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How to learn math?

MouthWash
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10/18/2012 1:02:29 PM
Posted: 4 years ago
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
Posts: 11,204
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10/18/2012 1:44:43 PM
Posted: 4 years ago
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Where do you want to apply it?
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Cody_Franklin
Posts: 9,483
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10/18/2012 1:56:14 PM
Posted: 4 years ago
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.
MouthWash
Posts: 2,607
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10/18/2012 2:32:04 PM
Posted: 4 years ago
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
Posts: 11,204
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10/18/2012 2:53:57 PM
Posted: 4 years ago
At 10/18/2012 2:32:04 PM, MouthWash wrote:
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.

Apply infinite regression analysis to anything and you won't understand how anything works. Eventually you have to go with the assumption that it is "self-evident" or that the proposition is unprovable and assumed to be true. I don't think that knowing the theory behind it will make it easier to understand. Sometimes memorization is the best root. I don't see the purpose of it either.
In any event, in any event most people don't bother doing long multiplication or division. They just get a calculator to do it for them.

Mathematics can be applied to many "real" concepts, but you have to first learn the background of these real concepts in order to apply it. Economics, physics, engineering, chemistry, and finance all require an understanding of math concepts. There are more subjects in the list, although they don't use mathematics as extensively.
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MouthWash
Posts: 2,607
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10/18/2012 5:18:23 PM
Posted: 4 years ago
At 10/18/2012 2:53:57 PM, darkkermit wrote:
At 10/18/2012 2:32:04 PM, MouthWash wrote:
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.

Apply infinite regression analysis to anything and you won't understand how anything works. Eventually you have to go with the assumption that it is "self-evident" or that the proposition is unprovable and assumed to be true. I don't think that knowing the theory behind it will make it easier to understand. Sometimes memorization is the best root. I don't see the purpose of it either.
In any event, in any event most people don't bother doing long multiplication or division. They just get a calculator to do it for them.

Mathematics can be applied to many "real" concepts, but you have to first learn the background of these real concepts in order to apply it. Economics, physics, engineering, chemistry, and finance all require an understanding of math concepts. There are more subjects in the list, although they don't use mathematics as extensively.

I just brute-force logic my way through math problems and I do them all in my head. Interestingly this has served me better than simply memorizing formulas because I actually understand the math.

I would like to apply math to all of those subjects. Just at basic levels, and preferably something relevant to real life because otherwise it isn't any better than a word problem.
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
Posts: 11,204
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10/18/2012 5:31:04 PM
Posted: 4 years ago
At 10/18/2012 5:18:23 PM, MouthWash wrote:
At 10/18/2012 2:53:57 PM, darkkermit wrote:
At 10/18/2012 2:32:04 PM, MouthWash wrote:
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.

Apply infinite regression analysis to anything and you won't understand how anything works. Eventually you have to go with the assumption that it is "self-evident" or that the proposition is unprovable and assumed to be true. I don't think that knowing the theory behind it will make it easier to understand. Sometimes memorization is the best root. I don't see the purpose of it either.
In any event, in any event most people don't bother doing long multiplication or division. They just get a calculator to do it for them.

Mathematics can be applied to many "real" concepts, but you have to first learn the background of these real concepts in order to apply it. Economics, physics, engineering, chemistry, and finance all require an understanding of math concepts. There are more subjects in the list, although they don't use mathematics as extensively.

I just brute-force logic my way through math problems and I do them all in my head.

Bad strategy, especially the more complex the problems get and the more background knowledge that is required. You can't just derive calculus on your own.

Interestingly this has served me better than simply memorizing formulas because I actually understand the math.

I would like to apply math to all of those subjects. Just at basic levels, and preferably something relevant to real life because otherwise it isn't any better than a word problem.

What do you mean "relevant to life"? You could go your whole life without using a lot of math or if its relevant to your work, you could spend a whole lot of time using math.

But here's one:

Assume you put $10,000 in the bank. There are two options:
a) continuous compound interest rate at 6.5%
b) annual compound interest rate at 6.8%

Which one will give you more money after 5 years, assuming that you do not withdraw from the funds.

