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### Course: Algebra (all content)>Unit 1

Lesson 1: Overview and history of algebra

# The beauty of algebra

Algebra is a language that helps us understand the world around us. It's not just about numbers, it's about abstract ideas that can be applied to many areas like economics, physics, and even the fundamental structure of the universe. Created by Sal Khan.

## Want to join the conversation?

• Why in algebra do you use letters instead of numbers?
• What is the best reason for learning Algebra?
• Algebra is the fundimental language of mathematics. Mathematics is fundimentally "why things are" - as we currently understand them to be. It is a science, but it is also an artform of logic - in a sense much like any spoken language. So much of our understanding of science is based on formulae and equations.. problems, variables..

Not only does Algebra offer us the universal syntax to understanding the language(s) of mathematics, it offers us the most basic toolkits to understanding the most complicated languages, proses, and poems of science and technology itself.

It is the most basic language of science from mathematics, to quantum phyisics to economics to .. well it can even be applied to psychology. It is logic in its almost purest form - dare i say the most important language we can ever have the opportunity to teach ourselves.
• why do we have to have algebra?
• Because it will make you better at life, if only you'll use it. "The human mind has never invented a labor-saving device equal to algebra." --J. Willard Gibbs.

Algebra creates abstractions which apply to tens, hundreds, or even thousands of scenarios. In other words by solving ONE algebra problem, you are solving hundreds of "regular" problems, all at once. Sounds nice, doesn't it? For example "maximization" and "minimization" problems (both involving quadratic equations) will help you, for example, fence in the most area with the least amount of fencing material (thus saving you money).
• what jobs would i use algebra for?
• Engineer (pretty much all types of engineers), physicist, economist, accountant, architect, chemist, teacher and professor (if one teaches math), pharmacist (to add in chemicals and/or drugs to each other), and a lot of other jobs. I think I'm missing some...but i think your getting the idea?
Hope this helped. =)
• If people take Algebra so seriously, then why did they invent the calculator?
• "If people take Algebra so seriously, then why did they invent the calculator?"
well, let me ask you some questions of my own:
if people take walking so seriously, then why did they invent the car?
if people take writing so seriously, then why did they invent the typewriter?
if people take talking so seriously, then why did they invent the telephone?
if people take X so seriously, then why did they invent the Y?
The answer to all these questions are the same, Y is a tool that makes doing X easier, faster, more efficient, optimal, convenient, and so on and so forth. Just because they are tools, however, doesn't make learning X any less important. Using Algebra, we can abstract the core idea of the question and answer any question with the same basic principle in place.
• Why do you find the discount by multiplying the discount by the price?
• But the easiest way to do it in your head is to find 10% (in this case \$2) and then multiply it by 3 to get 30% (or \$6).
• I want to become an interpreter (foreign languages are my passion!) Would I ever need to use Algebra in my day-to-day life? If I'm translating words and phrases for someone, aren't numbers universal? Why would I have to learn Algebra if I want to go into a field that deals with spoken language?

In all my years of school, nobody has ever given me an answer besides "it's required by the state." (I'm in the United States in my Junior year of High School.)
• Algebra isn't just used in jobs and careers. It can be applied to your everyday life. As an interpreter, you'll probably be making some good money. Any smart person budgets and keeps track of their money. I hope you do! Most people use Excel spreadsheets for their personal finances. A lot of algebra is used in that application.

So, don't assume you'll never have to use algebra in your day-to-day life. A lot of students complain about how "useless" it is... but don't even know they could very well be using it when they're older!
• Sal makes it seem like y = px is the answer to the universe.
So is algebra the answer to the universe?
• No, the answer to life, the universe, and everything is 42.
• Context is everything. Without the why its hard to care about what your learning.
• If people take algebra so seriously then why did they invent the calculator?
• The calculator is not meant to replace a human's ability to do math. Algebra gives us the necessary foundation in the rules of math to take real-world problems and rewrite them into mathematical problems.
The calculator is a mathematician's best friend. It allows us to quickly and accurately compute very large numbers that could take a person a lot of time and effort to find.
But what a calculator can't do is tell me how far a 4 kg ball would travel if I throw it with a velocity of 12.5 m/s at a 30-degree angle relative to the ground at a height of 2 meters, ignoring air resistance.
The calculator can't do anything with this information. It takes one who knows algebra and a little trig to convert this problem into one that a calculator can solve.
The answer would be: I convert the word problem into math.
0 = 1/2(-9.8)t^2 + 12.5*sin(30)* t+2

I rearrange this to solve for time (t).
t = -(12.5) +/- root((12.5)^2 - 4*(-4.9)(2))/2(-4.9)

Now, I can use a calculator to simplify what t is.
t = -0.15s and 2.7s

I have to interpret these answers to figure out which one I need (time can't be negative in this problem)"
t = 2.7s is the amount of time the ball is in the air.

I use this result to set up how far the ball moved in this time period:
DeltaX = (12.5)cos(30)*2.7

Using a calculator, I can solve for deltaX (the displacement in the x direction):
DeltaX = 29.2 meters.

Without me, a calculator would never have been able to solve this. Only once I translated the problem into a language the calculator could speak could I use it to do all the numerical math. Which just gives me numbers. But, even the equations I used were created using variables (letters to represent concepts) that could then be replaced by numbers to solve.
Now, could I have solved this without a calculator? Yes, but it would have been long, and many estimations would have been made (along with a couple of errors), but I'd eventually get the question. Calculators are a mathmeticains best friend.