Talk:Discrete mathematics

Guideline
In fact, the Association for Computing Machinery (ACM) amended the guideline so that a discrete methematics course is required.

What guideline? -- Wapcaplet 01:59 9 Jun 2003 (UTC)


 * I don't know. The textbook I am using says
 * Subsequently, discrete mathematics courses were endorsed by many groups for several different audiences, including mathematics and computer science majors. A panel of the mathematical Association of America (MAA) endorsed a year-long course in discrete mathematics. The Educational Acctivities Board of the Institute of Electrical and Electronics Engineers (IEEE) recommended a freshman discrete mathematics course. The Association for Computing Machinery (ACM) and IEEE accrediation guidelines mandated a discrete mathematics course.

I just summarised this. Do we have to specify what guideline? Is it really significant to do that? -- Taku 05:17 9 Jun 2003 (UTC)

AKA
So you could also call this fundamentally-unfundamental mathematics, fabricated mathematics or even pseudo-mathematics???


 * The first one, "fundamentally-unfundamental", is wrong, for discrete mathematics has a lot of important applications in the study of nature. The second one, "fabricated mathematics", can pull out a whole philosophical argument on the nature of mathematical objects, and I prefer to not go there. The third one, "pseudo-mathematics", not only denotes you don't understand the meaning of the therm "pseudo-mathematics", as it also makes you sound like a whiny, ignorant, stupid teenager.
 * The reason you think this way might be the fact that mathematics has evolved to serve physics during the majority of it's history, and only recently (one or two centuries ago) did new mathematical fields emerge with emphasis on other sciences. In the ancient times, mathematics was so close to physics that nowadays a strong misconception of what mathematics should be remains, since the self-titled "real mathematician" out there still claims that any topic not applicable to physics is "fake mathematics". The truth, though, is that mathematics is the study of formal objects, objects that might be models for phenomena in the physical world, but cannot be said to be present in it if not by abstraction. --201.21.181.131 (talk) 18:03, 20 July 2011 (UTC)

Finite Math
Finite Math is not the same as Discrete Math. On pages 7 and 8 of the following pdf, the "inventors" (Kemeny, Snell, and Thompson) of the term explain it's meaning: A few years ago [1950's], the department of mathematics at Dartmouth College decided to introduce a different kind of freshman course, which students could elect along with [the] more traditional [pre-calculus] ones. The new course was to be designed to introduce a student to some concepts in modern mathematics early in his college career. While primarily a mathematics course, it was to include applications to the biological and social sciences and thus provide a point of view, other than that given by physics, concerning the possible uses of mathematics.

In planning the proposed course, ...[o]ur aim was to choose topics which are initially close to the students' experience, which are important in modern day mathematics, and which have interesting and important applications. To guide us in the latter we asked for the opinions of a number of behavioral scientists about the kinds of mathematics a future behavioral scientist might need. The main topics of the book were chosen from this list.

Our purpose in writing the book was to develop several topics from a central point of view. In order to accomplish this on an elementary level, we restricted ourselves to the consideration of finite problems, that is, problems which do not involve infinite sets, limiting processes, continuity, etc. By so doing it is possible to go further into the subject matter than would otherwise be possible, and we found that the basic ideas of finite mathematics were easier to state and theorems about them considerably easier to prove than their infinite counterparts.

So, the fact that Finite Math avoids concepts of infinity, does not mean that variables can only take on discrete values. One topic covered in Finite Math is Gaussian Elimination, to solve systems of linear equations. Here the variables are generally real numbers (not just integers), and so they are continous. While there are an infinite number of real numbers, the concept of the infinite need not be discussed to apply Gaussian Elimination.

--DavidUhland (talk) 12:22, 21 January 2009 (UTC)-David


 * "Finite Mathematics" is a term used in many ways, unfortunately. Radagast3 (talk) 02:58, 28 March 2009 (UTC)


 * If a topic has a concept of continuity, it has a concept of the infinite. Gaussian elimination either works with some closed, finite, (and discrete) subset of the reals or the continuity is demonstrated by an infinite application of row operations or dividing by an infinitesimal or similar infinity-necessitating event. "finite" and "continuous" aren't terms used in many ways. Metaquanta (talk) 22:09, 28 August 2018 (UTC)

The article says that Most, if not all, of the objects studied in finite mathematics are countable sets, such as the integers. Are they? The article lists linear algebra and set theory as things included in discrete mathematics. In linear algebra one often studies vector spaces with countable dimension, but real and complex vector spaces of any dimension are obviously not countable. Clearly set theory is not restricted to countable sets. Josh Cherry 04:20, 7 Dec 2004 (UTC)

As you note, set theory, of course, goes above and beyond the countable, and is usually considered discrete math nonetheless. And, naturally, one could study uncountable graphs in graph theory, etc, so countability is hardly essential to discrete math. Nonetheless, I'm surprised to see linear algebra mentioned here. Is that really generally considered discrete math? I wouldn't have thought so; it doesn't have the right "flavor" in my mind. What are other people's opinions? -Chinju 19:46, 4 June 2006 (UTC)


 * Any set of finite graphs will be countable, certainly. And linear algebra is used in graph theory. Radagast3 (talk) 02:56, 28 March 2009 (UTC)

Discrete maths apply to ALL computer programming languages, etc.
"Discrete mathematics is a common type of mathematics used particularly in the web programming languages, PHP, ASP, and Perl."
 * Yeah, I just deleted that silliness. Josh Cherry 00:08, 14 Jan 2005 (UTC)

Music
I deleted the claims for application to musical areas, specifically atonality and muscial analyssi. I couldn't find anything in the articles linked to too support the claim that discrete mathematics was useful in these areas. And I have never heard it before.