Basics personal finance problem.
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darkkermit
Posts: 11,204
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10/18/2012 5:34:39 PM
Posted: 4 years ago
At 10/18/2012 5:31:04 PM, darkkermit wrote:
At 10/18/2012 5:18:23 PM, MouthWash wrote:
At 10/18/2012 2:53:57 PM, darkkermit wrote:
At 10/18/2012 2:32:04 PM, MouthWash wrote:
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.

Apply infinite regression analysis to anything and you won't understand how anything works. Eventually you have to go with the assumption that it is "self-evident" or that the proposition is unprovable and assumed to be true. I don't think that knowing the theory behind it will make it easier to understand. Sometimes memorization is the best root. I don't see the purpose of it either.
In any event, in any event most people don't bother doing long multiplication or division. They just get a calculator to do it for them.

Mathematics can be applied to many "real" concepts, but you have to first learn the background of these real concepts in order to apply it. Economics, physics, engineering, chemistry, and finance all require an understanding of math concepts. There are more subjects in the list, although they don't use mathematics as extensively.

I just brute-force logic my way through math problems and I do them all in my head.

Bad strategy, especially the more complex the problems get and the more background knowledge that is required. You can't just derive calculus on your own.

Interestingly this has served me better than simply memorizing formulas because I actually understand the math.

I would like to apply math to all of those subjects. Just at basic levels, and preferably something relevant to real life because otherwise it isn't any better than a word problem.

What do you mean "relevant to life"? You could go your whole life without using a lot of math or if its relevant to your work, you could spend a whole lot of time using math.

But here's one:

Assume you put $10,000 in the bank. There are two options:
a) continuous compound interest rate at 6.5%
b) annual compound interest rate at 6.8%

Which one will give you more money after 5 years, assuming that you do not withdraw from the funds.

Basics personal finance problem.

and how much money do you get under each condition.
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MouthWash
Posts: 2,607
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10/18/2012 5:43:38 PM
Posted: 4 years ago
At 10/18/2012 5:34:39 PM, darkkermit wrote:
At 10/18/2012 5:31:04 PM, darkkermit wrote:
At 10/18/2012 5:18:23 PM, MouthWash wrote:
At 10/18/2012 2:53:57 PM, darkkermit wrote:
At 10/18/2012 2:32:04 PM, MouthWash wrote:
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.

Apply infinite regression analysis to anything and you won't understand how anything works. Eventually you have to go with the assumption that it is "self-evident" or that the proposition is unprovable and assumed to be true. I don't think that knowing the theory behind it will make it easier to understand. Sometimes memorization is the best root. I don't see the purpose of it either.
In any event, in any event most people don't bother doing long multiplication or division. They just get a calculator to do it for them.

Mathematics can be applied to many "real" concepts, but you have to first learn the background of these real concepts in order to apply it. Economics, physics, engineering, chemistry, and finance all require an understanding of math concepts. There are more subjects in the list, although they don't use mathematics as extensively.

I just brute-force logic my way through math problems and I do them all in my head.

Bad strategy, especially the more complex the problems get and the more background knowledge that is required. You can't just derive calculus on your own.

Interestingly this has served me better than simply memorizing formulas because I actually understand the math.

I would like to apply math to all of those subjects. Just at basic levels, and preferably something relevant to real life because otherwise it isn't any better than a word problem.

What do you mean "relevant to life"? You could go your whole life without using a lot of math or if its relevant to your work, you could spend a whole lot of time using math.

But here's one:

Assume you put $10,000 in the bank. There are two options:
a) continuous compound interest rate at 6.5%
b) annual compound interest rate at 6.8%

Which one will give you more money after 5 years, assuming that you do not withdraw from the funds.

Basics personal finance problem.

and how much money do you get under each condition.

Hold up, I just spotted this.
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
MouthWash
Posts: 2,607
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10/18/2012 5:46:51 PM
Posted: 4 years ago
At 10/18/2012 5:34:39 PM, darkkermit wrote:
At 10/18/2012 5:31:04 PM, darkkermit wrote:
At 10/18/2012 5:18:23 PM, MouthWash wrote:
At 10/18/2012 2:53:57 PM, darkkermit wrote:
At 10/18/2012 2:32:04 PM, MouthWash wrote:
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.

Apply infinite regression analysis to anything and you won't understand how anything works. Eventually you have to go with the assumption that it is "self-evident" or that the proposition is unprovable and assumed to be true. I don't think that knowing the theory behind it will make it easier to understand. Sometimes memorization is the best root. I don't see the purpose of it either.
In any event, in any event most people don't bother doing long multiplication or division. They just get a calculator to do it for them.

