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Learning Math

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Re: Learning Math

#61

Post by fugue88 »

I have noticed that learning math from lectures (and similar means) versus learning math by reading a math book are very different skills.

Learning from lectures may be very good to get a handle on the basics. You may learn the facts faster, and keep motivation up.

But to learn beyond the basics, especially areas that are less likely to be covered at your local community college, you should learn how to learn from a book (this is different than learning from books in other subjects).

Perhaps, if you take some lectures, you may want to read a chapter or two ahead of the lecture, to get used to reading a math book as a primary source.

Good luck! Math is beautiful!

Re: Learning Math

#62

Post by sigstoat »

simplegeek wrote: post #13
dwaters wrote: post #10

Earlier quoted context omitted.

Simplegeek, thanks for the reply. I believe I am not at a level where I can go depth-first into a certain sub-branch. I want to start with the basics.

Alright. Well, I would suggest you to take a look at Martin Gardner's work( http://www.amazon.com/s/ref=nb_ss_gw/102-4845988-2776161?url... ). I think Martin Gardner did the same for Mathematics that Jon Bentley did for computer programming (or vice versa :o)). His books are fun to read. Some of the puzzles will be difficult for you, at first, but once you get the ball rolling you will be hooked. There are couple of…

"how to prove it" is by Velleman

Re: Learning Math

#63

Post by smopburrito »

asdflkj wrote: post #42
vitaminj wrote: post #39

Earlier quoted context omitted.

I certainly agree that logic, set theory, etc are the formal bases of mathematics, but I wouldn't say they are the basics. It'd be like learning the syntactic rules of grammar before learning words and constructing simple sentences by rote. Sometimes it's better to have an appreciation of the goals (which are easier to learn) before embarking on the fundamentals (which are rigorous but abstract). When I first started…

I agree about the zig-zag path, but I don't think it necessarily means you should study calculus before set theory (for example). Only that you shouldn't delve too deep on your fist pass over set theory. Obviously, AOC independence proof would not be suitable for high school students. But it doesn't take much effort to understand what a function is in terms of sets. And don't they teach Venn diagrams to kids in grade…

along these lines check out: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard and Hubabrd

http://www.amazon.com/Vector-Calculus-Linear-Algebra-Differe...

Re: Learning Math

#64

Post by kajecounterhack »

this might sound a little...retarded...

but honestly math.com is a great site. I've used it for enrichment and if you start at a topic that seems useful, it can be a great place to learn. Of course books are good for practice problems and all...

Re: Learning Math

#65

Post by euccastro »

iamwil wrote: post #44
curi wrote: post #43

Earlier quoted context omitted.

This is interesting. No one gives any reason I'm wrong about what I said. I don't quite see the purpose of downmodding a post that's already on the bottom and greyed out. But I guess no one is going to explain their reasons.

Generally, people that pervade hacker news are pretty sensitive to cultivate a high signal to noise ratio, probably because a lot of us have the 'slippery slope' mentality, and seen what can happen if you give and inch, if Reddit and Digg are any indication. In the guidelines: "Resist complaining about being downmodded. It never does any good, and it makes boring reading. " If your comments don't add any information…

If you honestly don't know why you're being downmodded it's legitimate to ask. That's not complaining, just learning.

Re: Learning Math

#66

Post by german »

projectileboy wrote: post #40

Funny you should ask... I took a lot of math classes all through college, but at every step I was reaching beyond my grasp, so I never had great understanding. And then after a few years, I forgot it all. So in my early thirties, I started over. Much more important than which text you use is your attitude, and a willingness to really walk through and understand the proof of a theorem, and a willingness to work throug…

Wow, that's a great list, I'll just add studying statistics. It's a really interesting topic and it really opens your eyes to a whole new world.

Good luck.

Re: Learning Math

#67

Post by falsestprophet »

curi wrote: post #43
curi wrote: post #36

Earlier quoted context omitted.

Wow. <3

This is interesting. No one gives any reason I'm wrong about what I said. I don't quite see the purpose of downmodding a post that's already on the bottom and greyed out. But I guess no one is going to explain their reasons.

Learned your lesson?

Re: Learning Math

#68

Post by rms »

falsestprophet wrote: post #67
curi wrote: post #43

Earlier quoted context omitted.

This is interesting. No one gives any reason I'm wrong about what I said. I don't quite see the purpose of downmodding a post that's already on the bottom and greyed out. But I guess no one is going to explain their reasons.

Learned your lesson?

What lesson?

Re: Learning Math

#69

Post by yummyfajitas »

projectileboy wrote: post #40

Funny you should ask... I took a lot of math classes all through college, but at every step I was reaching beyond my grasp, so I never had great understanding. And then after a few years, I forgot it all. So in my early thirties, I started over. Much more important than which text you use is your attitude, and a willingness to really walk through and understand the proof of a theorem, and a willingness to work throug…

If the original poster is a computer person, I'd recommend some changes to this list. This is "Math for physics" but "Math for Computer Science" is rather different, and might be more interesting.

I'd recomment calculus up to integration. Don't worry about integration tricks, except for integration by parts (the most important formula in mathematics) and u-substitution. All the other integration tricks are pointless crap used to fill up time in calc classes.

Vector math is useful if you like either computer graphics or physics, but is not crucial.

On the other hand, everyone should know probability, even the purest mathematicians. Just don't try to learn it out of an "Introduction to Probability and Statistics for Engineers" book, all such books should be burned. Real/functional analysis would also be useful to better understand probability.

I'd also suggest combinatorics/graph theory, and perhaps the theory of automata. That's edging towards computer science, but it is a fundamentally mathematical topic.

Also, it will be very slow going. It's not like picking up another computer language/framework; it's even harder than Haskell. I've have a Ph.D. in mathphys/num analysis, but it still takes me a long time to push through an introductory textbook in a field too far removed from my own. For instance, I sat through 4 semesters of abstract algebra (3 at the grad level), and I still don't understand it. Don't get discouraged.

Re: Learning Math

#70

Post by jrnewton »

I'm in the same boat, right now working towards calculus, running through an algebra review. The big problem I have with some of the "classic" texts (and wikipedia/mathworld) is that they go way over my head very quickly, usually due to my lack of knowledge regarding the nomenclature and symbols of math. Or that I lack the basic knowledge to understand why an equation can transform from state a -> b. I've found that the Barron's College Review series (on algebra and calculus) to be easy to digest. I'm also using Algebra & Trigonometry by Sullivan as a reference for issues that are fuzzy in the Barron's book. I also plan on visiting sets, graphs and logic.
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