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Discrete Mathematics: An Open Introduction, 3rd edition
- pooya72 6y agoI'm just a hobby programmer, but I've been looking to learn discrete math so I can get in to algorithms. Is this a good book? I've seen a lot of people recommend Epp's Discrete Mathematics with Applications. I've kind of been holding off the topic until I really hit a wall and discover what/how much I need to learn. Any advice would be great.
- kashfi 6y agoI just took a look at it and I think for self teaching this might be a great alternative to Rosen’s DMwA. Mainly because this book offers interactive Questions and Answers at the end of each section. Pair the book with an MIT OCW math for computer science or something similar and you should be more than good. Best of luck!
- pooya72 6y agoThanks! Nice username.
- swiley 6y agoIdk about the interactive thing. Personally having a bunch of fancy tools like that makes it harder to keep a flow of (try problem, get it wrong, figure out why, repeat) but I guess I’ve never tried that with a math book. In college I always found it was best to study math with a dumb pdf and a notebook.
- tty7 6y agoLet me use the, 'What programming language should i start with?!' analogy :) Just start reading the book (any discrete mathematics book!) :)
- weareconvo 6y agoOr to put it mathematically, the optimal amount of exploration time in this explore/exploit problem is far less than you might think.
- pooya72 6y agoActually, having gone through multiple programming books, I disagree with that. I highly recommend HTDP because of their design recipes. The book shows you an approach to solving problems with programs rather than just the syntax of a language. This book has had the largest impact on my (very humble) approach to programming.
- exceptione 6y agoI get the following error: Error on line 1. Unspecified reference named 'HTDP' in the expression 'I highly recommend HTDP' Any help?
- mcherm 6y agoClever! https://htdp.org/ https://htdp.org/
- spike021 6y agoI'd disagree. They're better off getting some feedback on books that might appeal to their learning style and background better. Otherwise they may tire quickly and not learn well-enough.
- mesaframe 6y agoI have read Sussane's book and it's really good.
- credit_guy 6y agoThis is a 400 page book. Very likely overkill for what you intend to do. Many algorithms books contain the necessary discrete math prerequisites, so I'm not sure you should go with this book.
- lordleft 6y agoI have to say that I quite like the visual design of this “open” textbook.
- jka 6y agoIt does seem neat, yep! It looks like it's based on a format called PreTeXt[1], and the interactive exercises (Q&A) are implemented using an extension called WeBWorK. [1] - https://pretextbook.org/examples.html https://pretextbook.org/examples.html
- xrd 6y agoThis is amazing. It works perfectly on mobile. The fact that it explains the concepts, and then has quizes right inline to test and reinforce knowledge is awesome. And, it is free. Wow.
- adnauseum 6y agoThis is a great introduction to discrete math. I found it valuable for deciding what topics to invest more study into. Good survey of discrete math. I'm about 70% through this book. I've done every exercise and have meticulously journaled about each concept as I encounter them into my Zettelkasten. Best part: you can read it online and then determine if you want the physical book (which I prefer for math).
- monster_group 6y agoI am curious to know why you are working through this book. Is it related to your career or are you doing just for fun? I am asking because I often face this dilemma of whether to invest time in furthering my career or doing something I like that is not going to help my career (although this book might given that it has theory of trees and graphs).
- ngcc_hk 6y agoWonder linear algebra is more useful.
- CrazyPyroLinux 6y agoThank you for introducing me to the idea of the "Zettelkasten" - I'm "one of the 10,000" for that idea today.
- Eugeleo 6y agoI don’t have much time, but look at: Tiago Forte’s blogpost about How to Take Smart Notes (also, see the book), Roam research, Obsidian, Zettelkasten.de (mostly English). Also, both Roam and Obsidian have Slacks (or Discords) full of friendly knowledge-management enthusiasts. Those are the things that I found most helpful on my recet foray into the Zettelkasten world. Could save you some time.
