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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 174

What are the methods you use to learn mathematics? Do you learn definitions, proofs, do problems etc? I just want some tips. I wonder if there's anything I can do to improve my learning or speed it up.

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

Do you learn definitions, proofs, do problems etc?

Problems, problems and more problems.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 174

bobbym wrote:

Do you learn definitions, proofs, do problems etc?

Problems, problems and more problems.

Doing easy problems only seems to help for a little bit. It just helps you get the procedure down. After that you literally repeat the procedure to solve the problem or use another procedure you know that works. Other than that only doing more difficult problems help me to get better because I think of steps to problem solve and refine my understanding of the rules.

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,555

Yes! I don't ever do any routine exercises - but I don't get them in my textbooks anyway.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

The thing about math is there really isn't any easy problems. You can only tell how hard a problem is when you start to work on it. It is an illusion to think that you will ever know everything even about a problem you can solve. For instance, you solve a problem and you are happy with your solution until someone comes up and shows you a better one and points out everything you missed. Happen to you yet? Do not worry, it will.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**eigenguy****Member**- Registered: 2014-03-18
- Posts: 78

bobbym wrote:

The thing about math is there really isn't any easy problems.

It was so tempting to post "2 + 2 = ?" in response to this.

But alas, if someone were to do that to me, I would have returned with a considerable discussion upon the meaning of "number", "addition", "2", and perhaps even "=". So I guess I have to acquiesce to the point.

One thing that I always found helpful is that when I would learned something, I always thought about how I would try to teach it to someone else. In particular, why this is the way it ought to be. This would force me to look at it in different ways, and often resulted in my developing a deeper understanding of the subject. (This was a learning exercise only, though! When I started teaching classes - part of any graduate program - I quickly learned that much of how I thought things ought to be taught was definitely NOT how they should be taught. I pity now those who endured through my first couple of years.)

"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,555

For me, especially through a more rigorous book like Rudin which is full of theorems and proofs, I like to read the explanation first. Afterwards, as soon as I encounter the word "Theorem", I stop and try to prove the theorem on my own. Thereafter I read whatever corollary or remarks and then move on to the problems.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 174

bobbym wrote:

The thing about math is there really isn't any easy problems. You can only tell how hard a problem is when you start to work on it. It is an illusion to think that you will ever know everything even about a problem you can solve. For instance, you solve a problem and you are happy with your solution until someone comes up and shows you a better one and points out everything you missed. Happen to you yet? Do not worry, it will.

This actually happened to me today. I used a verbose procedure to come to a solution. Then I saw there was a much simpler procedure that only involved a few steps. It was the same answer though. I don't really understand what you're saying yet though since I'm only doing the basics.

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

I don't really understand what you're saying yet though since I'm only doing the basics.

That is okay, I rarely understand what that fellow says either. He seems to speak gibberish, jabberwocky or kaboobly doo as he calls it.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**SteveB****Member**- Registered: 2013-03-07
- Posts: 557

Define the problem well and the meaning of things to avoid ambiguarity, make sure you have understood it correctly. Proofs are not always essential, but in practice courses will expect you to be able to prove things in maths so yes you do have to be able to prove things and it can help your understanding if you do prove them at some level at least. In practice exercises are essential because you need your brain to get the benefit of the exercise and it helps with understanding of any piece of maths to do some kind of exercise or exercises on the thing. Being a spectator and watching maths is not usually very good for learning it. It is rather like a sport - you have to do it in order to get better etc...

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