Best, fastest, most fun way to learn semi-advanced math? (calculus/linear algebra)

[Hygro]

I hate learning math at my university. I'm naturally decent at math. I really enjoy it when I'm doing it. But the way it's taught doesn't work well with me so I find it more productive to learn other things.


I managed to bypass a lot of college admission requirements, and so with what little high school math I learned, combined with forgetting it from being out of practice, I am like an 8th grade with some skills in geometry.


I would like to learn math through multi-variable calculus and linear algebra.

I want to do this becase

• Since age 15, not knowing calculus made me feel like an incomplete citizen.
• When I study math it makes me smarter in everything else.
• It would do wonders in opening up academic pathways
• Bridges would lower and gates would open for my future career options.
• It would be really bad ass and probably complete my story of overcoming things from my past.

So I have some questions.

• If I could devote 10 hours a week, could I go from relearning Algebra through multi-variable calculus and linear algebra in 6 months?
• If someone was asking you to tutor them and they were offering you a lump sum payment to teach them in those 6 (or whatever) months, what range would you charge?
• If you were in my shoes, how much would you shell out?
• Do you have any methods, resources, techniques that you can recommend me to help my learning?

Thanks in advance to anyone who can help me figure this out. This has been eating away at me ever since I realized in early high school that I wasn't going to get around to doing math and I'd really like to change this.

 

[Integral]

I can think of three strategies.

1. Buy textbooks, learn mathematics.
Buy three books: one on "college algebra," James Stewart's "Calculus," and a linear algebra textbook.
Work through the book. Read section, do exercises. Thrust, repeat until there are no more sections left.


2. Get online lecture notes.
Books are expensive. Notes are not. Google "college algebra notes," "calculus notes" and the like. You are looking for PDFs.
Alternatively, go HERE and get crackin'.

3. MIT OpenCourseWare. Possibly unnecessarily difficult.


General note: the only way to learn math is to do math. Do lots and lots of problems.

 

[Zelig]

If I could devote 10 hours a week, could I go from relearning Algebra through multi-variable calculus and linear algebra in 6 months?

Maybe, it will be close, I don't think it's an unreasonable goal, particularly if it's a real 10 hours per week.

If someone was asking you to tutor them and they were offering you a lump sum payment to teach them in those 6 (or whatever) months, what range would you charge?

I charge $30/hr for math tutoring. For someone putting in 10 hours of self-motivated work in per week, I'd ballpark maybe 90 minutes per week of one-on-one time, so around $1200.

If you were in my shoes, how much would you shell out?

Not much, I'd either work through it on my own or try to find people working on similar stuff to work together with me.

Do you have any methods, resources, techniques that you can recommend me to help my learning?

Not really. If I were trying to do that, I'd just find some good university courses to do online and work through the assignments/tests, referring to textbooks as necessary, but I've got no idea if that's a particularly good way of learning for other people.

 

[Imrahil91]

You could try using KhanAcademy as a resource. It's a nice site where one guy teaches a lot of subjects, especially maths, in short video lectures.
Many people love it. He may be a rising star, and you should definitely check it out.
Here's a nice TED-talk by the founder.

 

[warpus]

[*]If I could devote 10 hours a week, could I go from relearning Algebra through multi-variable calculus and linear algebra in 6 months?

Probably not.

I suppose it depends on the level you wish to attain though. I mean.. Linear Algebra can be made easy if you're not asked to prove anything and truly *understand* it. Or you could make it difficult by making it ALL theoretical. So it depends..

If you really want to be proficient enough with all the things you want to learn.. Then 6 months is probably not enough time. The best way to learn math is through practice, repetition (I hate to admit it, but it's true), and failure. I'm not necessarily talking about doing the same kind of problem 400 times, but like.. Mastering recursive proofs by induction by doing a couple different kinds of problems a week. Doing things that will get you thinking a certain type of way so that you are ready for the next level of BS that you'll encounter in linear algebra and then later of course multi-variable calculus.

Of course if you are a genius, disregard everything I just said. Start reading.

