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#1 2014-05-09 10:31:39

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Learning mathematics fast

Thank you bobbym for stating how important memorization is. Memorization has a bad rap but it's good. The reason it's bad is because people memorize the procedure and rules rather than understanding the underpinnings. They memorize the surface material. It is like a kid that memorizes and follows a recipe to make a cake vs a person that knows how to make cakes. The memorizer will follow the procedure not really understanding anymore than that. The cake maker will know why he uses the materials he does. The first knows "how", the second knows "why".

I think I have a new method to learn Mathematics very fast by doing less problems, but more memorizing and thinking. I actually want to start a challenge at the end of June to see how much I can learn in a period of time. It will be high school math stuff.

Algebra & Functions
Trigonometry
Sequences & Series
Coordinate Geometry
Algebra & Series
Differentiation
Integration


"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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#2 2014-05-09 12:47:31

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

I will start by what I think of your plan. It is almost precisely the same as what I did and it is a doable and good plan. I went through all that material in a week. After that, I did lots and lots of problems and went through the material rigorously.

With that plan, are you planning to use some of the books I advised you to?

Here is what I have to say about memorization (read it if you have time):
Note that memorizing and remembering are two different things.


While math is a very beautiful structure that you could possibly build up from scratch every time, nobody actually has the time for this. For example, if I have a differential equation to solve and have to show some integral converges, I can of course build up the entire integration theory from scratch. But that won't get me very far if I need to do it every time. It's better to have memorized the properties (and of course to understand why they're true!) and then just apply those properties to show that the integral converges.

A lot of people always say there is little memorization involved in mathematics, but I really disagree. You can't do advanced mathematics like functional analysis or differential geometry without remembering all the stuff that came before. In my students, I see that the person who still remembers a lot of the previous material has a real and definite advantage over the rest.

While memorization is derided in some quarters, knowing basic facts like the multiplication tables or how to carry out an algorithm like long division is always useful. If you have to stop and derive everything you do from first principles all the time, you'll never be able to progress.

Memorizing everything is not required as long as you can remember where to find the information you need. That's why it's important to have handy good reference works or to know how to search for information online or in a library.

Some things are useful to memorize, such as the quadratic formula, trig identities, and the pythagorean theorem. But it is much more important to learn when and how to apply these things than it is to memorize them. The ones that you use most often you will probably end up memorizing through repetition anyway.

The large majority of math involves understanding the underlying processes and how to apply them - basically why we use the formulas and methods we do, why they work, and (in higher math) how they were derived.

Remembering (though not necessarily by rote) things is a crucially necessary but insufficient condition to success in science or mathematics.

Last edited by ShivamS (2014-05-09 12:47:42)

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#3 2014-05-10 06:56:57

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

ShivamS wrote:

I went through all that material in a week. After that, I did lots and lots of problems and went through the material rigorously.
.

Either you were studying like 10 hours a day or you're smarter than you try to appear. lol I plan to go through all of that in 4-6 months. If I manage to do it faster I will be very happy.


"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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#4 2014-05-10 07:56:20

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

Hi;

I presumed that since you were out of school and did not have a job yet, you would be doing 10+ hours a day, which is why I mentioned that I did that material in a similar plan in a week.

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#5 2014-05-10 08:05:24

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

ShivamS wrote:

Hi;

I presumed that since you were out of school and did not have a job yet, you would be doing 10+ hours a day, which is why I mentioned that I did that material in a similar plan in a week.

<-- can't focus more than 90 minutes unless it's a video game. roflol  hence I do 3 hours max. I think I do 7 hours a week right now. That and I have other responsibilities like jobsearching to do. I will probably be forced to do some work soon.

Last edited by PatternMan (2014-05-10 08:07:21)


"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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#6 2014-05-10 08:06:31

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

Then it will take you longer, but doable in a few months.

Are you at least planning to do lots of problems afterwards?

Which books are you planning to use?

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#7 2014-05-10 08:09:12

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

ShivamS wrote:

Then it will take you longer, but doable in a few months.

Are you at least planning to do lots of problems afterwards?

Which books are you planning to use?

