Hello in this video, I want to show you a math book that is affordable and is pretty good for beginners. Now, it's not the easiest book in the world to read because this is not the easiest subject in the world, but it's actually pretty good. I do like this book. I've had it for over a decade.
It is called Introductory Discrete Mathematics and it is by V. K. Balakrishnan. This is a Dover book, which means it is a reprint. of an older book and that's really good because it's affordable.
So this is something you can buy, it's not going to cost tons of money, and it's also readily available. You should be able to find copies. What I will do is after I make this video, before I post it, I'll try to put a link in the description in case you want to check this book out. So I have read portions of this book, various sections, I've done some of the exercises, and again overall I think it's pretty good.
So let's just take a look at the inside so you can see what it covers. Here's the copyright, 1991 by V.K. Balakrishnan. Cool.
Yeah, and so this is a book you can use to learn discrete math on your own, or if you're in a class, I do think this serves as a fairly decent supplement. Again, no discrete math book is perfect. This one is really affordable though, that's why I wanted to make the video on this one.
It's not super expensive because it's a Dover book which... is a reprint, so it's a little bit less expensive. Set theory and logic. So it starts with the basic of sets. Most advanced math books start with set theory.
By the time you finish your math major, if you're a math major, you'll be an expert at set theory because you see it in like every single class. See what's on the next page. Combinatorics, that's the theory of counting. So it talks about two basic counting rules.
Then we have permutations and combinations, more on permutations and combinations, the pigeonhole principle, the inclusion-exclusion principle, and some notes and references. I've read this entire chapter, and I've read some of chapter two and some of chapter three. Generating functions, recurrence relations, these are really cool. You can use these to solve counting problems, and you can solve them in fun ways algebraically.
They're kind of fun to work through. Graphs and digraphs. So you do get some graph theory. This being a discrete math book, you are exposed to graph theory as well. More on graphs and digraphs.
Trees and their applications. Typically computer science majors are required to take a discrete math class. If you're thinking about going to college to learn computer science, then this can be something that you can have now and learn ahead of time. Spanning tree problems, shortest path problems, What is MP completeness?
And then we have answers to selected exercises. So let's just take a look here closer at the book. Here it says some stuff about the book.
Introductory Discrete Mathematics is a concise text for a discrete mathematics course at an introductory level for undergraduate students in computer science and mathematics. So there it emphasizes the computer science part. I was actually a double major for a while, computer science and math. And at that time, I took discrete math.
I eventually ended up switching to just mathematics. The essential components of any beginning level discrete mathematics curriculum are combinatorics graph theory with applications to some standard network optimization problems and algorithms to solve these problems. In this book, the stress is on these core components.
Cool. So it starts with set theory. And again, it's quite readable.
Again, I've read A decent amount of this book. Finite sets. It goes pretty quickly, so every time you see a word in bold here, that means that it's a definition. So it goes through pretty quickly. So compared to some other discrete math books, it is a little bit more advanced.
It's not like the easiest one in the world. But I like the size. I also like that it's a paperback because you can lay in bed and read it.
With hardcovers, it's just they're not as good for bedtime reading. So as much as I love hardcover books, I prefer softcovers for reading before bed. It's just easier to lay in bed with a softcover than it is with a hardcover book. Anyways, most Dover books, in fact all Dover books, are softcovers.
Power set of a set. That's the set of all subsets. Cartesian products.
You see how quickly it goes through stuff. So it gives you a really quick review of set theory. And you do have examples. So you see it does actually have worked out examples.
These books are fun because you learn a lot of math. You can sit down and you can read for like 45 minutes and you'll learn something. I mean, you'll learn some stuff. You don't have to understand everything.
Like, you're going to get stuck on stuff. My advice is try to work through it and if you can't, it's okay to move on and just learn some more stuff. Try to maximize your reading time, right?
Try to learn as much as possible in the time that you've allocated for your nighttime reading or daytime studying. Ooh, Zorin's Lemma. Yeah, Max Zorin.
