
Discrete Mathematics: An Open Introduction, 3rd edition - alokrai
http://discrete.openmathbooks.org/dmoi3.html
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stared
I really recommend Generatingfunctionology by Herbert Wilf
[https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf](https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf)

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pooya72
I'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.

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tty7
Let me use the, 'What programming language should i start with?!' analogy :)

Just start reading the book (any discrete mathematics book!) :)

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pooya72
Actually, 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.

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exceptione
I get the following error:

    
    
      Error on line 1. Unspecified reference named 'HTDP' 
      in the expression 'I highly recommend HTDP'
    

Any help?

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mcherm
Clever!

[https://htdp.org/](https://htdp.org/)

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adnauseum
This 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).

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CrazyPyroLinux
Thank you for introducing me to the idea of the "Zettelkasten" \- I'm "one of
the 10,000" for that idea today.

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Eugeleo
I 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.

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jwdunne
Just 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!

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rockwotj
The 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)

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aoe112020
If you don't know how to count, this book will teach you how to do it, a
legendary book by Grimaldi.

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xrd
This 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.

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ur-whale
Nice 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.

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sriram_malhar
This 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.

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lordleft
I have to say that I quite like the visual design of this “open” textbook.

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jka
It 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)

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oneiftwo
This 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.

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hnxs
This is great. Is there anything else of similar methodology and quality for
other math subjects? I would love any recommendations.

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yuanshan
There 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)

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ngcc_hk
Could all or nearly all discrete maths is just matrix manipulation in
disguise, if the function is closed in discrete number?

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generationP
Unlikely. 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.]

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willart4food
#RAD