[*]If someone was asking you to tutor them and they were offering you a lump sum payment to teach them in those 6 (or whatever) months, what range would you charge?

10 hours a week for 6 months? So that's 40 hours a month or so and 240 hours total. Let's say $25 an hour, so.. $6000 plus tip, plus expenses, plus tax, $7000

[*]If you were in my shoes, how much would you shell out?

I would save the money for future escapades involving drugs and hookers, and learn everything by yourself. That's how I learned everything in University.. Had to sit through hours and hours of calculus, stats, algebra.. combinatorics.. logic.. boring boring stuff. Anyway, what you do is you sit down and learn every concept one by one.. And you don't move on until you UNDERSTAND the concept you were learning. I guess everybody learns differently, and you'll know if you are capable of really learning new concepts on your own.. but give it a try. It is doable. All you need is motivation.

[*]Do you have any methods, resources, techniques that you can recommend me to help my learning?

Just keep at it. If you get stuck on a problem, go for a walk or a crap. or a shower. Those 3 places is where I solved most of my problems in University.

Do lots of examples.

PROVE a lot of stuff, from first principles, without looking up the proof first. FIGURE IT OUT. When you figure out how to prove something, you learn what it actually means.

If you really really really get stuck on something, just look it up. And good luck.

 

[Bootstoots]

I taught myself calculus when I was bored back in high school. It wasn't easy, but it was surprisingly doable once I really started working at it. All you really need is a good textbook with many problems and solutions (worked solutions if possible) in the back of the book. Then, just start at the beginning and work through it at your own pace, being sure to do as many problems as it takes to be sure you've mastered each section before you go on.

After about six months, I learned the material far better than anyone who was in my (rather crappy) school's calculus class, pulled a 5 on the AP exam, and was off to college to study physics!

It does take a lot of discipline, but if you can, teaching yourself really is the best way to learn something like calculus. You get to cover the material you want, at your own pace, without anything annoying like grades to worry about.

As for linear algebra, I'm not sure - I never did understand it as well as I wanted, but I never really sat down and tried to master it for myself like I did with calculus. I suspect the same sort of approach would work for it too.

 

[zjintz]

You could try using KhanAcademy as a resource. It's a nice site where one guy teaches a lot of subjects, especially maths, in short video lectures.
Many people love it. He may be a rising star, and you should definitely check it out.
Here's a nice TED-talk by the founder.

looks great!.

 

[Syterion]

To be honest, no, I don't think 6 months is enough, especially teaching yourself. I say take a night class at a nearby college, that will probably cost about 400 dollars in single variable calculus (unless you really need to practice trig and algebra), and suffer through it. Then if you can, attempt to teach yourself multivariable, differential equations, and linear algebra. All this stuff can be very difficult if you want to learn it at a high level. They can be not so hard to learn the basics. However, calculus is a whole new mode of thinking. I'd really recommend taking a college course in single variable calculus. My high school teacher was phenomenal, and because of how challenging her class was I had a strong foundation for learning the more theoretical and complex maths. Those later maths can be incredibly frustrating if you don't know backwards and forwards how almost everything in single variable works.

Teachers make things better. Maybe it doesn't work for you. But I can not imagine teaching myself calculus - I would get help.

 

[GoodGame]

I kind of agree that you are rushing Hygro, but I think you can expect to get up to a Calculus I level in six months. Progressively difficult calculus courses reasonably take a semester each to focus on. If you're in it to solve actual work problems (e.g. specific economics applications), I think you might be able to accelerate your understanding of calculus. In other words, I'd say understand the application first, then the theory, but approaching the theory first is really ideal.

There's a lot of different study aids, study guides, text books, video tutors, etc.. for Calculus I. Make use of everything that you can get a hold of as long as the authors are reasonably credentialed. Something should fit with your learning style.

 

[Gigaz]

I would like to learn math through multi-variable calculus and linear algebra.

There is one fail-proof way:

Find some friends who must learn exactly the same and discuss everything.
Ask someone who has already learned it about appropriate material.
Do many, many exercises.