He was a famous mathematician. Zorn's lemma is named after Max Zorn. some induction stuff. Then if we go to the very, very end, we have exercises. So the exercises don't appear until the actual end of the chapter, which is okay.
I mean, you get some reading and examples, so you do read quite a bit, and then you get some exercises. The exercises are really fun. I've done some of them. I think they vary in difficulty. You've got some easier ones, and you've got some harder ones as well.
But it's just kind of like a fun book. to work through. This is one of my favorite books.
Even though I don't think it's the easiest discrete math book, I think the easiest one might be the one by Epp. And if I remember, I'll try to leave a link in the description. But that one's way more expensive than this one.
And that one's hardcover and it's huge. I don't really think it's suitable for like bedtime reading. This is something I like for bedtime reading.
I know I keep saying that, but that's what I think about when I see this book, some bedtime reading, because I've read it before bed several times. Also, you can take it with you. One time I was at the mechanic.
I took this book with me and I sat there for two hours and I read this book for two hours straight. So that was kind of a fun experience. Sitting in a mechanic shop, learning mathematics. And if we go to the end of chapter one, let's look at the exercises there. You get tons of exercises as well over here.
And the exercises do have answers. So let's look at that. Wow, look at all these exercises, right? I just want to sit down like right now and start doing math problems.
I think I might actually after I make this video. I might sit down and read a little bit of this. You see you have answers to the odd numbered exercises, which is really quite nice. These are really fun.
It's a different type of mathematics, by the way. So if you don't know much about discrete math, it's a different way of thinking. And I think that's a good way to put it.
I remember when I was in statistical theory, which is a course which covers counting probability. and statistics, our teacher said that you had to think differently for the probability problems, the different way of thinking. And he was right. He was 100% correct. It is a different way of thinking.
Now, it looks like it's more than just the odds. You got some even-numbered answers here as well. So Balakrishnan does say selected exercises. So that could be just the odds, maybe the odds, and some more.
It's hard to tell. You've also got some references here. You've got a bibliography. It's got to give it a whiff here.
Ah, what a great book. So this is a book that is a very worthy purchase, and again, I will leave a link in the description in case you decide you want this book just for like bedtime reading or doing math or as a supplement, whatever. I think it's a good book worth owning and belongs in everyone's library. B.K. Balakrishnan is a great author.
He has other good books. This one is Introductory Discrete Mathematics, and I highly recommend it. If you want to learn mathematics, by the way, I do have courses.
They're on my website, mathsourcer.com. They're actually on the Udemy platform, but if you get my courses, please use the links from my website for two reasons. One, it helps me a lot because otherwise Udemy takes pretty much almost everything. They take a big chunk.
It's a lot. And two, I've lowered the price of all of my courses to the bare minimum. So if you use my links from my website, I'm pretty sure you're always going to get a very low price because I set the price at like the lowest level it let me set it at. So.
Again, it's mathsorcerer.com or just freemathvids.com. But check it out. I've got courses on algebra, calculus, some proof courses, abstract algebra, advanced calculus, et cetera.
So I don't have a discrete math course yet. Someday, maybe. But yeah, check it out.
And if you found any value in this content, feel free to hit subscribe if you want to. Also, I always forget to mention this, so I should. I do have another YouTube channel.
It's called The Internet Sorcerer. It's undergone some name changes. I think I'm going to keep it at The Internet Sorcerer. So it's kind of like more in line with The Math Sorcerer.
I post all kinds of stuff there, just random stuff. So anything goes on that. It's like an anything goes channel. So check that out if you want to follow me for more content and stuff like that. But yeah, very, very happy with this book.
I've had it for over a decade. It's one of a fun book. It's a fun book.
It's a soft cover. It's a Dover book. Yeah, I like it. I recommend it.
I hope it's been helpful. Good luck and keep doing mathematics.