Mathematics Thread

What is the hardest math you learned?

  • Calculus (specify in comments)

    Votes: 69 35.0%

  • Trigonometry

    Votes: 27 13.7%

  • (Enriched) Geometry

    Votes: 18 9.1%

  • Equations (specify)

    Votes: 7 3.6%

  • Graphing Equations (specify)

    Votes: 5 2.5%

  • Basic Algebra (specify)

    Votes: 9 4.6%

  • I can do better!

    Votes: 49 24.9%

  • What kind of math is that?!

    Votes: 13 6.6%
  • Total voters
    197
im a uk maths student in my final year ive done. (each item is 1 module)
1st year
-Geometry, Vectors & Complex Numbers
-Mathematical Thinking
-Intro to Applied Maths
-Computer Applications in Maths
-Sequences and Series
-Numbers
-Differential Equations
-Intro to Probability and Stats
-Calculus
-Linear Algebra

2nd year
-Communicating Mathematics
-Analysis
-Vector Calculus
-Modelling with Differential Equations
-Numerical Methods 1
-Probability Theory
-Fourier Analysis and Partial Differential Equations
-Complex Variables
-Ordinary Differential Equations and Calculus of Variations
-Numerical Methods 2
-Scientific Programming
-Statistical Modelling

Final year
-Number Theory
-Intro to Dynamical Systems
-Inviscid Fluid Mechanics
-Statistical Methods
-Graph Theory
-Intro to Differential Geometry
-Mathematics report
-Applied Complex Analysis
-Metric Spaces
-Linear Differential Equations
-Vibrations and Waves
-Mathematical Biology
 
brandbest1 said:
Somebody tell me what a differential equation is in an easy-to-understand-not-nerdy explanation?
Click to expand...
I can't quite remember the difference between a differential equation and a derivative, but a derivative is a graph of the slope. It's quite simple for a linear equation. Let's say you have y = 2x+3. The slope of that line is 2, so the graph of the derivative would just be a straight line, y = 2. It gets a bit trickier when you deal with more complex equations, but another thing to understand is that non-linear equations, such as parabolas, also have slopes. They just constantly change. For example, the slope of a parabola at it's vertex would be 0. If you zoomed in enough at that point, it would start to look like a straight, horizontal line.
 
tozies24 said:
Yep all three last year. Now I am taking partial differential equations, advanced multivarible, and then last semester I had advanced linear algebra.
Click to expand...

Ah that sounds like a blast. lol. I haven't taken any of those. I use the math I have taken sparingly enough as it is. Though we are using advanced linear algebra on some nuclear reactor design models now - and it's been 4 years since I've taken them so I'm just O___O atm.
 
Here's a math problem/riddle that no one can figure out.

There are four people that want to cross a bridge. Sam can cross in 1 minute, Joe can cross in 2, Jack can cross in 5, and Steve can cross in 10. They have one flashlight, and two can cross at a time, but they must go at the same pace. So if Steve and Sam cross together, they must go at 10 minutes. The partners must use a flashlight, and one must bring it right back. They must cross in 16 minutes or less. How?

I know how, but nobody else does, for some reason.
 
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Best i can do is 17 minutes on that Sam takes Joe(2), Sam comes back(+1 =3), Jack takes Steve(+10 = 13), Joe comes back(+2 = 15), Sam takes Joe back over(+2 = 17). Basically Sam and Joe are helping out their fat friends and their roles could be changed for the same time. How u get 16? pretty sure its impossible
 
brandbest1 said:
Somebody tell me what a differential equation is in an easy-to-understand-not-nerdy explanation?
Click to expand...
With a regular algebraic equation, the variables are signified with letters such as x and represent NUMBERS. In differential equations, variables (also signified with letters such as x) represent FUNCTIONS. An example of a function, as you know, is f (x) = x^2. So, instead of looking at an algebraic equation asking yourself "which number can I substitute in for all x's in the equation to have both sides equal," you ask the same thing, but instead of a number, you ask "what function..."

There are many different types of differential equations (DE's), and so the above explanation is very ambiguous and only partially true for the more complicated DE types.

Now, in algebra, as I have said already, the equations' variables represent numbers. In DE's, the variables are functions (such as f (x) ). So, once you have found the solution to the differential equation, you may substitute in numbers into the function you found to get a numerical value. A common numerical value letter used is t for TIME. Differential equations are at least partially made up of derivative variables, just as algebraic equations are at least partially made up of numerical variables. A derivative is a function which is the rate of change of another function. That is, when you substitute numerical values into the derivative function, you get the slope (rate of change) of the function it is a derivative of at that x-value (number you plugged into the derivative function).

Algebra
f (x)...=..., x is the variable: x = number

Differential equations
[f (t)]'...= ..., [f (t)]' is the variable, f (t) is a function, and t is a number (often represents a numerical time value).

[f (t)]' means "the rate of change of function f(t), or the derivative of f(t).

(So differential equations have one thing extra, derivatives).

Lastly, in algebra, if a single equation has more than one solution, it must have infinite solutions. For example, consider the single equation with TWO unknowns. x + 2y = 6. There are an infinite number of solutions for x and y. Similarly, differential equations have infinite solutions in the same sense because they can also have variables in them which represent numbers.

As an example of how an DE can have infinite solutions (by also having variables which represent numbers and not functions), here is one of the most simple differential equations (known as a single anti-derivative/integral problem in calculus):

[f (x)]' = 1
​

This is read "the rate of change (slope) of what function f (x) is equal to one for the given x value."

