I’m Professor Dave, and I wanna teach you about mathematics.
Not everyone loves math.
Many students wonder why it’s even necessary to learn in the first place.
Well, it may not always be obvious, but math really is everywhere.
Math is how our phones work, how airplanes fly, how social media knows who you’re going
to tag in a photo before you do.
Math can tell us how disease spreads, who is most likely to win an election, or the
odds of winning at casino games.
Math also goes far beyond our everyday experience.
It is the language of the universe itself, describing how all objects move, from tiny
atoms to entire galaxies.
Math governs everything from science to economics, so it is not an overstatement when we say
that math is everywhere.
But in another more tangible sense, math is also nowhere, in that it isn’t a concrete
physical object, like you, or your shoe, or your desk.
It is inherent in reality.
Objects in the night sky obey mathematical laws of motion that exist whether we write
them down or not, which means that mathematical truths have their own existence, independent
of humans and our symbols.
The fact that one plus one equals two does not rely on two people each putting an apple
into a basket and then agreeing that the resulting is two apples.
It’s just true.
The equation that represents this action was true before any humans were even born, and
it will be true long after they all die.
So where did the math we see in math class come from?
Did some caveman stumble across a Calculus textbook buried under a rock?
Is this knowledge bestowed upon us from the heavens, like a religious text?
For those of us who have difficulty with math, it definitely seems that way sometimes.
But the real story is much more interesting.
Math comes from us.
We make it.
And this does not strictly refer to the past.
Every day, thousands of mathematicians around the world are busy creating more math.
So how do we create math?
To answer this, we need to know what math really is.
In short, math is the study of questions that have definite answers.
That’s it.
This may seem incredibly broad, and it is, but this is what sets math apart from other
areas of inquiry.
Some questions don’t have definite answers.
What is the best form of government?
Who deserves the Oscar for best picture?
What’s better, pizza or cheeseburgers?
The answers to these questions are subjective; they vary from person to person, and no matter
what anyone says, no one can give a definite answer, because there simply isn’t one.
Even with science, if we do an experiment over and over and over, and our equations
always make highly accurate predictions about what will happen, we are very likely to be
right about a certain phenomenon.
But we can never be one hundred percent certain that we won’t get a different result in
the future.
Science can be consistent far beyond reasonable doubt, but it never claims complete certainty.
However, if I draw a circle and try to determine the angle between a radius and a tangent line,
I will either get ninety degrees, or I will be wrong.
There are no two ways about it.
Every mathematical question like this one has a completely inarguable answer.
Are there infinitely many prime numbers?
Yes, there definitely are.
Is there a fraction that, when multiplied by itself, gives the number two?
No, there definitely isn’t, and we will learn about these concepts in this course.
The job of the mathematician is to ask these kinds of questions and then come up with the
tools that are needed to answer them.
The answers themselves are fixed and completely out of our control.
They are part of the fabric of the reality in which we live.
Often times these answers are very surprising.
If we ask the question: “Is there more than one kind of infinity?”, the answer is yes.
In fact, there are infinitely many different kinds of infinities.
Humans did not decide that this was true, we simply decided to ask the question.
And that is what we’re going to do in this course.
We’re going to ask questions, and then build the tools we need to answer them.
The tools that we will build can be applied in virtually every aspect of life, from the
biological, to the technological, to the sociological, and even more astoundingly, they sometimes
show us the deepest of truths that have been lying in wait for us to uncover.
These are the ones that tell us about the nature of reality in a way that philosophers
can only dream.
So if you want to build up your understanding of math so that you can learn all kinds of
physics and chemistry and astronomy, you’ve come to the right place.
If you’re a math student at any level, and you need help understanding what your teacher
is talking about in class, you’re in the right place, too.
If you’re just someone who wants to figure out how much tip to leave at dinner, stick
around, all are welcome.
In this course, we will begin with the most elementary math there is, the basic arithmetic
that was developed at the dawn of civilization, and work our way through everything one would
learn in high school, and most of an undergraduate mathematics education.
Watch all the way to the end, or bail when you feel like you’re in over your head.
Either way, I bet you’ll get farther than you thought you could.
So grab a pencil, and let’s learn some math.