my goal to learn everything there is to learn in the entire branch of mathematics

[andrew112]

I have memorized a great deal about mathematics already, and would like to continue in doing so in order to achieve a permanent knowledge of everything about the entire branch of mathematics. everything that I have learned/memorized so far include various definitions, theorems and formulas from the folloing branches: algebra, trigonometry, geometry, properties and operations of complex numbers, calculus, properties and operations of vectors (although am a bit hazy in this sub branch right now because I have not reviewed that material in quite some time now), discrete algebra, and have touched a little bit on the subject of linear algebra. I still have yet to memorize absolutely everything about the above mentioned subjects, abstract algebra, advanced calculus, tensor calculus, and whatever other subjects there are in the field of mathematics, including the entire history of mathematics. I also have a severe learning/memorization disability which is making this much harder than it should be, so I expect that achieving this goal should take a very long time to achieve.

[pianoperformer]

Good luck. See you in 50 years.

Are you aiming for understanding as well as memorization? That might be slightly difficult (understatement).

[andrew112]

Originally Posted by pianoperformer

Good luck. See you in 50 years.

Are you aiming for understanding as well as memorization? That might be slightly difficult (understatement).

yes, I am also aiming for understanding as well.

[Footballman]

Good luck with that.
If you love mathematics and are very interested in it then it might be possible. For example, take a person who is really interested in flags...they don't need to 'try' and remember because that isn't how the mind works - they just remember things because they are very interested in them, perhaps aided by the odd recap.
My 'thing' is that I know a lot about soccer/football and I can remember players, matches, who scored, where the game took place, what boots they wore from a decade ago (i'm only in 20's). No memorization techniques are used, the mind just 'absorbs' it because it is interested in it.

So if you are interested in the entire branch of mathematics then it shouldn't be much of a problem.

[Daffy Duck]

In all of my math classes, and in my experience, I was taught that "memorizing" math formulas and procedures is not the best way. Eventually it can become hard to memorize it all when the steps become very complicated. "Understanding" math -- the WHY instead of the HOW -- is how you develop true math skill. It's about developing insight.

This link explains what I mean: Study Hacks » Blog Archive » How to Ace Calculus: The Art of Doing Well in Technical Courses

Are you taking college math courses? Teaching yourself?

[andrew112]

Originally Posted by Daffy Duck

Are you taking college math courses? Teaching yourself?

I am just reading textbooks on my own and teaching myself. the way that I figure it, why should I go to college when I can just learn all of that stuff on my own?

[Daffy Duck]

Originally Posted by andrew112

I am just reading textbooks on my own and teaching myself. the way that I figure it, why should I go to college when I can just learn all of that stuff on my own?

Whew. You must really be dedicated. Do you give yourself tests?

I do much better learning in a classroom environment. Back in Fall '08 I tried teaching Trig to myself (since my online teacher was practically a ghost) and found it much more difficult than normal. I received my first B, which isn't bad, but below normal. I also learned to not take online math classes. Good semester!

This site has helped me greatly with Calculus: Pauls Online Math Notes

[andrew112]

Originally Posted by Daffy Duck

Whew. You must really be dedicated. Do you give yourself tests?

yes, I do give myself tests. for example, I will mentally ask myself, "ok, so what are the three definitions for the limit (in great detail and word-for-word exactly the way the textbook expalins it)?" and then I will try to write down or mentally recite all three definitions of the limit, or whatever else I may ask myself. I also try to review the same material over and over again to ensure that I really drill the information deep down into my brain, or, in a way, "tatoo" or "imprint" my brain with the information.

[pianoperformer]

OK, but word-for-word memorization is useless in math. You'd be better off reading about a concept, and doing a bunch of example problems to make sure you understand it.

What's your goal for this whole thing? I mean it could take you years to do this, all for what end?

[andrew112]

Originally Posted by pianoperformer

OK, but word-for-word memorization is useless in math. You'd be better off reading about a concept, and doing a bunch of example problems to make sure you understand it.

What's your goal for this whole thing? I mean it could take you years to do this, all for what end?

word-for-word memorization is not useless in math because if one wants to memorize a formal definition of, let's say, the limit word-for-word, that is not useless.

I am not really sure what exactly my goal is in memorizing and understanding the entire branch of mathematics. all I know is that atleast it is something positive, or in other words, something that contributes towards overall health.

[Daffy Duck]

Have you tried written tests?

If I send you a Calculus 1 test I took in the past, would you like to give it a try and see how you do? Might help assess what you know. I have the solutions.

[andrew112]

Originally Posted by Daffy Duck

Have you tried written tests?

If I send you a Calculus 1 test I took in the past, would you like to give it a try and see how you do? Might help assess what you know. I have the solutions.

I have not studied the entire branch of calculus yet so I would probably not do well on the test, as the test can consist of anything in the branch of calculus.