From the slope intercept formula, y(x) = mx + b, m is the slope. (Note that f (x) and y(x) mean the same thing: both are functions of x). m here is equal to [f (x)]' and happens to be a number and not a function. (I wrote below the DE, "the rate of change (slope) of what function f (x) is equal to one for the given x value." The given x value IS x, that is, it represents ALL possible values of x.)

You probably can guess that the solution is f (x) = x, because

f (x) = 1x is the same as f(x) = x.
​

However, this solution is actually infinite because, isn't the slope of f(x) = x + 5 also 1? Yep. So the solution to the DE above is really f(x) = x +c, where c can be any number (y-intercept = (b of the slope intercept formula) ).

I hope that helps. It's difficult to define what a differential equation is with the person describing it to doesn't know calculus yet, as Sarah said.
 
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This thread is like Finnegan's Wake, I can only understand half the words.
 
IanTheCuber said:
Here's a math problem/riddle that no one can figure out.

There are four people that want to cross a bridge. Sam can cross in 1 minute, Joe can cross in 2, Jack can cross in 5, and Steve can cross in 10. They have one flashlight, and two can cross at a time, but they must go at the same pace. So if Steve and Sam cross together, they must go at 10 minutes. The partners must use a flashlight, and one must bring it right back. They must cross in 16 minutes or less. How?

I know how, but nobody else does, for some reason.
Click to expand...
I have to ask: is this some cheesy riddle with one of those really stupid answers like "they made another flashlight," or "the other two swam next to the bridge," or is there a genuine way to do this?
 
IanTheCuber said:
Here's a math problem/riddle that no one can figure out.

There are four people that want to cross a bridge. Sam can cross in 1 minute, Joe can cross in 2, Jack can cross in 5, and Steve can cross in 10. They have one flashlight, and two can cross at a time, but they must go at the same pace. So if Steve and Sam cross together, they must go at 10 minutes. The partners must use a flashlight, and one must bring it right back. They must cross in 16 minutes or less. How?

I know how, but nobody else does, for some reason.
Click to expand...

After getting 17, I believed it was impossible to get 16 (I had my reasons to believe it), so I looked it up.
I found this, which is basically the same thing (just different wording). According to this, 17 is the lowest that is possible, so 16 is in fact impossible.
 
IanTheCuber said:
Here's a math problem/riddle that no one can figure out.

There are four people that want to cross a bridge. Sam can cross in 1 minute, Joe can cross in 2, Jack can cross in 5, and Steve can cross in 10. They have one flashlight, and two can cross at a time, but they must go at the same pace. So if Steve and Sam cross together, they must go at 10 minutes. The partners must use a flashlight, and one must bring it right back. They must cross in 16 minutes or
less. How?

I know how, but nobody else does, for some reason.
Click to expand...

Are you sure about your "solution"?

If they don't have to go at the same pace:
Sam and Steve go, with Steve carrying the flashlight. Steve stops after a minute (when Sam finishes crossing), and goes back. (2 mins)
Steve and Joe go, with Steve carrying the flashlight. Steve stops after 2 minutes (when Joe finishes crossing), and goes back. (4 mins)
Steve and Jack go, with Jack being right behind Steve the whole time. (10 mins)

This doesn't completely make sense though since Sam and Joe don't travel with the flashlight, but it's only a bridge that takes them one and two minutes to cross.


edit: Maybe Steve can aim the flashlight to the end of the bridge so that Sam and Joe can see their way to the end.
 
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I love maths. I've been doing research on my own on various problems and theorems, even came up with something on my own.

I'd like to see different ways to solve this:

Proof that

3h7q8.png
 
So I'm homeschooling 5th grade, but I'm doing Algebra 1a and 1b. The hardest part to me is the equations, I don't know why.
 
I'm a homeschooled highschool freshman (that's fun to say). I took Algebra 1 and 2 combined last year in 8th grade, so I'm in Geometry in 9th. I'm speeding through Geometry, because it's pretty easy, so I'll probably start Trig in a couple weeks. I don't know how long that'll take, so I might be doing that partway into next year, and then I guess I'll take pre-calc, as a sophmore/junior and Calculus I as a junior/senior. Hopefully I can finish trig this summer, and then I could be in Calculus II as a senior!

Poll: I'm voting for Equations, because I struggled with Algebra I equations - like time, motion (especially), age problems, etc, but Algebra II and Geometry are easy.

What is the "standard" system of math for public schools? Is it 8th = prealgebra, 9th = Algebra I, 10th = Geometry, 11th = Algebra II, 12th = Trig? Or is it Algebra I in 8th, Geo in 9th, Algebra2 in 10th, trig in 11th, and precalc in 12th?
 
Ickathu said:
What is the "standard" system of math for public schools? Is it 8th = prealgebra, 9th = Algebra I, 10th = Geometry, 11th = Algebra II, 12th = Trig? Or is it Algebra I in 8th, Geo in 9th, Algebra2 in 10th, trig in 11th, and precalc in 12th?
Click to expand...
In our school system, we have either Pre-Algebra 7th, Algebra 8th, Geometry 9th, Algebra II 10th, and so on. You could also have Pre-Algebra in both 7th and 8th, Algebra I in 9th, and so on. There's also Algebra in 7th, Geometry in 8th, and so on. The most advanced kids at my school are in Geometry as 6th graders, so Algebra II in 7th, Pre-Calculus in 8th and so on.
 
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