In my experience, 120 hours of work will get you trough any university test and that is propably more than you want.

 

[dutchfire]

I hate learning math at my university. I'm naturally decent at math. I really enjoy it when I'm doing it. But the way it's taught doesn't work well with me so I find it more productive to learn other things.


I managed to bypass a lot of college admission requirements, and so with what little high school math I learned, combined with forgetting it from being out of practice, I am like an 8th grade with some skills in geometry.


I would like to learn math through multi-variable calculus and linear algebra.

I want to do this becase

• Since age 15, not knowing calculus made me feel like an incomplete citizen.
• When I study math it makes me smarter in everything else.
• It would do wonders in opening up academic pathways
• Bridges would lower and gates would open for my future career options.
• It would be really bad ass and probably complete my story of overcoming things from my past.

So I have some questions.

• If I could devote 10 hours a week, could I go from relearning Algebra through multi-variable calculus and linear algebra in 6 months?
• If someone was asking you to tutor them and they were offering you a lump sum payment to teach them in those 6 (or whatever) months, what range would you charge?
• If you were in my shoes, how much would you shell out?
• Do you have any methods, resources, techniques that you can recommend me to help my learning?

Thanks in advance to anyone who can help me figure this out. This has been eating away at me ever since I realized in early high school that I wasn't going to get around to doing math and I'd really like to change this.

I think the amount of time required to learn math really changes from person to person. I've you have always found math easy then you will probably learn it quickly. 10 hours a week, 6 months won't get you to advanced maths, but it will get you somewhere.
I usually ask €10-15 / hour for tutoring, but that also depends heavily on how much you expect from your tutor. Do you want him to just answer your questions, or do you also expect him to set up a schedule and make exercises etc?
If I were you, I'd try to get a series of maths books/notes and study from them. You might still have some of your high school books, otherwise, maybe some people can recommend books. Books with integrated exercises are good.

Don't forget the maths thread on CFC: http://forums.civfanatics.com/showthread.php?t=314282. You can always stop by for a short question or explanation.

 

[aelf]

How did you get a banking job with so little math skills? Every time I read that an employer is asking for quantitative skills, I shudder a little. And I've done some (admittedly fairly basic) maths and stats modules in university.

 

[warpus]

There is one fail-proof way:

Find some friends who must learn exactly the same and discuss everything.

Do tough problems together on a blackboard.

That really helped me with concepts I did not fully grasp on my own.

 

[JohnRM]

So I have some questions.

• If I could devote 10 hours a week, could I go from relearning Algebra through multi-variable calculus and linear algebra in 6 months?

• 
  
  My instructor asked, in the beginning of our course; "If you study three hours a night, do you know what grade that guarantees you?"
  
  C.
  
  That is 21 hours a week, over four months. Unless you consider yourself exceptionally talented at Math, you are going to need a lot more time for this.

 

[Dreadnought]

Honestly, it depends on your objectives.

Since I assume you want to actually learn the math in depth, then it will take quite a bit of time. If you're just trying to pass a class, then it doesn't require too much work.

 

[Thedrin]

There is one fail-proof way:

Find some friends who must learn exactly the same and discuss everything.
Ask someone who has already learned it about appropriate material.
Do many, many exercises.

In my experience, 120 hours of work will get you trough any university test and that is propably more than you want.

This was the single most effective study method I had when I was an undergraduate (maths and physics), though I don't think I came close to 120 hours on any subject.

 

[Kozmos]

I was wondering the same myself...I'm also revitalizing my math skills and want to learn...well everything. So I dug around the blacker parts of the web and found some 60 GBs worth of Math Instruction videos and loads of other pdfs. Once it downloads I'll give you feedback.

 

[madviking]

You could try using KhanAcademy as a resource. It's a nice site where one guy teaches a lot of subjects, especially maths, in short video lectures.
Many people love it. He may be a rising star, and you should definitely check it out.
Here's a nice TED-talk by the founder.

This.

 

[azzaman333]

Find a good textbook with lots of problems, preferably with worked solutions, and do as many problems as required til you understand the concepts you're wanting to learn.