Maths for Programmers: Introduction (What Is Discrete Mathematics?)

Transcript:

In this video, I will be explaining what Discrete Mathematics is, and why it's important for the field of Computer Science and Programming. Discrete Mathematics is a branch of mathematics that deals with discrete or finite sets of elements rather than continuous or infinite sets of elements. Imagine trying to run a program that requires an infinite number of executions to complete a task. It's obvious to say, that the program would run forever and the task would never be completed because there is an infinite number of executions. In order to avoid this problem, we approximate the continuous sets with discrete sets. Now you may be thinking, I never use math that involves infinite sets, but I promise that you do. The simplest example is with a circle. A circle by definition is an infinite number of points equally distant from a fixed point. The problem with this is that if we try to write a program that prints out all of these points, it will run forever because there is an infinite number of points and therefore an infinite number of executions. So, this is physically impossible, that's why if we zoom in here, you can see that when you come down here, there is all these points, but in reality we should have even more points between these points. And if we zoom in on those, we should have more points between those points, and we can never complete the task. Now we've all seen circles on computers, how is this possible, because we just established that it's impossible. The answer is, is that there is approximations. For example, consider regular polygons. Regular Polygons, like a triangle, or a square, or a pentagon. They don't really look like circles. However, if you keep increasing the number of vertices. Eventually you will get hexagons, octagons, decagons, hexadecagons, icosagons. You can see that these regular polygons, the more and more you increase the number of vertices, which the vertices are equally distant from a fixed point, they will eventually approximate a circle, and eventually they will be indistinguishable to the naked eye and will look identical to a circle.

We're busy people who learn to code, then practice by building projects for nonprofits. Learn Full-stack JavaScript, build a portfolio, and get great references with our open source community.

[MinistryOfMagic_DoM]

As someone who is about to take Discrete Mathematics, Thank you for this simple explanation. I've been trying to explain what it is to my family, most of who did engineering in other disciplines and took different math courses, what discrete math is. Now I'll just show them this video instead.

[LTTheReal]

Thanks a lot, I was looking around for an answer that made sense and this did it for me.. thought discrete math was just doing math while not telling anybody you were doing math lmao.

[Poison]

You sir are a legend, this was literally discrete mathematics in 2 mins. Nice video!

[shawniscoolerthanyou]

I like how your second to last zoomed-in inset of the circle is approaching a line. A nice nod to linearization of functions, even if not intentional.

[steventanner]

This is a great video! It helped me dread the class less since I know it will be more applicable to my major than other maths. Thank you. (Also kept it short and to the point)

[imranabdi]

Hands down, the best sounding engine ive ever heard of

[maximorodriguez]

wow. I was so confused on what discrete math was but now I think its actually pretty cool. Thanks

[paganizondasroadster]

Loves how he explained the circle. Falling in love with mathematics again.

[ceebaby]

Thanks for the video! I can feel that this handsome instructor has a true passion for discrete mathematics given his smiles during the video lol

[hamsack]

Just started this class. I will be back to this channel for sure.

[esaht]

what a short and captivating video. really answers a lot of questions.

[collegemathematics]

great explanation... full of info and yet simple, , I noticed your graphs and notes in the whiteboard you look like a perfectionist

[williamkoleszar]

this is mind blowing when you think about it... very concise!

[joe_zupko]

Good simple explanation :) I have to take a discrete math course for my comp sci major and was worried it would be more nonsense like my calc courses (beyond derivatives and integrals it's kinda tedious :p)

[electronix]

Lol, when I was enrolling into Discrete math for my double majors, I was like "so it's math that is discrete". I never really knew what that meant. Now I do. This reminds me of Calculus BC class or something.

[aniltheblogger]

Thanks a ton for this series. But one humble request. If possible can you put the transcript of the video in the description just to get the words (buzzwords) right. Would be of much use for foreign people.

[rudzisilima]

Thanks dude. Your video was super clear and helpful!

[noahdavis]

thank you. such a simple video that explains its importance

[PratikPatil-yvhe]

Well I sucks in maths I came to learn maths for programming hope yours video will help me

[fazalr]

Task Completed Agent 47, Great Video! Your next assignment? Find out how many sides to a polygon until it is indistinguishable from a circle.