[aelle]

Given that math is still being researched all over the world and that numerous new theorems are published daily, this sounds like a Danaides' barrel to me...

But hey, good for you for picking such an ambitous goal and pushing it as far as you can.

[alainplus]

I'm also not saying you shouldn't do it. If you love it go ahead, but I believe a field as old as mathematics has a substantial amount of material that you probably will never get through. If anything, at most, all you will do is get summarizations of different branches. In any case, you're going to find yourself favoring a certain branch of mathematics over others, in the same way you favor mathematics over say... evolutionary biology.

It's like saying, I'm going to read every good piece of literature in the world. You can't. You wouldn't even be able to get through the decent books published in the last 50 years. Or even 10 years.

In the long run, it's always best to opt for specialization instead of generalizing.

[Daffy Duck]

Originally Posted by andrew112

I have not studied the entire branch of calculus yet so I would probably not do well on the test, as the test can consist of anything in the branch of calculus.

The test wouldn't consist of anything. It's a Calculus One course. Single variable.

But anyway, that's cool. I was just trying to be helpful.

[ChaosKiwi]

Wow andrew112 this makes me excited about math! And I failed calculus in a pretty big way in high-school! (I know the responsibility was on me but the calculus teacher was my arch nemesis)

I wish you all the best in this endeavor. I would love to do something like this with technical drawing as the subject.

[thenzengineer]

andrew, all the best. I think its real great of you to do what you are doing, especially since you have a learning difficulty. Keep at it, don't expect to observe everything in the mathematics branch but try as much as you can. Wish you success in your endeavour.

[Plato]

What do you love most about mathematics?

My humble opinion is that this will be very unlikely without an incredible passion for the mathematical approach. The people who devote their lives to the subject absolutely love it.

I did a year of a mathematics degree, and my lasting impression was that the professors were obsessed with the subject. It clearly rocked their worlds.

[gbarv]

You may like to use a Spaced Repetition System, it works great to learn foreign words, but I don't know how it would work for math formulas. But be sure to understand before commiting to memory.

If been also experimenting with incremental reading, it may be useful.

[andrew112]

Originally Posted by Plato

What do you love most about mathematics?

My humble opinion is that this will be very unlikely without an incredible passion for the mathematical approach. The people who devote their lives to the subject absolutely love it.

I did a year of a mathematics degree, and my lasting impression was that the professors were obsessed with the subject. It clearly rocked their worlds.

I think my favorite branch of mathematics so far is discrete algebra and complex numbers (properties and operations of complex numbers), probably because they are a couple of the more obscure and abstract branches of mathematics. complex numbers deal with both real and imaginary numbers. discrete algebra deals with aspects such as sequences and sums, summation formulas (which I find fascinating for some reason), infinite series, etc. I have just recently started studying calculus (limits), and am enjoying that as well.

[Brutha]

Memorizing math is besides the point. Books are good at remembering.
At university we usually get one or two pages of paper that we can take with us into math exams as remembering that stuff isn't the point. In one exam we could even take as many books as we would like with us.

If you want to understand math the mathematical way you have to ask yourself how you can use the definition for the limit to prove the theorems that you have at your course.

word-for-word memorization is not useless in math because if one wants to memorize a formal definition of, let's say, the limit word-for-word, that is not useless.

But in math you don't get any advantage from knowing the word-for-word definition.
It doesn't help you to understand what the definition is about.

Either you can use the definition of the limit to prove things or you can't. Knowing the words of a particular expression doesn't help.

Or you just want to use math to solve real world problem but then you don't need definitions at all.

Could you write out a proof of the mean value theorem from hand (you can look up definitions but not the proof itself)?

[andrew112]

Originally Posted by Brutha

Memorizing math is besides the point. Books are good at remembering.
At university we usually get one or two pages of paper that we can take with us into math exams as remembering that stuff isn't the point. In one exam we could even take as many books as we would like with us.

If you want to understand math the mathematical way you have to ask yourself how you can use the definition for the limit to prove the theorems that you have at your course.
But in math you don't get any advantage from knowing the word-for-word definition.
It doesn't help you to understand what the definition is about.

Either you can use the definition of the limit to prove things or you can't. Knowing the words of a particular expression doesn't help.

Or you just want to use math to solve real world problem but then you don't need definitions at all.

Could you write out a proof of the mean value theorem from hand (you can look up definitions but not the proof itself)?

I have not gotten to the proof for the mean value theorem from scratch yet, but I do know how to prove limits of both linear and quadratic functions using the epsilon-delta definition of limit.

Here is a proof for the limit of 3x - 2 as x approaches 2, which equals 4. Throughout the proof I will use "[" and "]" to notate absolute value.

lim (3x - 2) = 4.
x->2

We must show that for each epsilon>0, there exists a delta>0 such that [(3x - 2) - 4]<epsilon whenever 0<[x - 2]<delta. Because our choice of delta depends on epsilon, we need to establish a connection between the absolute values of [(3x - 2) - 4] and of [x - 2].

