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#1 2014-06-08 10:17:39

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

What is useful to memorize?

So I have been going through a lot of  basic math I kind of already know and haven't been finding it ridiculously easy which it should be. I have been noticing some gaps in my knowledge when doing some problems too. For example I barely know my times tables to 10 and know my square numbers to 12. Cube numbers to 6. I was doing a multi - step problem which took me forever because I didn't realize these two, 3-4 digit numbers were cube numbers which could be factored out and then I would have the difference of two squares. Also I have found out things like prime factors in the denominator tell you whether you have a rational or irrational number. I'm just wondering what is useful to memorize now since I'm lacking.

I'm just wondering what it is I should memorize:
times tables up to what?
square and cube numbers upto what?
2^n ? 3^ ???]
divisibility rules
prime numbers upto what?
cumulative, commutative, associative laws
definitions?
proofs?
identities?

I'm not interested in calculus or any college mathematics yet. I just want to make sure I am mastering 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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#2 2014-06-08 11:55:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

Hi PatternMan;

Why listen to what I have to say about it? When something is bothering you deeply there is a reason for that. It means do something about it. I think you already know what you need and want to do.

For example I barely know my times tables to 10 and know my square numbers to 12. Cube numbers to 6. I was doing a multi - step problem which took me forever because I didn't realize these two, 3-4 digit numbers were cube numbers which could be factored out and then I would have the difference of two squares.

Looks like you have already established how much of each you need. Do it and see if that makes you feel better because your performance is better. At the next brick wall you will have new ideas...

Rant:

I will tell you why I hate the modern school system. I do not know about other countries but they took the times table out of the learning process over here. Kids do not know what 7 x 6 is anymore. Can not subtract 17 from 20. The school board and the rest of the creatures that determine what will be and will not be taught said it was cruel to make a kid learn those things. Arithmetic is part of computation and computation they said was not math.

hysterical-laughter-smiley-emoticon.gif

Pardon that burst of laughter but I do not often get a chance to laugh at their conclusions.

Those same creatures then said no calculators. Now here is my question, if he/she can not add or multiply and are not going to be taught how, is it really a good idea to take the calculators away? They think so!

Do not believe me? Here is a conversation I had with a teacher from the Big Apple.

http://www.mathisfunforum.com/viewtopic … 78#p148978

End Rant:

Now for my advice, if not knowing the times table is hindering your learning, then the answer is simple.


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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#3 2014-06-08 12:43:56

ShivamS
Member
Registered: 2011-02-07
Posts: 3,629

Re: What is useful to memorize?

PatternMan wrote:

times tables up to what?

 

To be honest, you need none. Know what it means by multiplication and you should be able to do it easily. If you want a number, do it until 12. I don't really know beyond that either, but I can calculate the multiplication of three-digit numbers in a couple of seconds. Is it because I memorized it? No.

PatternMan wrote:

square and cube numbers upto what?
2^n ? 3^ 5
divisibility rules

As much as you want.

PatternMan wrote:

prime numbers upto what?

Doesn't really matter.

PatternMan wrote:

cumulative, commutative, associative laws

You need to memorize all the axioms including those, but they are obvious enough especially with intuition. What is the cumulative law?

PatternMan wrote:

definitions?

Well, you need to know what the words mean but you don't have to memorize definitions verbatim.

PatternMan wrote:

proofs?

Learn how to prove instead.

PatternMan wrote:

identities?

Learn the common ones, derive the others.

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#4 2014-06-09 09:19:17

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

Re: What is useful to memorize?

bobbym wrote:

Hi PatternMan;
Rant:

I will tell you why I hate the modern school system. I do not know about other countries but they took the times table out of the learning process over here. Kids do not know what 7 x 6 is anymore. Can not subtract 17 from 20. The school board and the rest of the creatures that determine what will be and will not be taught said it was cruel to make a kid learn those things. Arithmetic is part of computation and computation they said was not math.

http://www.sherv.net/cm/emo/laughing/hysterical-laughter-smiley-emoticon.gif

Pardon that burst of laughter but I do not often get a chance to laugh at their conclusions.