Mathematics can be applied to many "real" concepts, but you have to first learn the background of these real concepts in order to apply it. Economics, physics, engineering, chemistry, and finance all require an understanding of math concepts. There are more subjects in the list, although they don't use mathematics as extensively.

I just brute-force logic my way through math problems and I do them all in my head.

Bad strategy, especially the more complex the problems get and the more background knowledge that is required. You can't just derive calculus on your own.

Interestingly this has served me better than simply memorizing formulas because I actually understand the math.

I would like to apply math to all of those subjects. Just at basic levels, and preferably something relevant to real life because otherwise it isn't any better than a word problem.

What do you mean "relevant to life"? You could go your whole life without using a lot of math or if its relevant to your work, you could spend a whole lot of time using math.

But here's one:

Assume you put $10,000 in the bank. There are two options:
a) continuous compound interest rate at 6.5%
b) annual compound interest rate at 6.8%

Which one will give you more money after 5 years, assuming that you do not withdraw from the funds.

Basics personal finance problem.

and how much money do you get under each condition.

$3,250
And I don't know how to translate numbers to percentages; otherwise I could do the next one in my head.
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
Posts: 11,204
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10/18/2012 5:50:11 PM
Posted: 4 years ago
At 10/18/2012 5:46:51 PM, MouthWash wrote:
At 10/18/2012 5:34:39 PM, darkkermit wrote:
At 10/18/2012 5:31:04 PM, darkkermit wrote:
At 10/18/2012 5:18:23 PM, MouthWash wrote:
At 10/18/2012 2:53:57 PM, darkkermit wrote:
At 10/18/2012 2:32:04 PM, MouthWash wrote:
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.

Apply infinite regression analysis to anything and you won't understand how anything works. Eventually you have to go with the assumption that it is "self-evident" or that the proposition is unprovable and assumed to be true. I don't think that knowing the theory behind it will make it easier to understand. Sometimes memorization is the best root. I don't see the purpose of it either.
In any event, in any event most people don't bother doing long multiplication or division. They just get a calculator to do it for them.

Mathematics can be applied to many "real" concepts, but you have to first learn the background of these real concepts in order to apply it. Economics, physics, engineering, chemistry, and finance all require an understanding of math concepts. There are more subjects in the list, although they don't use mathematics as extensively.

I just brute-force logic my way through math problems and I do them all in my head.

Bad strategy, especially the more complex the problems get and the more background knowledge that is required. You can't just derive calculus on your own.

Interestingly this has served me better than simply memorizing formulas because I actually understand the math.

I would like to apply math to all of those subjects. Just at basic levels, and preferably something relevant to real life because otherwise it isn't any better than a word problem.

What do you mean "relevant to life"? You could go your whole life without using a lot of math or if its relevant to your work, you could spend a whole lot of time using math.

But here's one:

Assume you put $10,000 in the bank. There are two options:
a) continuous compound interest rate at 6.5%
b) annual compound interest rate at 6.8%

Which one will give you more money after 5 years, assuming that you do not withdraw from the funds.

Basics personal finance problem.

and how much money do you get under each condition.

$3,250
And I don't know how to translate numbers to percentages; otherwise I could do the next one in my head.

which condition?
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MouthWash
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10/18/2012 5:55:26 PM
Posted: 4 years ago
By the way, it's pretty obvious that B would give me more money. This would be interesting if B had a lower interest rate but was compound.
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
Posts: 11,204
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10/18/2012 5:55:54 PM
Posted: 4 years ago
At 10/18/2012 5:50:11 PM, darkkermit wrote:
At 10/18/2012 5:46:51 PM, MouthWash wrote:
At 10/18/2012 5:34:39 PM, darkkermit wrote:
At 10/18/2012 5:31:04 PM, darkkermit wrote:
At 10/18/2012 5:18:23 PM, MouthWash wrote:
At 10/18/2012 2:53:57 PM, darkkermit wrote:
At 10/18/2012 2:32:04 PM, MouthWash wrote:
At 10/18/2012 1:56:14 PM, Cody_Franklin wrote:
At 10/18/2012 1:02:29 PM, MouthWash wrote:
Who would I learn math? I need to learn how to apply it rather than simply learn it abstractly- I've relearned the same concepts over the years and it won't stick. I also want to understand the logic behind the math instead of thinking of it as a bunch of 'number tricks.'

