Disability solely in mathematical comprehension

[FishmanGeertz]

I have a severe learning disability solely in mathematical comprehension, possibly dyscalculia. I was given a lot of special assistance in high school to help me graduate. I was able to graduate with a diploma with only basic arithmetic. Most of the algebra, geometry, trigonometry and so forth, were omitted. I excelled in every other subject and got a 3.6 GPA.

I have some questions about advanced-level mathematics.

*What do the letters (variables) mean in algebraic equations?

*What do the symbols, like the greek letters (constants) mean in calculus?

*What applications do algebra, geometry, trig and calculus have in daily life?

I want to continue my education and get a good job, but a lot of these schools have advanced mathematics on their admission tests, and I have no idea what I'm doing when it comes to these matters.

 

[chiro]

I have a severe learning disability solely in mathematical comprehension, possibly dyscalculia. I was given a lot of special assistance in high school to help me graduate. I was able to graduate with a diploma with only basic arithmetic. Most of the algebra, geometry, trigonometry and so forth, were omitted. I excelled in every other subject and got a 3.6 GPA.

I have some questions about advanced-level mathematics.

*What do the letters (variables) mean in algebraic equations?

*What do the symbols, like the greek letters (constants) mean in calculus?

*What applications do algebra, geometry, trig and calculus have in daily life?

I want to continue my education and get a good job, but a lot of these schools have advanced mathematics on their admission tests, and I have no idea what I'm doing when it comes to these matters.

Hi there.

1)

The Letters (variables) mean things that can change and that are not fixed. Say you have one variable, picture a piece of string: if go forward (ie to the right), the value of the variable increases and if you go to the left the value decreases.

You can like systems of variables where some variables have constraints (ie they can't be anything they want, they have rules about what they can be).

2)

I'm not exactly sure what you mean by greek letters, so maybe if you could give more information, I might be able to answer

3)

Lets start with algebra.

Algebra allows us to make sense of things involving variables. Linear algebra provides the tools to look at variables that have a power of 1. For example x + y = 2 is a linear equation but x^2 + y = 2 is not a linear relationship because of the x^2.

Typically what happens in mathematics is that we have information and we turn that into some kind of mathematical expression.

So here is a practical example: a fishery. Let's say you have an ocean, lake, whatever where your fish are and where the fishers get their fish.

Now you've got a couple of situations, the fishers can take too much fish and after a while they will go extinct, you can get a certain number of fish each year and the birth rate will be the same as the fishing rate which means the number of fish should roughly stay the same, and the third is that you don't get many fish and fish breed fast which makes the population of the fish grow over time.

So the mathematician (or scientist) creates a set of mathematical expressions that says if we get so many fish and if the fish breed at this rate then there will be this many fish left after a harvest.

So after the mathematician (or scientist) figures out the value where if you fish more than the value they become extinct, they write up a presentation and presents to some body like department of agriculture or something of that sort that in order to have fish next year you have to fish less than a certain value.

So what has happened is that the mathematician (or scientist) has basically helped save the fish from coming extinct so that we can fish after every harvest to eat.

Trigonometry

This is used everywhere.

Video games use it. When you are playing your Halo, or Doom, or any other 3D game, the computer will do many sine and cosine functions per frame. When the player rotates, a matrix full of these sine and cosine things are calculated. When you play your Half-Life 2 and shoot a box, again many cosine and sine terms are calculated.

Physics requires trigonometry especially when resolving forces relative to some basis. Think about building structures when you've got all of these different forces and stresses acting on the structure.

Geometry.

Again in video games, everything is geometry. You collide into a wall, you need a way to detect that and to do that you need to work with things like planes in 3 dimensions as well as rays. You need to calculate lighting? You need geometry. Take for example the latest games like Doom 3 (I know its not "latest" but anyway). You see some pretty good lighting methods. Basically the intensity is calculated with regard to the angle between the light vector and the surface vector.

Also shadows are geometric. Poly-type classification uses geometry. Binary Spaced Partition Trees use it, Convex Hulls use it, pretty much every kind of poly-type classification uses it.

Any kind of engineering and science uses geometry.

Think about designing aircraft, buildings, bridges, and so on. You will create things with geometry.

There are tonnes more things, but hopefully that will give you a taste of how this kind of stuff is used in the real world.

 

[FishmanGeertz]

Hi there.

1)

The Letters (variables) mean things that can change and that are not fixed. Say you have one variable, picture a piece of string: if go forward (ie to the right), the value of the variable increases and if you go to the left the value decreases.

You can like systems of variables where some variables have constraints (ie they can't be anything they want, they have rules about what they can be).