http://www.mathisfunforum.com/viewtopic … 78#p148978

End Rant:

I actually never learnt my timestables because I noticed shortcuts. I just realized that multiplication was just counting the number n amount of times, or repeated addition. Well you could call it the distributive property. Doubling is the 2 times table. 4 and 8 are double doubles or triple doubles. without memorizing timestables you can work the rest out only knowing addition and subtraction. 3 * table = double the number and add it to itself. 5* table ended up in memory without trying. 6 table = 5 table + 1. 9 = 10 table - 1. That only leaves the 7 and 8 times table which may take a bit longer. But yes it's better to memorize for the long run.


"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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#5 2014-06-09 09:30:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

Hi;

What I meant is it is better to know them then to not to. If you can calculate them quickly that is fine, if you can not then you should memorize them.


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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#6 2014-06-09 12:30:52

Chris2
Member
From: Gallifrey
Registered: 2014-04-23
Posts: 1,761
Website

Re: What is useful to memorize?

bobbym wrote:

Hi PatternMan;

I will tell you why I hate the modern school system. I do not know about other countries but they took the times table out of the learning process over here. Kids do not know what 7 x 6 is anymore. Can not subtract 17 from 20. The school board and the rest of the creatures that determine what will be and will not be taught said it was cruel to make a kid learn those things. Arithmetic is part of computation and computation they said was not math.

About the same here, we don't do maths we read maths and we have to write a long poem to follow it afterwards. its like a literature class...

Last edited by Chris2 (2014-06-09 12:32:31)


Love your enemies and those who persecute you. Forgive others the way God forgives you.
Time Lord from Gallifrey also a M.

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#7 2014-06-09 12:38:55

ShivamS
Member
Registered: 2011-02-07
Posts: 3,629

Re: What is useful to memorize?

Before university, if we didn't define something word by word, we would get a mark off.

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#8 2014-06-09 19:34:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

we have to write a long poem to follow it afterwards. its like a literature class...

You have to write a poem about math? That is interesting.


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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#9 2014-06-09 19:38:12

Chris2
Member
From: Gallifrey
Registered: 2014-04-23
Posts: 1,761
Website

Re: What is useful to memorize?

I mean how we feel about the question like was it hard or easy how did you solved it and the likes. I hate it!


Love your enemies and those who persecute you. Forgive others the way God forgives you.
Time Lord from Gallifrey also a M.

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#10 2014-06-09 19:40:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

It is good practice to do things you hate, it prepares you for when you will be working.


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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#11 2014-06-09 20:13:18

Chris2
Member
From: Gallifrey
Registered: 2014-04-23
Posts: 1,761
Website

Re: What is useful to memorize?

bobbym wrote:

It is good practice to do things you hate, it prepares you for when you will be working.

I know, but these are unnessasory. Who the hell read maths? We have to remember how to write how we feel and how we did it in our exams. It's time consuming. And also, it's unfair for those that is not good in english.


Love your enemies and those who persecute you. Forgive others the way God forgives you.
Time Lord from Gallifrey also a M.

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#12 2014-06-10 02:04:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

Seems that school is the same all over.


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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#13 2014-06-10 02:14:22

Chris2
Member
From: Gallifrey
Registered: 2014-04-23
Posts: 1,761
Website

Re: What is useful to memorize?

PatternMan wrote:

I'm just wondering what it is I should memorize:
times tables up to what?
square and cube numbers upto what?
2^n ? 3^ ???]
divisibility rules
prime numbers upto what?
cumulative, commutative, associative laws
definitions?
proofs?
identities?

I'm not interested in calculus or any college mathematics yet. I just want to make sure I am mastering the basics.

Don't think about calculus or college mathematics for now, you should know the times table well ( This might help http://www.mathsisfun.com/timestable.html).
Cube numbers to 15 and square numbers to 30.
You don't have to know "prime numbers up to what" A prime number is a number that is not inside the multiplication table.

Last edited by Chris2 (2014-06-10 02:17:02)


Love your enemies and those who persecute you. Forgive others the way God forgives you.
Time Lord from Gallifrey also a M.