Also, "applying math" isn't the same as "understanding the logic"--the latter is what "learning it abstractly is". Computational math, which is what application tends to be, is what all the tricks are for--use this equation, plug in some numbers, derive answer. Computational math is what you learn in hard disciplines--engineering, architecture, etc. Mathematics as a discipline is where you start to learn it as a grammar.

I find it difficult to remember things unless I practice them in real life. I also want to understand the logic behind math. For instance, when my teacher taught me in first grade how to stack numbers and add them vertically to solve double digit or triple digit addition, I didn't understand why it worked. I just thought of it as a shortcut or trick that I couldn't comprehend. Now I do; not because anyone taught me but because as I got better at understanding numbers the process became clearer.

Math would be a lot easier if I understood these things instead of just memorizing formulas (I have this problem with graph equations now). I never said that applying math and understanding it were the same thing- I want to do both.

Apply infinite regression analysis to anything and you won't understand how anything works. Eventually you have to go with the assumption that it is "self-evident" or that the proposition is unprovable and assumed to be true. I don't think that knowing the theory behind it will make it easier to understand. Sometimes memorization is the best root. I don't see the purpose of it either.
In any event, in any event most people don't bother doing long multiplication or division. They just get a calculator to do it for them.

Mathematics can be applied to many "real" concepts, but you have to first learn the background of these real concepts in order to apply it. Economics, physics, engineering, chemistry, and finance all require an understanding of math concepts. There are more subjects in the list, although they don't use mathematics as extensively.

I just brute-force logic my way through math problems and I do them all in my head.

Bad strategy, especially the more complex the problems get and the more background knowledge that is required. You can't just derive calculus on your own.

Interestingly this has served me better than simply memorizing formulas because I actually understand the math.

I would like to apply math to all of those subjects. Just at basic levels, and preferably something relevant to real life because otherwise it isn't any better than a word problem.

What do you mean "relevant to life"? You could go your whole life without using a lot of math or if its relevant to your work, you could spend a whole lot of time using math.

But here's one:

Assume you put $10,000 in the bank. There are two options:
a) continuous compound interest rate at 6.5%
b) annual compound interest rate at 6.8%

Which one will give you more money after 5 years, assuming that you do not withdraw from the funds.

Basics personal finance problem.

and how much money do you get under each condition.

$3,250
And I don't know how to translate numbers to percentages; otherwise I could do the next one in my head.

which condition?

Yea, you got that wrong either way. Your basing it on a linear interest rate. Compound interest rate is based on exponential increase. The formula is as followed for yearly compounding:
P(i+1)^(t)
P = principle, or initial amount. In this case 10,000
i = interest rate. In this case, 6.8%, or 0.068
t = time, in this case 5 years.
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MouthWash
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10/18/2012 5:57:24 PM
Posted: 4 years ago
Hold on, both of them are compound? Sorry, I misread. >.<
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
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10/18/2012 5:58:21 PM
Posted: 4 years ago
At 10/18/2012 5:55:26 PM, MouthWash wrote:
By the way, it's pretty obvious that B would give me more money. This would be interesting if B had a lower interest rate but was compound.

How about an annual interest rate of 6.8% vs. a compound interest rate of 6.7%.
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darkkermit
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10/18/2012 5:59:00 PM
Posted: 4 years ago
At 10/18/2012 5:57:24 PM, MouthWash wrote:
Hold on, both of them are compound? Sorry, I misread. >.<

sure you did.......
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MouthWash
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10/18/2012 5:59:54 PM
Posted: 4 years ago
At 10/18/2012 5:55:54 PM, darkkermit wrote:
Yea, you got that wrong either way. Your basing it on a linear interest rate. Compound interest rate is based on exponential increase. The formula is as followed for yearly compounding:
P(i+1)^(t)
P = principle, or initial amount. In this case 10,000
i = interest rate. In this case, 6.8%, or 0.068
t = time, in this case 5 years.

I don't understand this. (i+1)^(t)? What does that even mean? Why add 1?
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
MouthWash
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10/18/2012 6:02:10 PM
Posted: 4 years ago
At 10/18/2012 5:58:21 PM, darkkermit wrote:
At 10/18/2012 5:55:26 PM, MouthWash wrote:
By the way, it's pretty obvious that B would give me more money. This would be interesting if B had a lower interest rate but was compound.