Books
Basic Mathematics
Understanding pure mathematics - D. W. S Thorning

websites
mathisfun.com

video tutorials
www.examsolutions.net 
www.m4ths.com

Last edited by PatternMan (2014-05-10 08:13:31)


"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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#8 2014-05-10 08:11:18

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

If you do not plan on doing the problems, "Basic Mathematics" is easily doable in a week with a couple of hours each day. I suggest you complement "Basic Mathematics" with "Geometry" by Lang and the NCERT books, at the very least.

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#9 2014-05-10 08:22:54

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

ShivamS wrote:

If you do not plan on doing the problems, "Basic Mathematics" is easily doable in a week with a couple of hours each day. I suggest you complement "Basic Mathematics" with "Geometry" by Lang and the NCERT books, at the very least.

I ordered basic mathematics and geometry together so I will do. I might not go through the NCERt books so much. I will only do basic problems at first. I might go through tougher problems after learning the material.


"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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#10 2014-05-10 08:25:13

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

OK, that is a good plan.

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#11 2014-05-13 06:27:47

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

I bought myself a whiteboard to do maths problems on. Now I can put my butt in front of a computer and do problems while being lazy and wipe clean.

$(KGrHqJ,!roFHn-+pV1MBSDJdcD3f!~~60_12.JPG

Last edited by PatternMan (2014-05-13 06:28:02)


"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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#12 2014-05-16 06:46:59

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

Does anyone know of any websites with practice maths questions with solutions? I have a whiteboard I want to do problems on in fron of the pc.

Last edited by PatternMan (2014-05-16 06:47:26)


"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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#13 2014-05-16 06:51:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,455

Re: Learning mathematics fast

Hi;

Have you looked at Mathopolis, 8000+ questions there? Have you tried ganesh's threads, I do them every day?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#14 2014-05-16 07:57:09

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

You will find thousands of interesting but difficult problems from contests on Art of Problem Solving and the books you ordered have many difficult problems to keep you busy.

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#15 2014-05-17 06:18:46

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

ShivamS wrote:

You will find thousands of interesting but difficult problems from contests on Art of Problem Solving and the books you ordered have many difficult problems to keep you busy.

I decided not to do the difficult problems yet. They can be intimidating since you really need mastery of a lot of the basics to understand them. I'm just learning the rules and methods first. Then I'll loop back on myself and go through more difficult problems. Also those books wont be arriving for a little while.


"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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#16 2014-05-17 07:12:37

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

bobbym wrote:

Hi;

Have you looked at Mathopolis, 8000+ questions there? Have you tried ganesh's threads, I do them every day?

Yes I wanted something like this. xD No trig there though.

Last edited by PatternMan (2014-05-17 07:13:21)


"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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#17 2014-05-17 07:19:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,455

Re: Learning mathematics fast

I see about 550 trig questions there.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#18 2014-05-17 07:29:29

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

bobbym wrote:

I see about 550 trig questions there.

links? 
I see this
http://www.mathopolis.com/questions/champions.php


"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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#19 2014-05-17 07:33:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,455

Re: Learning mathematics fast


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#20 2014-05-17 08:09:45

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

Thankyou


"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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#21 2014-05-17 10:27:39

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

You can't do routine problems without the concepts either.

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#22 2014-05-22 05:07:35

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

I recieved my Geometry book today. The book puts most I have read to shame. It explains in a way that gives you a clear framework to conceptualize every concept. If I didn't have a shallow understanding already it would probably be a bit more different. My only qualm with it is that it doesn't have answers to the exercises.


"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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#23 2014-05-22 07:48:59

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

Is it the one by Lang? It will likely be much better than the other books you read, mainly because it has more of a focus on proofs and understanding the material.

Most of the books you will be using henceforth will likely not have any answers because
a) the books are widely used (especially some of the books you will use later are used at several universities, so no solutions book to prevent cheating)
b) many of the problems are not numerical ones (e.g. many of them require proofs)

If there is a problem you can't solve, try to google that problem (you usually can find the solution online, but make sure it is correct and that you understand it) and if that doesn't work post it here.

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#24 2014-05-22 08:47:41

PatternMan
Member
Registered: 2014-03-08
Posts: 181

Re: Learning mathematics fast

Yes it's Serge Lang & Gene Murrow. Okay I will post here if I have any problems. The main problem is I want to make sure I have understood properly.


"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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#25 2014-05-22 08:53:02

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Learning mathematics fast

I have a copy of that book too and I really enjoyed it.

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