Direction Needed-Mathematics Question

In My Humble Opinion
1

I would like to teach myself the following: Diiferential and Integral Calculus,vector calculus,matrix algebra and group theory.

Problem: My current math education is limited to a vague recollection of high school algebra. Where should I begin? I dont want to take classes, I want to learn it myself. Is it possible w/o instruction? Any ideas on books,or perhaps what order i should begin studying?

Assuming i’m able to commit an hour or two a day for study, how long should i expect it to take me to have a deep knowledge of these subjects?

Thanks.

2

It’s going to take a long time.

“The study of mathematics is apt to commence in disappointment.” – Alfred North Whitehead, the first sentence of his book An Introduction to Mathematics.

But once you get the pessimism out of the way, it’s easy. Go to the library and start reading books, until you find one that makes sense to you. Do the problems (so, you’ll need one with answers in the back–try not to peek). Doing it alone is going to make it tougher, of course, so here’s my email address. Let me know if you have trouble.

3

Refresh on your algebra, then begin with geometry. That’s the most intuitive form of pure math out there. After that, move on to calculus. After that, the order isn’t so relevant–although group theory will be easier once you’ve had matrix algebra.

I can’t give any book recommendations right now, cause most of my books are at home, and I’m at school. However, I can tell you that, unless you’re willing to go to school, it will be very difficult for you to attain a deep knowledge. There is some consolation, though–after a few months, you should be ahead of most laymen.

4

My e-mail is in my profile, and you’re welcome to e-mail me (or have you already?).

5

If this is a hobby, seek help! :smiley: But, seriously…

I’d start with a book on the subject of College Algebra. This will teach you many concepts which are applied in Calculus while refreshing your advanced algebraic skills. Next, you should get a Trig book to brush up on working with trig functions, vectors, and such aspects of trig. This shouldn’t take you too long to get re-acquainted. Lastly, find a book on Linear Algebra to get you familiar with the ins and outs of working working with matricies and determinants. This isn’t hard, either, really. Most of it is just algebra. (Except some upper-level concepts can get a little abstract…Eigen values? Kernel? Ug!)

After this, you’ll want to get a Calc book and start digging in. Some calculus gets kinda hairy, but most of it you should be able to self-teach without trouble. Some complex integrals (at the Calc II level) get quite ugly because they require tricky approaches outside the norm.

higher level calculus gets into 3-D problems. This isn’t too bad, and if you’ve mastered the matricies of the Linear Algebra I mentioned, this won’t be too hard.

Lastly, depending on how much calc you like, you can even teach yourself Ordinary Differential Equations (ODE) often known as “Diffy Q”. This is where your algebra teacher was correct - you’ll need to use that confounded quadratic equation over and over. And then, if you master this, YOU can teach ME Non-linear (or non-ordinary) Diffy Q! :wink:

I don’t know group theory…is this about Venn diagrams?

If you’ve mastered all this, then you can be like my college roommate: a 4.0 Physics major (now Ph.D. in astrophysics) who was proving the integrals tables AND deriving solutions for integrals beyond this!!!

Quoting my profs’ understatement of the past century, as they’d beat this mantra into us: “It’s just basic algebra, what don’t you understand!!!” (Yeah, right buddy!) - Jinx

6

Nah,its not really a hobby,at least not the pure mathematics. I have a strong interest in physics, esp. Quantum Mechanics. I’ve realised that i’m never going to understand this stuff w/o a strong math background.

The second reason is that I just feel ignorant, kind of like someone who never learned to read.

Thanks for the reply’s so far.

7

Nope.

I did learn group theory before calculus though.

8

And I just found this Introduction to Group Theory page, which may or may not be worth anything, but its philosopy is interesting: Dog School of Mathematics.

9

I totally disagree!

I agree that geometry is very intuitive. But that makes it almost useless for calculus.

I got A+ in math almost my entire life. Loved the stuff. Arithmetic, geometry, algebra, trig – all of them can be drawn on paper, and I could usually do it in my head without the paper. Then I got to calculus in 12th grade. Diagrams were useful for the first month, and then it was over. None of it was intuitive or drawable anymore. I was lucky to pass the course.