How about an annual interest rate of 6.8% vs. a compound interest rate of 6.7%.

Easy. 3,400.
Again, I can't figure the next one out.
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
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10/18/2012 6:02:49 PM
Posted: 4 years ago
At 10/18/2012 5:59:54 PM, MouthWash wrote:
At 10/18/2012 5:55:54 PM, darkkermit wrote:
Yea, you got that wrong either way. Your basing it on a linear interest rate. Compound interest rate is based on exponential increase. The formula is as followed for yearly compounding:
P(i+1)^(t)
P = principle, or initial amount. In this case 10,000
i = interest rate. In this case, 6.8%, or 0.068
t = time, in this case 5 years.

I don't understand this. (i+1)^(t)? What does that even mean? Why add 1?

Do you know what exponential functions are?
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MouthWash
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10/18/2012 6:05:30 PM
Posted: 4 years ago
At 10/18/2012 6:02:49 PM, darkkermit wrote:
At 10/18/2012 5:59:54 PM, MouthWash wrote:
At 10/18/2012 5:55:54 PM, darkkermit wrote:
Yea, you got that wrong either way. Your basing it on a linear interest rate. Compound interest rate is based on exponential increase. The formula is as followed for yearly compounding:
P(i+1)^(t)
P = principle, or initial amount. In this case 10,000
i = interest rate. In this case, 6.8%, or 0.068
t = time, in this case 5 years.

I don't understand this. (i+1)^(t)? What does that even mean? Why add 1?

Do you know what exponential functions are?

Of course I do. I just don't know how they are solved.
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
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10/18/2012 6:07:42 PM
Posted: 4 years ago
At 10/18/2012 6:02:10 PM, MouthWash wrote:
At 10/18/2012 5:58:21 PM, darkkermit wrote:
At 10/18/2012 5:55:26 PM, MouthWash wrote:
By the way, it's pretty obvious that B would give me more money. This would be interesting if B had a lower interest rate but was compound.

How about an annual interest rate of 6.8% vs. a compound interest rate of 6.7%.

Easy. 3,400.
Again, I can't figure the next one out.

you realize you are getting these answers wrong right?

I'll explain it to you.

10,000*.068 = $680 the first year
This is added onto the next sum so that the next sum is:
10,680*.068 = $726.24 gained the second year
Same thing again.
11,406.24*.068 = $775.62 gained the third

However there's a simplified way of doing this which I showed you. This is what you learn in high school math (algebra II), but you dropped out.
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darkkermit
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10/18/2012 6:12:16 PM
Posted: 4 years ago
At 10/18/2012 6:05:30 PM, MouthWash wrote:
At 10/18/2012 6:02:49 PM, darkkermit wrote:
At 10/18/2012 5:59:54 PM, MouthWash wrote:
At 10/18/2012 5:55:54 PM, darkkermit wrote:
Yea, you got that wrong either way. Your basing it on a linear interest rate. Compound interest rate is based on exponential increase. The formula is as followed for yearly compounding:
P(i+1)^(t)
P = principle, or initial amount. In this case 10,000
i = interest rate. In this case, 6.8%, or 0.068
t = time, in this case 5 years.

I don't understand this. (i+1)^(t)? What does that even mean? Why add 1?

Do you know what exponential functions are?

Of course I do. I just don't know how they are solved.

the ^ means its an exponential function. For example 2^4 = 16
2*2*2*2 = 16, which is what 2^4 stands for. Multiplying 2, four times.

Whenever you have exponential growth, you use the equation: (1+growth%)^t.

t = time. So for example if growth rate is 2% a year, you will have (1.02)(1.02)*amount in two years.
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MouthWash
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10/18/2012 6:19:19 PM
Posted: 4 years ago
At 10/18/2012 6:07:42 PM, darkkermit wrote:
At 10/18/2012 6:02:10 PM, MouthWash wrote:
At 10/18/2012 5:58:21 PM, darkkermit wrote:
At 10/18/2012 5:55:26 PM, MouthWash wrote:
By the way, it's pretty obvious that B would give me more money. This would be interesting if B had a lower interest rate but was compound.