- jwdunne 6y agoJust added Forte’s blog post to my reading list! This seems similar in benefits to the idea of a Common Place Book. I’ve just had some more hardback notebooks delivered for that purpose. I’ve been keeping one for a year, filled up 2 notebooks and it’s been night and day for me. I’ve been able to comprehend subjects that I’ve struggled with before, e.g linear algebra, abstract algebra or any topic I take an interest in. One thing my notebooks don’t have is structure and a system of referral. This makes it hard to reference previous ideas and concepts. In fact, I don’t because it’s so difficult - it’s just one big stream of consciousness. And it seems Zettelkasten does that!
- hnxs 6y agoThis is great. Is there anything else of similar methodology and quality for other math subjects? I would love any recommendations.
- yuanshan 6y agoThere is an open abstract algebra book that is similar, also rendered by pretextbook framework. http://abstract.pugetsound.edu/aata/aata.html http://abstract.pugetsound.edu/aata/aata.html
- benrbray 6y agoThe following both have very well-thought out exercises that guide the reader through discovering the topic mostly on their own: > Pinter, "Abstract Algebra" > Tao, "Introduction to Measure Theory" (and "Epsilon of Room, Vol. 1")
- joshvm 6y agoThere is a gallery and catalog of Pretext books: https://pretextbook.org/catalog.html https://pretextbook.org/catalog.html
- rockwotj 6y agoThe book I used in college is super good, still have a copy on hand. Discrete and combinatorial mathematics by Ralph Grimaldi https://g.co/kgs/1Yx3N4 https://g.co/kgs/1Yx3N4
- aoe112020 6y agoIf you don't know how to count, this book will teach you how to do it, a legendary book by Grimaldi.
- willart4food 6y ago#RAD
- ngcc_hk 6y agoCould all or nearly all discrete maths is just matrix manipulation in disguise, if the function is closed in discrete number?
- generationP 6y agoUnlikely. Lots of mathematicians' hearts jump every time someone finds a slick algebraic approach to some messy combinatorics, but it's not a very frequent occurrence (I think of finding such approaches as the main part of my job). In a typical discrete maths course, the main "arbitrage" you get from algebra is the "method" of generating functions, which is a technique for dealing with integer sequences and counting problems using polynomials. If you like matrices, you can encode polynomials as Toeplitz matrices, so you can view products of polynomials as matrix products. But generating functions are not a panacea for counting, and you usually have to seed the ground with some combinatorial results before you can water it with generating functions. Also, there are some neat uses of matrices in understanding Pascal's triangle ( http://www-math.mit.edu/~gs/papers/pascal-work.pdf http://www-math.mit.edu/~gs/papers/pascal-work.pdf ) and other sequences. In graph theory, the matrix-tree theorem lets you count spanning trees using a determinant, and the Dijkstra algorithm for path finding can be regarded as a matrix power over the max-plus semiring. But that's about all you get out of linear algebra in a typical first discrete maths course. Matrices become more useful if you go deeper into graphs or into counting, but never take center stage. [And before the next question comes: I haven't seen many monads used in discrete maths either.]
- oneiftwo 6y agoThis is a fantastic resource. I've long lamented the difficulty of finding textbooks. Since colleges buy them back every semester to control demand, it's actually hard to find something that should be cheap and common. It's tragic. Good to see they're at least here online, though it's also shameful that I didn't find this on Google when I searched for it a year or so ago. Tried to buy a calculus textbook to teach a friend - only overpriced latest editions by and large were available.
- stared 6y agoI really recommend Generatingfunctionology by Herbert Wilf https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf
- ur-whale 6y agoNice book with very clear explanations (sometimes a little too elementary). However, I found the chapter on generating functions a little frustrating: it gives a very good explanation of what they are, tells you they're super useful, and gives no example of an actual problem where they're used.
- sriram_malhar 6y agoThis book seems truly well written. Even though the material is familiar to me, I liked the chapter on generating functions for its stepwise treatment. The online exercises are wonderful too.