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 VK balakrishnan this is a do 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 it's also readily available like 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 extra sizes 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 VK 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 discreet math book is perfect uh this one is really affordable though that's why I wanted to make the video on this one it's not super expensive cuz 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 uh 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 pigeon hole principle the inclusion Exclusion Principle and some notes and references I've I've read this entire chapter and I've read some of chapter 2 and some of chapter 3 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 um they're kind of fun to work through graphs and digraphs so you do get some graph Theory this being a discret math book you are 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 just take a look here closer at the book here it says some stuff about the book introductory discret Mathematics is a concise text for a discret 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 um I uh took discret math I eventually ended up switching to just mathematic matics 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 starts with set theory and again it's quite readable again I've read a decent amount of this book finite sets it it goes pretty quickly so every time you see a word and bold here that's that means that it's a definition so it goes through pretty quickly so compared to some other discret math books it is a little bit more advanced it's not like the easiest one in the world but I like the size uh I also like that it's a paperback because you can lay in bed and read it with hard covers it's just they're not as good for bedtime reading so as much as I love hard cover books I prefer soft covers for reading before bed it's just easier to lay in bed with a soft cover than it is is with a hard cover book anyways most do books in fact all do books are soft covers power set of a set that's the set of all subsets cartisian 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 uh 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 o Zorn's Lemma yeah Max zor he was a famous mathematician Zorn's Lemma is named after Max zor some induction stuff then if we go to the very very and uh we have exercises so the exercises don't appear until the actual end of the chapter which which is okay I mean you get some 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 VAR 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 uh to work through this is this is one of my favorite books even though I I don't think it's the easiest discret math book I think the easiest one might be the one by app and if I remember I'll try to leave a link in the description but that one's way more expensive than this one this one and that one's hard cover and it's huge I don't really think it's suitable for like bedtime reading this is something um I like for bedtime reading I know I keep saying that but that that's what I think about when I see this book some bedtime reading because I've read it before bed um several times and 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 uh 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 uh as well over here and the exercises do have answers so let's 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 might sit down and read a little bit of this you see you have answers to the odd-numbered exercises which which is really quite nice oh these are really fun it's a different type of mathematics by the way so if you if you don't know much about discret math it's a different way of thinking uh and I think that's that's a good way to put it I remember when I was in statistical Theory uh which is a course which covers counting probability uh and statistics our teacher said that you had to think differently for the probability problems a different way of thinking and he was right right he was 100% correct it is a different way of thinking now it looks like it's it's more than just the odds you got some even numbered answers here as well so B chrisan does say selected exercises so that could be just the odds maybe the odds and some more um it's hard to tell you've also got some references here you got a bibliography it's got to give it a whiff here ah what a great book so this is a 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 or doing math or as a supplement whatever I think it's a good book worth owning and belongs in everyone's Library BK balakrishnan is a great author he has other good books this one is introductory discret Mathematics and I highly recommend it if you want to learn mathematics by the way I do have courses they're on my website math sour. 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 udem me takes pretty much almost everything they take a big chunk it's a lot and two I've lowered the price on 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 math sourcer docomomo calculus and proof courses abstract algebra Advanced calculus Etc so I don't have a discret math course yet Sunday 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 uh 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 sourcer so it's kind of like more in line with the math sourcer I post all kinds of stuff there just random stuff um so anything goes on 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 uh I've had it for over a decade uh it's one of a fun book it's a fun book it's a soft cover it's a do book yeah I like it I recommend it I hope it's been helpful good luck and keep doing mathematics