Help with advanced learning

kr1305 · 2010-05-02 03:19:34

Hey guys,

Basically, I did maths at school to GSCE standard and loved every bit of it. I left school to join the armed forces, more specifically the RAF, in the position of an ICT Technician. I do electrical engineering, radar theory, electronic fundamentals, networking, servers and all that sort of stuff. My job is loosely related to maths in an ICT based way so we don't do anything too difficult, mainly binary and basic mathematics.

However, I have a real passion for maths and i am very good at quick arithmetic, I can divide and multiply large numbers in seconds and have always been able to do this. Whenever I see a number written down, I always take it apart, add the separate units, divide them, multiply them, or whatever! I've always done this, it's a really weird habit!

But apart from being good at arithmetic, I have no knowledge of some advanced formulae or any of the mathematical functions. My question to you, is can someone give me a structured learning plan or any resources that I should use to further my knowledge?

I know this is a big ask, but I can only really self teach, so I need some advice on how to go about it. If anyone can give me the sort of things I should learn, in which order to do it, where I can learn online and HOW I should do it, it would be a huge help.

Thanks guys :]

Kevin

bobbym · 2010-05-02 04:01:14

Hi Kevin;

That is very interesting I also had that ability to do arithmetic very quickly on large numbers, also the ability to play blindfold chess. These abilities disappear as you get older, at least they did with me.

About your main question. If you want to teach yourself math you have chosen a very difficult task indeed. It can be done to a certain extent. Just remember your self education will be fragmented. You success will be based on your talent and your ability to work, not on how much schooling you've had. This can be heady stuff when you succeed because you have done it by yourself. It can also be extremely depressing when you fail as you can only blame yourself.

Here is what I suggest.

How good are your programming skills? If they are good then:

1) Specialize in a few fields to start. Since you are obviously computer oriented begin with calculus,combinatorics, probability, numerical analysis, linear algebra, graph theory. You will find these will allow you to use your computer skills to assist.

2) Try to get your hands on some CAS. Scour the net you will find them. They will act as a tutor. You can continuously ask them questions and they will answer. They will refine your understanding.

3) Do as many problems in the above fields as you can. I mean that, get them wrong, get them right, it doesn't matter. Just do many problems. Develope your problem solving skills.

4) Hang on forums and butt heads with the best people they have there. Answer questions. Don't be afraid, they will try to push you around at first. As your skills increase you will gain respect. You will develope your own style of problem solving.

5) Begin to expand on the edges of your favorite fields, try to absorb some set theory, topolgy, group theory etc, always expanding on what you already know. This is not too difficult because mathematics has much overlap between specialties.

6) Read, read, read. You will find your own favorite books. Read them until the methods and the books are memorized. Use the internet, it is all there for you.

7) Last, patience you will meet lots of resistance, obstacles.

Will all this take me a very long time? - Caine
Only a lifetime, perhaps a little bit more. - Po

Last points: If you understand these you will always be optimistic.

1) Math is infinite you will never know more than a tiny bit.
2) There will always be someone who knows more than you do, expect that.
3) Some problems will always stump you.
4) Mistakes are part of doing anything, you will always make them.

kr1305 · 2010-05-02 04:56:57

Thank you for a very informative post. Combinatorics interest me a lot! I know barely anything about them but I love the way they work in number patterns and things like that. Alas, my programming knowledge is very basic. I'm limited to basic to intermediate python and little bits of javascript, vb, perl and C++. Apart from that, my knowledge is really limited.
I know nothing of calculus, literally no idea what it involves but I know it is very widely taught and known, so I feel a tad ashamed that I have no prior knowledge of it. However, this will be my first endeavour. I will attempt to teach myself calculus, combinatorics and probability :].

Do you know of any specific websites where there are resources to learn any of the above fields?

Thanks

bobbym · 2010-05-02 05:27:39

Hi kr1305;

You know that is the toughest question to answer. You will have to Google and look through the pages one by one for the ones that will grab you. I don't have specific websites to offer you.

I use these whenever I need them for lots of background math:
http://www.mathsisfun.com/
http://www.mathsisfun.com/algebra/index-college.html
http://www.purplemath.com/modules/index.htm

Books, the best are:

For combinatorics, books by ( Villenkin , Alas S. Tucker, Riordan, Mizrahi and Sullivan ).
For all of it, "Finite mathematics with applications" - Mizrahi and Sullivan 4th ed. - good introductory, easy to learn!

"Numerical analysis 2nd ed." Francis Scheid - a classic. For more, anything by the great Forman S. Acton, the best in the world.

"Learning Mathematics with Micros" Adrian Oldnow - cute but interesting.

When I was 17 I went through "Introduction to Analytical Geometry and Calculus" by Smail, by myself, you can too. Could only get part of it but...

You don't have get this all at once. If you can through a book and get one thing that you can use, you will be lucky. You go back later on to get more.

Whatever your stuck on, post it here and someone will help you with it. This is a tremendous asset, don't waste it. No one has to learn totally on their own anymore.

Math Is Fun Forum

#1 2010-05-02 03:19:34

Help with advanced learning

#2 2010-05-02 04:01:14

Re: Help with advanced learning

#3 2010-05-02 04:56:57

Re: Help with advanced learning

#4 2010-05-02 05:27:39

Re: Help with advanced learning

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