History UsefulNotes / MathCurriculum

** HISTORY: before calculators, people used slide rules (which were themselves invented in the 1600's), which work sliding rulers with logarithmic scales.

*** "ln" is Log[[subscript:''e'']] and is called the "natural log". It uses "euler's[[note]]Pronounce "euler" as "oil-er"[[/note]] number". ''e'' is special like pi, but instead equals "2.71828...".

->''"Calculus isn't scary, but the amount of ''algebra'' you have to do for it '''is''' scary."''

->''"Mathematics as we know it ... could never have come into being without some disregard for the dangers of the infinite."''
-->-- '''David Bressoud'''

Calculus isn't actually scary, but the amount of ''algebra'' you have to do for it is the scary part. Sometimes the derivative of an equation can be far more complicated than the original equation.

* Algebra introduces '''variables''', which are denoted by letters (Usually "x", but ''any'' letter or symbol will do).

** While we are on word problems no one is expecting you to frequently come across some of the problems you will see in class and on tests. "Bob is 16 and is four times as old as Alice. How old will Bob be when he is twice Alice's age?", You'll see these because they requires multiple steps of algebra to complete. (Assign values, find a formula, solve the formula, check your work, etc)

** While we are on word problems no one is expecting you to frequently come across some of the problems you will see in class and on tests. "Bob is 16 and is four times as old as Alice. How old will Bob be when he is twice Alice's age?", but you'll see it because it requires a few steps of algebra to complete. (Assign values, find a formula, solve the formula, check your work), and ''the unknown you will be looking for will not actually be the answer to the question''.[[note]]The Bob and Alice question is a real word problem, and the answer is Bob will be 24, and Alice will be 12. The unknown you'll need to solve it for is "how many years before or after right now will they reach that age?''[[/note]]

** While we are on word problems no one is expecting you to frequently come across some of the problems you will see in class and on tests. "Bob is 16 and is four times as old as Alice. How old will Bob be when he is twice Alice's age?", but you'll see it because it requires a few steps of algebra to complete. (Assign values, find a formula, solve the formula, check your work), and ''the unknown you will be looking for will not actually be the answer to the question''.[[note]]The Bob and Alice question is a real word problem, and the answer is Bob will be 24, and his sister will be 12. The unknown you'll need to solve it for is "how many years before or after right now will they reach that age?[[/note]]

* Math and English will collide as you spend some time ''learning how to translate word problems into an equation you can solve''.

* Math and English will collide as you spend some time '''learning how to translate word problems into an equation you can solve'''.

** Example: What temperature can humans live at? You already know there's more than a single temperature. There's the set of numbers near "room temperature" where we're comfortable, the set of numbers where we need a jacket or air conditioning, and we have the set of many, many temperatures (to infinity both ways) where humans [[SpontaneousHumanCombustion burn to death]] or [[KillItWithIce freeze to death]].

** You need to know your algebra rules here because [[ForWantOfANail one mistake will topple your whole answer]].

Many people point out that calculus isn't actually scary, but the amount of ''algebra'' you have to do for it is scary - and ''they're right''.

*** When typing a fraction in an environment you can't put one over the other (like here on Website/TVTropes); the top goes first and then a slash, like this: Numerator[=/=]Denominator. It's lined up just like when using a division symbol.

But it's not really ''that unpleasant'' a journey, and the view is really spectacular from up there.

The following is a trip down the general [[UsefulNotes/{{Mathematics}} mathematic]] curriculum (classroom plans) through calculus. You're currently somewhere on this path, or can point to a spot you gave up on it. Mind you there are lots of side paths not shown below -- here we're trying to show how one concept moves on to the next level, how simple addition leads up to high-level calculations.

Feel free to read past the point where you understand to. There are no tests or comprehension questions here, but you may learn something new, and may realize you know more math than you thought!