[(3x - 2) - 4] = [3x - 6] = 3[x - 2].

So, for a given epsilon>0 we can choose delta = epsilon/3. This choice works because

0<[x - 2]<delta = epsilon/3
implies that
[(3x - 2) - 4] = 3[x - 2]<3(epsilon/3) = epsilon.

And that is how my textbook taught me to use the epsilon-delta definition of limit to prove the limit of a linear function. I also know how to use the same definition to prove the limit of a quadratic function.

[Plato]

Originally Posted by andrew112

I think my favorite branch of mathematics so far is discrete algebra and complex numbers (properties and operations of complex numbers), probably because they are a couple of the more obscure and abstract branches of mathematics. complex numbers deal with both real and imaginary numbers. discrete algebra deals with aspects such as sequences and sums, summation formulas (which I find fascinating for some reason), infinite series, etc. I have just recently started studying calculus (limits), and am enjoying that as well.

What is it about discrete algebra and complex numbers that you really love? Why are they your favourite?

Do you find beauty in the solutions? Do you enjoy the challenge of trying to solve a problem and then enjoying the *click* when you finally get it.

I always found there are few greater highs in life than solving a tough problem. Then I discovered binge drinking and girls and it all went haywire.

[andrew112]

Originally Posted by Plato

What is it about discrete algebra and complex numbers that you really love? Why are they your favourite?

Do you find beauty in the solutions? Do you enjoy the challenge of trying to solve a problem and then enjoying the *click* when you finally get it.

I always found there are few greater highs in life than solving a tough problem. Then I discovered binge drinking and girls and it all went haywire.

probably because they are the more abstract and obscure branches of mathematics, and because they are not the more common branches.

[CoolBee]

Originally Posted by Plato

I always found there are few greater highs in life than solving a tough problem. Then I discovered binge drinking and girls and it all went haywire.

I still haven't found a guy as satisfying as solving a really big hard math problem. I spent 60 hours solving a general relativity problem once and the high I got from that was fantastic, my brain and body were on fire for hours.

Unfortunately I told my boyfriend it was better than s*x ... erm... he was very pissed off and dumped me. C'est la vie

[Plato]

Originally Posted by CoolBee

I still haven't found a guy as satisfying as solving a really big hard math problem. I spent 60 hours solving a general relativity problem once and the high I got from that was fantastic, my brain and body were on fire for hours.

Unfortunately I told my boyfriend it was better than s*x ... erm... he was very pissed off and dumped me. C'est la vie

Hahahaha.

You are awesome.

[AlwaysLearning]

This thread makes me really happy, since I'm a 3rd year math phd student myself Just getting ready to take the generals in the summer, then only the dissertation remains

About memorization. A lot of people are echoing the sentiment, "rote memorization is bad". I believe this is a rare example of mathematical dogma. What started as a loose rule of thumb-- try to understand things, not just memorize them-- is often taken way overboard until memorization is demonized.

People need to put more faith in their subconscious minds. When you're enthusiastic about a subject, memorizing it will AUTOMATICALLY lead to understanding it.

Compare it to languages. If you try to learn, say, Japanese by carefully understanding every detail of the grammar, you'll never learn the language. Even if you already had all the vocabulary, consciously thinking about grammar is just too freakin slow when tongues are flapping and words are flying. The only way to learn the language is to get the grammar in your subconscious mind through tons and tons of exposure and practice-- in other words, rote memorization.

I wrote an article about rote memorization in math: Rote Memorization In Mathematics

[Daffy Duck]

That's hilarious, CoolBee.

Good points, AlwaysLearning. I think a balanced look at the whole works best. Of course not all memorization is bad, but it usually needs to be combined with other techniques and ways of understanding.

I'm not ever that excited by math. My passion is computers and since I'm in computer engineering, math is an important tool but not something I live for. It is an extremely interesting topic though. One of my professors just loves math to death.

[aelle]

Originally Posted by CoolBee

I still haven't found a guy as satisfying as solving a really big hard math problem. I spent 60 hours solving a general relativity problem once and the high I got from that was fantastic, my brain and body were on fire for hours.

Unfortunately I told my boyfriend it was better than s*x ... erm... he was very pissed off and dumped me. C'est la vie

Aw yeah. Mathematical orgasms are the best.

[blondandfun]

I have a similar desire to understand the world... I think it's very cool of you.

This actually gives me an idea of an information product (which i'm keeping secret).

As an engineer who's applied math to real world I feel like I know more than my old math professors in some subjects, and that I could teach it better.

I think that math is just words in another language. It's my opinion that words alone can replace math if done correctly.

For example one of five means 1/5, etc...