceding Probability and Statistics was supposed to be an 8 followed by a ). lol
July 28th, 2008 at 1:33 pm
Yes, you are very correct. I only formulated the list based on order in my bookmarks toolbar on Firefox. I’ll adjust them shortly.
As far as already working through Linear Algebra goes, I’m yet to suffer any setbacks so far, or anything that’s required calculus. I’m over halfway through the content I’ve seen only one reference to Differential Equations and countless references to why certain aspects of Linear Algebra isn’t the same as Calculus. The sole reason I decided to do Linear Algebra first was after watching the first lecture to get a feel for it and just sticking with it.
I’ve never really ’struggled’ with Maths, just with the fact that I need more Maths than what pre-16 education had taught me. Once I am on the right path things tend to progress very smoothly.
Either way, thank you for your comment. I will restructure what I attempt and give the order you’ve proposed a try.
August 3rd, 2008 at 4:08 pm
Davy has some good advice: reorder your learning once you move on from linear algebra. Statistics and discrete can be done in any order, but definitely make sure you are up-to-date on trigonometry before you even think of moving on to calculus. From Calculus II-equivalent material (integration — foundation and special methods — applications of definite integrals, basic differential equations, sequences and series), you will require a thorough understanding of trigonometry. Being solid in that will help you immensely.
Another area you stick your nose into is physics. Going through the material of an introductory physics class will help in that you will see a lot of applications for the material you learn in calculus and differential equations.
Good luck with your learning! I’m very impressed that you’re taking it upon yourself to learn all those areas of mathematics.