How about an annual interest rate of 6.8% vs. a compound interest rate of 6.7%.

Easy. 3,400.
Again, I can't figure the next one out.

you realize you are getting these answers wrong right?

I'll explain it to you.

10,000*.068 = $680 the first year
This is added onto the next sum so that the next sum is:
10,680*.068 = $726.24 gained the second year
Same thing again.
11,406.24*.068 = $775.62 gained the third

However there's a simplified way of doing this which I showed you. This is what you learn in high school math (algebra II), but you dropped out.

I am not learning that in high school. I was learning basic graphing, which I should have known before elementary school ended. As a first grader I found pre-algebra easy, which should tell you something about the education I get.

I reduced the 10,000 to 100 in my head. I then multiplied 5 by 6 to get 30. I took the .8 and multiplied it by ten to give me 8 (38) then divided it in half to get .8 X 5 (34). So 134. I moved the decimal over and got 13,400 which is 10,000 + 3,400.
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
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10/18/2012 6:23:52 PM
Posted: 4 years ago
At 10/18/2012 6:19:19 PM, MouthWash wrote:
At 10/18/2012 6:07:42 PM, darkkermit wrote:
At 10/18/2012 6:02:10 PM, MouthWash wrote:
At 10/18/2012 5:58:21 PM, darkkermit wrote:
At 10/18/2012 5:55:26 PM, MouthWash wrote:
By the way, it's pretty obvious that B would give me more money. This would be interesting if B had a lower interest rate but was compound.

How about an annual interest rate of 6.8% vs. a compound interest rate of 6.7%.

Easy. 3,400.
Again, I can't figure the next one out.

you realize you are getting these answers wrong right?

I'll explain it to you.

10,000*.068 = $680 the first year
This is added onto the next sum so that the next sum is:
10,680*.068 = $726.24 gained the second year
Same thing again.
11,406.24*.068 = $775.62 gained the third

However there's a simplified way of doing this which I showed you. This is what you learn in high school math (algebra II), but you dropped out.

I am not learning that in high school. I was learning basic graphing, which I should have known before elementary school ended. As a first grader I found pre-algebra easy, which should tell you something about the education I get.

I reduced the 10,000 to 100 in my head. I then multiplied 5 by 6 to get 30. I took the .8 and multiplied it by ten to give me 8 (38) then divided it in half to get .8 X 5 (34). So 134. I moved the decimal over and got 13,400 which is 10,000 + 3,400.

You dropped out, hence why you never learned it. Its something you learn in algebra II.
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MouthWash
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10/18/2012 6:36:44 PM
Posted: 4 years ago
At 10/18/2012 6:23:52 PM, darkkermit wrote:
At 10/18/2012 6:19:19 PM, MouthWash wrote:
At 10/18/2012 6:07:42 PM, darkkermit wrote:
At 10/18/2012 6:02:10 PM, MouthWash wrote:
At 10/18/2012 5:58:21 PM, darkkermit wrote:
At 10/18/2012 5:55:26 PM, MouthWash wrote:
By the way, it's pretty obvious that B would give me more money. This would be interesting if B had a lower interest rate but was compound.

How about an annual interest rate of 6.8% vs. a compound interest rate of 6.7%.

Easy. 3,400.
Again, I can't figure the next one out.

you realize you are getting these answers wrong right?

I'll explain it to you.

10,000*.068 = $680 the first year
This is added onto the next sum so that the next sum is:
10,680*.068 = $726.24 gained the second year
Same thing again.
11,406.24*.068 = $775.62 gained the third

However there's a simplified way of doing this which I showed you. This is what you learn in high school math (algebra II), but you dropped out.

I am not learning that in high school. I was learning basic graphing, which I should have known before elementary school ended. As a first grader I found pre-algebra easy, which should tell you something about the education I get.

I reduced the 10,000 to 100 in my head. I then multiplied 5 by 6 to get 30. I took the .8 and multiplied it by ten to give me 8 (38) then divided it in half to get .8 X 5 (34). So 134. I moved the decimal over and got 13,400 which is 10,000 + 3,400.

You dropped out, hence why you never learned it. Its something you learn in algebra II.

