Mohamed Omar

What undergraduate math topics would you like to see covered in a 3-5 video series?

Hi all. As you might have noticed, I've been posting a few new videos! After the holiday break I'll be making a few more using my iPad style (works better for my accommodations). I wanted to ask you what topics you might want to see in a video miniseries! See you after the holidays!

2 years ago | [YT] | 32

Mohamed Omar

Thanks everyone! The channel has hit 10,000 subscribers. I haven't posted much in the last several months. As I play with returning to the channel now and again, my health condition reminds me to step back and take things easy. I'll be making posts here and there though.

I especially appreciate those who have been consistently with the channel over a long period of time. Much appreciated!

3 years ago | [YT] | 50

Mohamed Omar

I came across an interesting phenomenon recently, and that's using algebra techniques to prove interesting number theory facts. For instance, here are couple of examples. In the first one, p is a prime.

These actually come as consequences of using a theorem in group theory called Lagrange's Theorem, and in a nice way.

Do people have thoughts on different ways to prove these instead? Or, do people have ideas on other number theory facts that can be proved in interesting, non-number theoretic ways?

4 years ago (edited) | [YT] | 46

Mohamed Omar

Hi everyone! For those interested, I made a book on introductory Graph Theory concepts!

www.amazon.com/dp/B09HG4VY65?ref_=pe_3052080_39751…

I'm hoping to have a playlist where I talk about the content in the different chapters, in an intuitive way. The intended audience is people who haven't seen any Graph Theory and want to learn the fundamentals.

4 years ago | [YT] | 17

Mohamed Omar

After a hiatus involving physical rehab and a home renovation, I've posted a new video!

4 years ago | [YT] | 24

Mohamed Omar

Hi all! I've had a book on Graph Theory that is an introduction to the beginning/basics of the subject for people interested in knowing some terminology, and for people to get a jump start on it if they are doing independent study or graph theory research of some kind.

It's about 50 pages or so. I know some channel subscribers were interested in this for many other reasons too.

I wanted to publish this in May but things came up. So the question is, when would you want to see this come out?

4 years ago | [YT] | 22

Mohamed Omar

On Wednesday I have a video coming out on interesting limit techniques. What are your fave techniques for computing limits? Any particularly fascinating or obscure ones?

4 years ago | [YT] | 24

Mohamed Omar

Hi all. No new video today but we will be back with a new one on Monday.

I wanted to share this cool source with you all. Do you like the Fibonacci numbers? Did you know there is a journal dedicated to them? It's called the Fibonacci quarterly, and there are back issues available going back decades!

Each issue has some discovery articles with Fibonacci numbers, and two problems sections. It is completely filled with problems all about these numbers.

One property of them that I had no clue about and saw on Instagram yesterday actually appeared in a very old issues of the Fibonacci quarterly, and I've pasted it in the image below.

Have a great weekend!

4 years ago | [YT] | 60

Mohamed Omar

The game SET is a card game where you each card has four attributes: Color, number, shape, and shading. Each attribute has 3 types: each card is purple, red or green; oval, diamond, or squiggle; has 1,2 or 3 items on it; and is clear, lightly shaded, or filled in. A set consists of three cards that satisfy the following condition: in each attribute they are either all the same or all different.

The total number of cards in the game is 3^4 since there are 4 different attributes and each attribute has 3 types. One of the most interesting questions about the game is, what is the maximum number of cards you can lay down on a table and have no SET whatsoever.

It turns out the answer is 20, and there are reasons for this that come from linear algebra! Using linear algebra in 4-dimensions, where vectors have components being integers mod 3, one can prove that no matter what 21 cards you lay down on a table, there *has* to be a SET.

The image shows a glimpse of 12 of the cards in a 20 card table that has no SET.

4 years ago | [YT] | 23

Mohamed Omar

A fun mathematical question I received lately. Suppose you have a cell phone and you are required to select a 6-digit password using the digits 0,1,2,3,4,5,6,7,8,9. You want a password that is most difficult for someone who finds your phone to guess.

How do we assess this? Well imagine someone picks up your cell phone and sees smears on the phone on some of the digits. For example, they see smears on the digits 1,3,4,7. Then they know that your passcode is a 6-digit code that *exactly* uses the digits 1,3,4,7. They can enumerate through all possibilities of 6-digit passcodes that use all of the digits 1,3,4,7 (I say all because you've seen smears on all the buttons).

So what's best for a 6-digit code? Is it best to have a code that uses exactly 6 distinct digits (so that someone will see 6 smears)? Or is 5 smears better? Or 4 better? What's optimal?

What about a 7-digit code? How many distinct digits should we pick so that our passcode is hardest to guess?

Leave your thoughts!

4 years ago | [YT] | 34