# Introduction to Mathematics

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.

Good video

Thankyou professor Dave i was waiting for this series😍

I'm learning math for about two months by now, trying to be better at chemistry.

I trust the you teach, since I've watched your chemistry lessons. So yeah Professor Dave, Teach us math!

Please make video on Lichatier principle

Thank you

Math was not invented

it was discoverd

Please do explain what is discrete math?

I'm waiting

At what Pace will those Videos come out and when start? Thanks

Ive never heard someone explain it in that way before, it was certainly interesting.

Thank you for this. I've always had the least amount of confidence in mathematics

Professor Dave is a god amongst men

I am eagerly waiting for them☺

Thank you professor Dave. you make math easier than before.

OMG! I'm so excited! I've always wanted to learn math!

you deserve a prize!

Very interesting way of introducing math!!

OMG YESSSSSS GET IN SON

Mathematics is very likely not intrinsic to the universe and you shouldn't have passed that belief of as fact. We create axioms which are based on our experience and then see what is necessarily true based on those axioms being true. For example the statement 1+1=2 only means anything because we came up with counting due to the fact that we deal with discrete objects and we came up with integers. If our experience was of continuously changing things like concentrations then we would come up with different ways of representing quantities. Our axioms do help us model our experiences very well but that's just because we chose our axioms from our experiences it is very likely our axioms differ subtly from reality so some mathematical statements will be true according to axioms but not reflect reality

plzz start this series as soos as possible or upload daily one vedio

I need algebra, trigonometry, differential equations , partial fractions

I'm taking calculus this year and I could really use these new videos

Awesome, I'm so glad I found your channel. I'm currently going through your classical physics & biochemistry playlists.

I'm super excited to this series, since I kinda did not do the high school math that he had and since then I'm eager to learn it. Let's hope that I will atleast brush the dust off of my old knowledge 😀 (great intro btw)

I was was waiting for your new videos very eagerly

Thanks in advance, professor!

We've been waiting A LOT for this!

Don't wear this shirt in a video please, it's messing with my eyes 😀

Sounds weird hearing 'math', it's called 'maths' in England.

Wow, amazing video and channel!

mathimatika milto!!

man, that was clever dude. Thanks

YOu motivate me so hard man, I should watch one of your videos every day.

We need all the videos please bro

I commend your work as always, but there isn't a complete axiom of mathematics that always holds true without contradicting itself. There are some famous examples of these mathematical paradoxes that have been explained by famous YouTubers, such as Vsuace covering the Banach-Tarski paradox.

You're right to say mathematics produces completely inarguable answers, but then paradoxically, it creates an argument to an inarguable truth. The universe refuses to give up its secrets easily…

Edit: This isn't usually a topic taught to children who haven't learned to appreciate the value of science because it can easily call into question everything which we're told to accept, but again, it doesn't make it any less true. Strangely I am a firm believer that somethings have to be taught wrong, before they can be taught right, because as a geneticist, the first inaccurate fact we learn is that every cell in our body contains the exact same DNA.

https://youtu.be/s86-Z-CbaHA

https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

so intresting,!

From the heart, thank you sir

You are awesome

You're amazing! Thank you so much! Studying for my GRE and you are really good and math is starting to make sense!:)

Thanks Prof. Very helpful lesson about Math. You make it awesome 👏👏

I like the way you explain and the English you use

Make a lesson on directional derivative sir . Please

GOOD

From simple additions/substations to calculus and more!, your mathematics section is really very diverse!

My favourite one is :- " We are merely explorers of infinity in the pursuit of absolute perfection. We do not invent these formulae, they already exist and lie in wait for only the very brightest of minds, ever to divine and prove them. "

You make math simple and interesting.

hey professor jesus, what are advanced topics of math? and how long are you going to continue creating videos about math after completion of advanced topics of math…?

@3:45 "There are no two ways about it." Well that's not exactly true. You could come up with a bound, saying it must be greater than 60 degs and less than 120 degs, and then try to narrow it down from there. I know this is a trivial example, so duh it's 90 degs, but it's a perfectly valid proof technique to try to put a useful bound on things for very complex proofs. Remember the polygonal exhaustion method to determine pi? That was also putting a bound on pi, not determining it exactly. There was nothing invalid about it that proof.

Simply explains the use and philosophy of math. Thanks. Very helpful for the math fearing people.

Wow, a little off the mark… Infinity is NOT a number.

You state that there are 'infinitely many' numbers/primes/yadayada. Typical but wrong.

That means; the "number of numbers" is a non-number number.

Hmmm… Bad phrasing… or just traditionally bad maths concepts.

Is there a blue or cow number of numbers? Blue and cow are non-numbers, too.

Bear in mind, that you do not even fully understand even and odd (2n or 2n+1) numbers or 3x+1.

Otherwise, the Collatz Conjecture would be the Collatz Theorem… Funny, huh?

I luv u Professor Dave…all the stuff I want to know!!

Prof Dave, this series is incredible. I'm in the process of returning to school, and I needed a bunch math through calculus for prerequisites into my desired program. My highest prior math class was algebra. Crunched for time (somewhat), I knew I could test into at least trig just by using this math series of yours. Well guess what? I tested right into calculus. Cannot tell you how pumped I am and how awesome your channel is! I bought a Prof Dave Explains T-shirt and wear it all the time, haha. Love that shirt! Thank you so much. Keep crushing it.

Bruh he teaches better than my actual maths teacher. PROOF you learn more online than in actual school.

I'm starting to watch the series because math class here in Finland was wayyy too obvious and simple for me. I hope this can bring out the fun of math for me.

👍👍👍👏🏻👏🏻

Mathematics is the basis of everything

in the Universe,from the Big Bang to

the present day.It also applies to what

was before the Big Bang as well.I know

what was before the Big Bang.It is all

down to the Laws of Physics(E=mc2)

and especially the Laws of Thermodynamics.I am an Engineer

and Scientist.

Brilliant video. The reason I majored in math is because I could find an answer and draw a box around it.

Thanks Dave, glad I found your channel! Been looking for some good content in this kind of format.

Hopefully, will be completely registered and embarking on an undergrad Maths adventure this October; with some physics thrown in too!

Onward and upward; let's do this 🙂

KIRK: The old ones programmed you, too, but it became possible to destroy them.

RUK: That was the equation! (seizes Kirk) Existence! Survival must cancel out programming.

I don't know why, but this talk reminded me of an early episode of Star Trek.

"All are welcome." The Church of Mathology.

You don't have to believe a single thing. Everything will be proven.

But how do you learn maths, each time ive tried it doesnt sink in all the formulas and equations

This is the problem with math…I thought I'd brush up – having finished my last maths class 35 years ago. I thought, 'In case I miss anything, I'll start at the beginning'.

Then everything is fine until the root 2 statement! I use the square root of 2 all the time…? Looking more carefully you say no 'fraction' can….But I'm already confused. It's my English not my math I am having issue with…

May I take this moment to say I think you are the ideal teacher, really a remarkable chap. I have watched your Flat earth Response video countless times. It is an absolutely perfect video. And I'm sure when I finish watching them all, I will have learned they are all just as good. (Edit: They are so far). Thanks Prof.

We do not create math! He is contradicting his own opening remarks. Off to a bad start but it is philosophy of math.

This Introduction to Mathematics is truly EXCELLENT !

You are amazing 😍

Prof, I want you to say that high school math teachers have NO idea how to teach; I also want to hear that I'm not completely at fault for not understanding certain key concepts on the subject.

I know I'm in no position to make demands, but if you do this, I will watch every video in the series.

¡Salúd!