I don't care; I don't need school to learn it. Now, what exactly is wrong with my solution?
"Well, that gives whole new meaning to my assassination. If I was going to die anyway, perhaps I should leave the Bolsheviks' descendants some Christmas cookies instead of breaking their dishes and vodka bottles in their sleep." -Tsar Nicholas II (YYW)
darkkermit
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10/18/2012 6:48:30 PM
Posted: 4 years ago
At 10/18/2012 6:36:44 PM, MouthWash wrote:
At 10/18/2012 6:23:52 PM, darkkermit wrote:
At 10/18/2012 6:19:19 PM, MouthWash wrote:
At 10/18/2012 6:07:42 PM, darkkermit wrote:
At 10/18/2012 6:02:10 PM, MouthWash wrote:
At 10/18/2012 5:58:21 PM, darkkermit wrote:
At 10/18/2012 5:55:26 PM, MouthWash wrote:
By the way, it's pretty obvious that B would give me more money. This would be interesting if B had a lower interest rate but was compound.

How about an annual interest rate of 6.8% vs. a compound interest rate of 6.7%.

Easy. 3,400.
Again, I can't figure the next one out.

you realize you are getting these answers wrong right?

I'll explain it to you.

10,000*.068 = $680 the first year
This is added onto the next sum so that the next sum is:
10,680*.068 = $726.24 gained the second year
Same thing again.
11,406.24*.068 = $775.62 gained the third

However there's a simplified way of doing this which I showed you. This is what you learn in high school math (algebra II), but you dropped out.

I am not learning that in high school. I was learning basic graphing, which I should have known before elementary school ended. As a first grader I found pre-algebra easy, which should tell you something about the education I get.

I reduced the 10,000 to 100 in my head. I then multiplied 5 by 6 to get 30. I took the .8 and multiplied it by ten to give me 8 (38) then divided it in half to get .8 X 5 (34). So 134. I moved the decimal over and got 13,400 which is 10,000 + 3,400.

You dropped out, hence why you never learned it. Its something you learn in algebra II.

I don't care; I don't need school to learn it. Now, what exactly is wrong with my solution?

Because the amount of money you receive increases exponentially. Your making the money increase linearly. With exponential growth, you receive a greater share of money the next year then the previous year. I already showed you why this is:

10,000*.068 = $680 the first year
This is added onto the next sum so that the next sum is:
10,680*.068 = $726.24 gained the second year
Same thing again.
11,406.24*.068 = $775.62 gained the third

Notice how your getting more and more money each year. Your assuming 680 each year. But that's not how it works. If you don't understand it, that's fine: I'm not a teacher. But you can easily do a youtube search for "compound interest rates" or "exponential functions" to learn this.

Of course you don't need a high school degree to learn this stuff, but at the very least you need motivation and discipline, in which you convey neither?

Why do you want to learn this stuff? Most of the crap you learn in high school is completely useless. Unless you want a career that requires you to learn this stuff or there's specifically something you want to do that requires you to do this, its worthless.
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Korashk
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10/18/2012 6:58:34 PM
Posted: 4 years ago
At 10/18/2012 6:36:44 PM, MouthWash wrote:
I reduced the 10,000 to 100 in my head. I then multiplied 5 by 6 to get 30. I took the .8 and multiplied it by ten to give me 8 (38) then divided it in half to get .8 X 5 (34). So 134. I moved the decimal over and got 13,400 which is 10,000 + 3,400.

I don't care; I don't need school to learn it. Now, what exactly is wrong with my solution?

I can't speak for darkkermit, but I have no idea why you're doing anything after you moved the decimal to make 10,000 into 100. If you explain your rationale I could critique your methods.
When large numbers of otherwise-law abiding people break specific laws en masse, it's usually a fault that lies with the law. - Unknown
bossyburrito
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10/18/2012 7:07:52 PM
Posted: 4 years ago
Math has always been hard for me for the same reason. I'm realllyyyy bad at memorization.
#UnbanTheMadman

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Or lose the race to rats
Get caught in ticking traps
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To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

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darkkermit
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10/18/2012 7:13:59 PM
Posted: 4 years ago
At 10/18/2012 7:07:52 PM, bossyburrito wrote:
Math has always been hard for me for the same reason. I'm realllyyyy bad at memorization.

you just solve enough problems and it becomes memorized automatically. I don't consider math to be memorization though. Maybe languages or history, but not math. I rarely studied for exams. Probably the only few times were in college and for my AP calculus exam.
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