I blamed it on the teacher, so I still planned on majoring in math in college, but the same thing happened when I took calculus there too. And I concluded that the fault was not that of the teacher, but of the subject matter. Or, more specifically, my inability to conceptualize the subject matter.

The most very elementary portions of calculus (e.g.: finding the area under a curve by dividing it into an infinitely large number of infinitely narrow rectangular slices) can be diagrammed. But soon it is all over, and these basic formulas are then used as the basic for more complicated formulas, which do not relate directly to any real of imaginable thing. But because they are developed with the tools learned in algebra, you are confident that the equation is true. And you just gotta memorize these equations, without any handle to the real world.

And that’s why I say that if you want to learn calculus, make sure that your algebra is very strong, and don’t worry about your geometry.

And on a personal note: A psychologist I met once decided that I have a rather analytical mind, and then asked what my best subject was in school. As soon as I said “Math -”, he chimed in with “until calculus”, before I got a chance to say it. So please do not take this post as a rant against calculus, only a description of how very different it is from the lower maths.

(Okay, if that wasn’t enough to get this moved into GD, I don’t know what will.)

10

As someone who taught himself calculus, I can say that most textbooks I have seen are very difficult to “do-it-yourself” with.

In the interest of rigor, they include way too much information, and it’s easy to get lost and frustrated. Most math textbooks seem more interested in formally “proving” each point than in teaching.

I learned from a great do-it-yourself book. It may have been called “Teach yourself calculus,” but I can’t remember. It was set up like a choose your own adventure book, and you went from box to box, solving problems, and being corrected when you went astray. But I doubt there are books like this for all the subjects you want to learn.

Why don’t you want instruction? If it’s the money, it’s not too hard to “crash the gates” of a freshman math class at most universities. Just ask around to find out who the best teachers are.

Alternatively, there are businesses that sell videotapes of (supposedly) the best professors in the world teaching various subjects. I’ve never tried them, but I bet they are pretty good.

There may be some good tutorials out there on the internet – it’s probably worth googling a little.

11

Since this is not a question that has a factual answer, I am moving it to IMHO

DrMatrix - General Questions Moderator

PS Good luck. You could to to a college bookstore and find a text book. Or go to the Math section of the public library and browse until you find a book that makes sense.

12

Actually, that’s not true. Geometry is theorem-proof, which is the style of all higher mathematics, including advanced calculus. Many times proving that a formula applies to your problem is non-trivial.

13

Huh? Sorry, but pretty much all of physics, a science that attempts to model real-world behavior, is just applied calculus. If you were having that much trouble visualizing what you were learning, perhaps taking a physics course at that same time would have helped…

-LV

14

Martin Gardner, who ran Scientific American’s “Mathematical Games” columns for decades, recently updated what he thought was a very good introductory calculus book. It’s name is “Calculus Made Easy”, and it was originally written by Silvanus Thompson in 1921. If Gardner’s involved in something, it’s worth at least looking at.

15

I’ll toss in a suggestion to get ahold of a Schaum’s Outline book on calculus. They advertise online, and most college bookstores have a section of them. I think there are many on the subject of calculus, and other math topics. Some folks look down upon the Schaum’s outlines as the “Cliff Notes” of technical subjects, but I think they’re a very helpful companion to a textbook. The worked-out problems are fantastic for filling in the voids of typical textbooks.

I was a freshman with a D slip at mid-term in integral calculus, and unsure of my future as an engineer, I got a Schaums and started burning the midnight oil. Pulled me up to a respectable B, and probably saved my career.

Kept me outta Ag school, anyway.

16

I learned calculus from Calculus Made Easy, mentioned above, when I was in the 10th grade, and I ain’t no Stephen Hawking, if you get my meaning. I like Silvanus Thompson’s motto: “What one fool can do, another can.”

But you have to be a little careful if you plan to go on in mathematics much further than calculus. Thompson constructs some bogus “proofs” to avoid introducing the concept of a limit. You may end up having to un-learn his wacky derivations, although you can calculate perfectly well using his rules.