Generally given to teenagers, algebra helps us look at math problems in a new light, showing that some back door work in unexpected directions can give an answer which seemed originally impossible to know. (This part is sometimes it's own class - Algebra 1)

*** Using a calculators' log[[subscript:10]] button you'll see that, log[[subscript:10]] 2 = 0.3010 and log[[subscript:10]] 3 = 0.4771. We know that 2 × 3 = 6. Add those two together (log[[subscript:10]] 2 + log[[subscript:10]] 3)and you get 0.7781... which equals log[[subscript:10]] 6. So, what good is it? Well, before calculators people would sometimes use big books of logs to double-check their multiplication - to multiply 2 by 3 you just had to look up those logs, add them, and then look up the matching answer.

** HISTORY: If you add two logs together, you get the log of the number they give when multiplied. Using a calculators' log[[subscript:10]], log[[subscript:10]] 2 = 0.3010 and log[[subscript:10]] 3 = 0.4771. We know that 2 × 3 = 6. Add those two together (log[[subscript:10]] 2 + log[[subscript:10]] 3)and you get 0.7781... which equals log[[subscript:10]] 6. So, what good is it? Well, before calculators people would sometimes use big books of logs to double-check their multiplication - to multiply 2 by 3 you just had to look up those logs, add them, and then look up the matching answer.

*** "log" is Log(10).
*** "ln" is Log(''e'') and is called the "natural log". It uses "euler's[[note]]Pronounce "euler" as "oil-er"[[/note]] number". ''e'' is special like pi, but instead equals "2.71828...".

** HISTORY: If you add two logs together, you get the log of the number they give when multiplied. Using a calculators' log(10), log 2 = 0.3010 and log 3 = 0.4771. We know that 2 × 3 = 6. Add those two logs together and you get 0.7781... ''which is the log of 6''. So... what good is it? Before calculators, people would sometimes use big books of logs to multiply "quickly" - to multiply 2 by 3 you just had to look up those logs, add them, and then look up the matching answer! This was usually used to double-check a person's multiplication.

*** "ln" is Log(''e'') or "euler's number"[[note]]Pronounce "euler" as "oil-er"[[/note]]. (It's special like pi, but equals 2.71828...), and is called the "natural log".

*** "ln" is Log(''e'') or "euler's number" (It's special like pi, but equals 2.71828...), and is called the "natural log".

** Logs are actually super simple to use but they aren't taught until now because they are based in exponent functions, and math teachers don't want to teach you something you don't have the background for no matter ''how'' helpful it may be.

** There is a log function for every number, but your calculator only has buttons for the two that come up a lot. *** "log" is Log(10).

** HISTORY: If you add two logs together, you get the log of the number they give when multiplied. Using a calculators' log(10), log 2 = 0.3010 and log 3 = 0.4771. We know that 2 × 3 = 6. Add those two logs together and you get 0.7781... ''which is the log of 6''. So... what good is it? Before calculators, people would sometimes use big books of logs to multiply "quickly" - to multiply 2 by 3 you just had to look up those logs, add them, and then look up the matching answer! This was usually used to double-check multiplication.

** HISTORY: If you add two logs together, you get the log of the number they give when multiplied. Using a calculators' log(10), log 2 = 0.3010 and log 3 = 0.4771. We know that 2 × 3 = 6. Add those two logs together and you get 0.7781... ''which is the log of 6''. So... what good is it? Before calculators, people would sometimes use big books of logs to multiply "quickly" - to multiply 2 by 3 you just had to look up those logs, add them, and then look up the matching answer!

** HISTORY: If you add two logs together, you get the log of the number they give when multiplied. Using a calculators' log(10), log 2 = 0.3010 and log 3 = 0.4771. We know that 2 × 3 = 6. Add those two logs together and you get 0.7781... ''which is the log of 6''. So... what good is it? Before calculators, people would sometimes use big books of logs to multiply "quickly" - to multiply 2 by 3 you just had to look up those logs, add them, and then look up matching answer!

** HISTORY: If you add two logs together, you get the log of the number they give when multiplied. Using a calculators' log(10), log 2 = 0.3010 and log 3 = 0.4771. We know that 2(3)=6. Add those two logs together and you get 0.7781... which is the log of 6. So what good is it? In history, people would use big books of logs to multiply quickly - to multiply 2 by 3 you just had to add those logs up and then look up the answer!

** HISTORY: These days you use a calculator to find these functions, but before the the calculator people had to look them up on tables.