Math for Computer Science

In this video I will show you a very good book on discrete math. This book has lots of the math that you need for computer science. It also has full solutions to every single problem. The book is titled Concrete Mathematics and it was written by Graham, Knuth, Patashnik.

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[evanperez]

Applied Math Major here! I thought I was crazy for having a whole book shelf full of math books and computer science books haha. Love your content!

[leadrevolver]

What a great book! I recall using it for a hellish discrete math course back when I did my bachelors.
Don Knuth is also famous for "The Art of Computer Programming", which is like the bible for computer science. Highly recommended!

[samijee]

I cant believe I was just thinking about what would be the necesarry math for computer science and thought about you. I open your channel and 4 hours ago you posted "Math for Computer Science". This is crazy!
Thank you so much!

[robertovolpi]

Solutions to ALL the problems?

I already love it.

[economicist]

The typefaces used are listed in a short paragraph on the very last page.

*TLDR:* _Concrete Roman_ for the main text, _Concrete Italic_ for the sidebar notes or anything italicized in the text, and _AMS Euler_ for the mathematical notation.

"""
THIS BOOK was composed at Stanford University using the TEX system for technical text developed by D. E. Knuth. The mathematics is set in a new typeface called AMS Euler (Version 2.1), designed by Hermann Zapf for the American Mathematical Society. The text is set in a new typeface called Concrete Roman and Italic, a special version of Knuth's Computer Modern family with weights designed to blend with AMS Euler. The paper is 50-lb.-basis Clearfield Opaque, which has a neutral pH and a life expectancy of several hundred years. The offset printing and notch binding were done by Halliday Lithograph Corporation in Hanover, Massachusetts.
"""

[piegames]

Love how you post constantly with new stuff, keep up the work math

[anoopverma]

I am a Computer Science teacher with Masters in Physics, your videos have forced to buy some books and re-study Maths, just for the fun of it. Prof. Knuth is almost a God-like personality and a book from him in Mathematics must be a Bible. Will try to have it in my personal library.

[spacegoat_d]

Never thought I’d be interested in getting better at math but here I am

[anarchistalhazen]

That is cool.. I am from Saudi Arabia as well. There are not many Saudi mathematicians. Mainly because higher education in Saudi Arabia is about two generations old.

[quintrankid]

The name of the typeface for mathematics is in the preface. Designed by Hermann Zapf and called AMS Euler. There's more info in the preface.

[kdub]

So many of the fun and interesting topics that a lot of us missed out on are lumped together under the banner of "discrete math". I think many of us missed out on some of it because by the time we are deemed ready to learn it, the material was sometimes deemed too "elementary" to be worthy of inclusion in our course of study!

They often teach elementary combinatorics and the binomial theorem in grade school or junior high. But fancier counting with Stirling and Bell numbers isn't taught until CS (for those of use who take it). Same goes for algorithmic graph theory (spanning trees and shortest paths). Number theory is for egg head mathematicians! We physics guys - at least back when I was in school - worshipped at the altar of mostly centuries old continuous math, basically vector and tensor analysis, orthogonal function systems arising from linear differential operators, and then the complex plane (mainly just for residue tricks to do definite integrals).

I was never required to take a discrete math course (and didn't really know what it was), and only started learning some topics many years after I finished school because I wanted to understand algorithms. Then one thing led to another, and I'm really enjoying the landscape.

[cybervigilante]

I can see concrete engineers picking this up by accident.

[aaronclair]

Euler is actually pronounced "Oiler", like you suspected. Euler was from the German part of Switzerland, and in German "eu" makes an "oyy" sound.

[andrewchen]

I've been tackling Concrete Mathematics on and off. It's quite dense. I've probably spent >100 hours over a couple months and still in Chapter 3.
It'll get me more math literate though, so I hope to finish it before undergrad ends. If I do so, I'll ping you to let you know I made it :)

[leocomerford]

12:04 Fortunately Unicode now has characters for the faces of a six-sided die: ⚀⚁⚂⚃⚄⚅ . Not all software may have a font to display them though.

12:31 There's a colophon or pseudo-colophon at the end of the book (on p. 657) which covers this:

"THIS BOOK was composed at Stanford University using the TeX system for technical text developed by D.E. Knuth. The mathematics is set in a new typeface called AMS Euler (Version 2.1), designed by Hermann Zapf for the American Mathematical Society. The text is set in a new typeface called Concrete Roman and Italic, a special version of Knuth's Computer Modern family with weights designed to blend with AMS Euler. [...]"

[-TheBugLord]

I love applied math. Whenever I learn something, I imagine it as a tool I can put in a toolbox. Applied math is great because it often has direct uses in the field of Computing

[sophiaisabelle]

This seems like a very useful book to read. We hope to see more of your recommendations. May God bless you as always.

[MuantanamoMobile]

This book (Concrete Mathematics) is a good precursor to tackling the "Art of Computer Programming Vol. 1-4B" series of books by Knuth.

*Generally*, one would have a much smoother time going through it if they had some background in basic set theory (what sets are, what operations on sets means etc).
- Have some comfort in what an induction proof is and how they generally look (yes the book does discuss them in general, but spends more time on application.)
- Know what a Riemann sum is and what Riemann integration means.
- Be comfortable with sequences and series.
- Knowledge of complex numbers.

And of course as usual, a willingness to work through problems and natural curiosity.

[Crw]

That is a great book. Someone recommended it to me back in 2005 and I got a copy pretty cheap on Amazon back then.

[TheChocolateChiken]

I went into a second hand bookstore and saw a book called, "Concrete Mathematics" and got excited because I thought it was this book, only for me to pull it out and realise it was a civil engineering book about concrete.