2)

I'm not exactly sure what you mean by greek letters, so maybe if you could give more information, I might be able to answer

3)

Lets start with algebra.

Algebra allows us to make sense of things involving variables. Linear algebra provides the tools to look at variables that have a power of 1. For example x + y = 2 is a linear equation but x^2 + y = 2 is not a linear relationship because of the x^2.

Typically what happens in mathematics is that we have information and we turn that into some kind of mathematical expression.

So here is a practical example: a fishery. Let's say you have an ocean, lake, whatever where your fish are and where the fishers get their fish.

Now you've got a couple of situations, the fishers can take too much fish and after a while they will go extinct, you can get a certain number of fish each year and the birth rate will be the same as the fishing rate which means the number of fish should roughly stay the same, and the third is that you don't get many fish and fish breed fast which makes the population of the fish grow over time.

So the mathematician (or scientist) creates a set of mathematical expressions that says if we get so many fish and if the fish breed at this rate then there will be this many fish left after a harvest.

So after the mathematician (or scientist) figures out the value where if you fish more than the value they become extinct, they write up a presentation and presents to some body like department of agriculture or something of that sort that in order to have fish next year you have to fish less than a certain value.

So what has happened is that the mathematician (or scientist) has basically helped save the fish from coming extinct so that we can fish after every harvest to eat.

Trigonometry

This is used everywhere.

Video games use it. When you are playing your Halo, or Doom, or any other 3D game, the computer will do many sine and cosine functions per frame. When the player rotates, a matrix full of these sine and cosine things are calculated. When you play your Half-Life 2 and shoot a box, again many cosine and sine terms are calculated.

Physics requires trigonometry especially when resolving forces relative to some basis. Think about building structures when you've got all of these different forces and stresses acting on the structure.

Geometry.

Again in video games, everything is geometry. You collide into a wall, you need a way to detect that and to do that you need to work with things like planes in 3 dimensions as well as rays. You need to calculate lighting? You need geometry. Take for example the latest games like Doom 3 (I know its not "latest" but anyway). You see some pretty good lighting methods. Basically the intensity is calculated with regard to the angle between the light vector and the surface vector.

Also shadows are geometric. Poly-type classification uses geometry. Binary Spaced Partition Trees use it, Convex Hulls use it, pretty much every kind of poly-type classification uses it.

Any kind of engineering and science uses geometry.

Think about designing aircraft, buildings, bridges, and so on. You will create things with geometry.

There are tonnes more things, but hopefully that will give you a taste of how this kind of stuff is used in the real world.

http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering

 

[Robert1986]

In simple arithmetic, you might have to solve a problem like this:

what is 5 + 3?

or

what is 5-3

or

what is 6*3

or

what is 6/3?Hopefully you know the answers to these questions. In algebra, however, you answer questions like this:

If 6+a = 9, what does a equal?As you go on in algebra, this will turn into something else, but to be honest, that takes a lot to explain. If you haven't done algebra, don't even open a calculus book. Get an algebra book. When you read the algebra book, come back and ask more specific questions.

 

[Fredrik]

I have a severe learning disability solely in mathematical comprehension, possibly dyscalculia. I was given a lot of special assistance in high school to help me graduate. I was able to graduate with a diploma with only basic arithmetic. Most of the algebra, geometry, trigonometry and so forth, were omitted. I excelled in every other subject and got a 3.6 GPA.

I have some questions about advanced-level mathematics.

*What do the letters (variables) mean in algebraic equations?

*What do the symbols, like the greek letters (constants) mean in calculus?

*What applications do algebra, geometry, trig and calculus have in daily life?

I want to continue my education and get a good job, but a lot of these schools have advanced mathematics on their admission tests, and I have no idea what I'm doing when it comes to these matters.

You should probably post specific problems that you're having difficulties with so that you can get more specific advice. The letters represent numbers. It's as simple as that. Some letters are considered "constant symbols" or "constants", while others are considered "variable symbols" or "variables". The only difference between variables and constants is that variables can represent different numbers in different math problems (or even in different calculations that are part of the solution to a single math problem), while constants (like pi) always represents the same number. Unfortunately, some letters are sometimes used as constants and sometimes as variables.

Using letters to represent numbers is very useful e.g. when you want to say something about all numbers. For example, you know that 5+3=3+5, and that 4+6=6+4, but you can't list every pair of numbers, so when you want to say that the order can always be reversed, in a clear, unambiguous way, you say something like this: "For all numbers x and y, x+y=y+x".

If you're concerned about equations, the right question to ask is "what does 'solve this equation' mean?". If you're asked to "solve the equation x²-2x+1=0", you're being asked to "find all numbers that you can substitute for x in that equality without making the equality a false statement".