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#14 2014-06-10 02:20:08

ShivamS
Member
Registered: 2011-02-07
Posts: 3,629

Re: What is useful to memorize?

To be honest he should know perfect squares to 20^2 = 400 and cube to about 5^3 = 125 or 6^3. He can calculate the rest if needed.

Last edited by ShivamS (2014-06-10 03:54:05)

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#15 2014-06-10 02:22:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

6^3, 7^3, 11^3, 10^3 of course and the powers of 2 will come in handy and eventually get memorized.


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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#16 2014-06-10 03:51:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: What is useful to memorize?

I agree on 6^3. I'm not sure why you would need 7^3 and 11^3, though.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#17 2014-06-10 03:53:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

Can you immediately tell me what they equal? I bet you can, that means you have seen them so much you have memorized them. Why wait?


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.

Offline

#18 2014-06-10 03:53:53

ShivamS
Member
Registered: 2011-02-07
Posts: 3,629

Re: What is useful to memorize?

bobbym wrote:

Can you immediately tell me what they equal? I bet you can, that means you have seen them so much you have memorized them. Why wait?

Yes, but only because I have used it in certain problems. Not every one encounters the same problems.

Last edited by ShivamS (2014-06-10 04:00:45)

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#19 2014-06-10 03:56:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: What is useful to memorize?

bobbym wrote:

Can you immediately tell me what they equal? I bet you can, that means you have seen them so much you have memorized them. Why wait?

7^3, no. 11^3  neither, but I can calculate that one pretty quickly in my head.

I agree on 6^3, though, because everyone who does even a little bit of combinatorics will see that number.

10^3 is pretty straightforward.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#20 2014-06-10 04:00:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

7^3 = 343, I have seen it so much I know it off hand. 11^3 also because it pops up in recreational number theory questions.


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.

Offline

#21 2014-06-30 04:12:59

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

Re: What is useful to memorize?

Currently memorizing:

cube numbers upto 12
divisibility rules
binomial expansion to degree 5, difference of squares

I'm wondering if I should bother trying my own proof and memorizing the proofs for things such as:
(-a)(-b) = ab

I didn't even learn any of these rules. I just know   
+ times + = +
- times - = +
- times + = -   

or the same signs = + different signs = -   I had no idea these worked because of other rules that are derived. I'm just wondering if it will hurt me later on. I just learnt a=-b if a+b = 0. I could write a basic proof because of this new knowledge where I substituted or the identity. I wouldn't have been able to write the proof. This is so basic and I did not know. I'm wondering how much it would benefit me and if I need to prove and memorize these rules and identities because it will take me a while. I don't want any it to haunt me later if I don't memorize them like timestables.

Last edited by PatternMan (2014-06-30 04:21:51)


"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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#22 2014-06-30 04:20:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

cube numbers upto 12 - marginally important
divisibility rules  - What rules do you mean?
binomial expansion to degree 5, difference of squares - Binomial not needed.

+ times + = +
- times - = +
- times + - 

Those are super important.


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.

Offline

#23 2014-06-30 04:24:40

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

Re: What is useful to memorize?

bobbym wrote:

cube numbers upto 12 - marginally important
divisibility rules  - What rules do you mean?
binomial expansion to degree 5, difference of squares - Binomial not needed.

+ times + = +
- times - = +
- times + - 

Those are super important.


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I just learnt this
+ times + = +
- times - = +
- times + - 

and  BIDMAS,  only add like terms, indice rules, linear+quadratic equations, a bit of coordinate geometry. and that pretty much completes your algebra education at school to the degree of a 16 year old.

Last edited by PatternMan (2014-06-30 04:28:23)


"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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#24 2014-06-30 04:31:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: What is useful to memorize?

Math is like any other game. It has rules. It also resembles a language. The more terms you know the more fluently you speak.


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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#25 2014-07-11 02:51:27

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

Re: What is useful to memorize?

Finished memorizing all the above. xD I'm starting to think I can actually get good at math in the time I wanted.


"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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