If you're wondering why you're allowed to e.g. add the same number to both sides of an equation, the reason is (think before you put your mouse pointer over the spoiler)

Spoiler

that the equality sign means that you already have the same number on both sides, so when you add 3 to both sides of the equation x-3=1, you're really adding 3 to both sides of 1=1, and 1+3=1+3 is certainly true whenever 1=1 is true. (It always is of course).

 

[AC130Nav]

I have a severe learning disability solely in mathematical comprehension, possibly dyscalculia. I was given a lot of special assistance in high school to help me graduate. I was able to graduate with a diploma with only basic arithmetic. Most of the algebra, geometry, trigonometry and so forth, were omitted. I excelled in every other subject and got a 3.6 GPA.
I have some questions about advanced-level mathematics.
*What do the letters (variables) mean in algebraic equations?
*What do the symbols, like the greek letters (constants) mean in calculus?
*What applications do algebra, geometry, trig and calculus have in daily life?
I want to continue my education and get a good job, but a lot of these schools have advanced mathematics on their admission tests, and I have no idea what I'm doing when it comes to these matters.

I have a young friend whom I help with her homework (hates math). She couldn't write her questions so coherently. Why do I think these questions are, perhaps, part of gathering ideas for a paper?

 

[Angry Citizen]

*What do the letters (variables) mean in algebraic equations?

It depends on the context. When you have expressions (called functions) that look like this:

y=mx+b

Then m is a real number (in other words, 2 or 6 or 11/7 or 3.14159265359 or 1.717), b is also a real number, x is the letter you 'plug' real numbers into, and y is what gets spit out as a result. x is nearly always what you might call the 'independent variable'. It's called an 'independent variable' because it's usually the letter you replace with a number in order to calculate the value of y. But of course, in mathematics, none of the letters need to be exactly the same for the expression to be essentially the same thing. For instance:

z=at+b

Is the exact same expression. The exact same expression, mind you. All that would change is the value of a or the value of b.

When you're thoroughly grounded in calculus, you are introduced to the idea of functions in two, three, four, five, ... , n variables. In this context, 'n' is simply however many variables you could ever possibly want. You could have functions with ten trillion, five hundred and one billion, three hundred and sixty two million, hundred and eighty six thousand, thirteen variables -- though I think if anything but a Cray supercomputer looked at it, they'd faint!

*What do the symbols, like the greek letters (constants) mean in calculus?

Same thing they mean in algebra. Pi is an interesting number that pops up all over the place in calculus. So is e (2.717 -- it's the natural base discovered by a man named Euler). Delta is often used to express the idea of a 'change'. For instance, if I wanted to know the 'change in the variable x', I'd label the expression delta-x. Usually it means that you take some second value of x, then subtract it from a first value of x. When you get into calculus, it becomes much clearer what happens when that change gets really really small. In fact, the entire language of calculus is based on what happens as delta-x becomes infinitely small.

*What applications do algebra, geometry, trig and calculus have in daily life?

Well, most skills in algebra aren't going to be used much in the direct sense, no matter what profession you're in. Algebra like that taught in schools is mostly a toolbox. You learn to be comfortable with expressions involving letters, how to manipulate them, how you change them, etc. This is all just preparation for really useful stuff, like trigonometry and calculus, which uses these techniques quite a bit. I will say this though: algebra is great at making people understand and be comfortable with numbers.

Can't tell you anything about geometry. Never took a course in it. I regret it somewhat thought. I've seen some instances where it'd be useful to know something from geometry when dealing with a physics problem.

Trig is everywhere. Trig is one of the most useful things you could ever know. Trig is in physics (anything that has repetitive motion has a trig function in it, such as the motion of an ideal spring), in chemistry (helpful for modeling the geometric interpretations of molecular structures), in biology (the double-helix famously seen in DNA is in fact a representation of two trig functions related parametrically -- don't worry if you don't understand what parametric equations are, you learn about them in calculus), in espionage (for instance, if a spy satellite captured an image of a person with the sun at a good angle, you could use trigonometry to estimate the person's height based on his shadow, which gives you an indication of if he's a male or female), and in innumerable other applications.

Calculus is everything. I can't name anything in modern society that doesn't need to be analyzed with calculus. With calculus, you can calculate how to price some object for sale based on its demand. You can use calculus to approximate complicated math problems through the use of differentials. Your car's shape was probably dictated by an optimization of wind flow through the use of calculus. Your computer is pretty much screwed without vector calculus. Calculus is the language of the gods.

I hope this helps.