If someone wants to put it back in I think they should summarise what the applications consists of here.

Dewarneb
What does "Dewarneb" have to do with discrete math?

Actually, if I were a registered user I would nominate Dewarneb for deletion, seeing as it gets no google hits outside of WP and seems unverifiable. 70.231.146.142 22:14, 23 December 2005 (UTC)

"Logic"?
Do you mean mathematical logic, or just plain logic? I'm pretty sure it's the former, but I'm not going to change it due to lack of experience in the field (but I'm taking a class in university). -Matt 16:07, 27 January 2007 (UTC)

Regional definitions of "Finite Mathematics"
The page for Finite Mathematics redirects here. When I took finite at a university in the USA, it was business math--definitely below the level of the discrete math classes. We did amortization, annuities, etc. etc. (It was horrible and I wish I'd just taken calculus.) After discussing these differences with a Canadian friend, who took a finite class that was what I'd call discrete math, I did some googling. What I found was that some US schools call anything beyond calculus "finite," some treat it as "intro to discrete," and some equate it with "business math." Could someone who knows this stuff better than I do clear it up a little if you think it would be useful? I think it might be helpful to new college students (if only to alert them that they might want to check with the instructor to see what the course really is!). --Wintersweet 21:35, 29 June 2007 (UTC)

Another "not so good" article
This is such a frequently viewed article and is unfortunately not so good. Personally I am not a discrete mathematician but even the first sentence is not correct. It initially said "discrete objects are objects that are not continuous". Unfortunately a large proportion of the population think that R is 'continuous' and that the integers are 'not' but don't know the formal mathematical term for this (linear continuum or connected space but both are in fact equivalent for ordered sets with the order topology). I changed it but I am still not totally conformatable with the new term. Could someone please fix this up? PST

Silly rabbit added "fact" to that statement with the explanation that graphs are connected. Although I agree that the statement in imprecise, the set of all vertices (or nodes) in a graph is disconnected so that is probably why graphs are under discrete mathematics. PST


 * Actually not all graphs are connected: see connected graph. -- PS T  15:50, 19 January 2009 (UTC)

The very concept of "discrete mathematics" itself is somewhat unsatisfactory
The thing is, analysis is like anything else in mathematics. It can be built up from the basic principles of counting. That is, the simplest principles that build the addition function, which we think of as the number of elements in a union of finite disjoint sets of given sizes, and the multiplication function, the exponentiation function, etc, and anything required for general talk of "the" number of objects corresponding to some act of counting, that is, to prove that it is well defined. These basic counting principles are responsible for all of mathematics, including analysis. There is only one mathematics. There is no distinction between discrete and continuous mathematics that is not exposed as an illusion if you look hard enough. There are no walls.

It's fine to think about discrete mathematics in the same sort of loose way that people think about the distinction between number theory and combinatorics. For example, the Goldbach conjecture is easily stated combinatorially, and that's fine as long as you recognise the inherent looseness in what these two areas of mathematics represent. An article about "discrete mathematics" can never be very good. All it can say, is that discrete mathematics is a hodgepodge of areas of mathematics which do not implictly involve the areas of real or complex analysis, or topology, for their study. Anything else would be far from the truth. I say "implicitly", because real and complex analysis, and topology to some extent, can be very useful in these areas. —Preceding unsigned comment added by 212.183.136.194 (talk) 23:21, 29 January 2009 (UTC)

Article rewrite
I have begun a reorder/rewrite. The article still needs work, but is no longer a stub. Radagast3 (talk) 05:05, 28 March 2009 (UTC)


 * Looks good. Keep going! Jakob.scholbach (talk) 12:38, 28 March 2009 (UTC)


 * Thanks! But I think I might take a rest right now and let others expand the article a bit. Radagast3 (talk) 00:34, 29 March 2009 (UTC)

Relationship to Outline page
Currently this is the main Discrete Mathematics article (linked from Portal:Discrete mathematics), but there is also an Outline of discrete mathematics, which is largely a topic list. What is (or should be) the relationship between these? Radagast3 (talk) 00:31, 14 August 2009 (UTC)

The first sentence
As of writing, the first sentence in the article reads:
 * "Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous."

Apparently, discrete math is discrete. Can we try a non-tautological introductory sentence? @harej 01:19, 3 October 2009 (UTC)
 * Well, it tells you that discrete mathematics isn't continuous. The rest of the lead paragraph explains in more detail. "Discrete mathematics" is hard to capture in one single lead sentence, although you're welcome to suggest a better one. — Radagast3 (talk) 06:22, 3 October 2009 (UTC)
 * Good point. After reading more of the first paragraph and thinking about it, I think "Discrete mathematics is the branch of mathematics concerned with functions and other mathematical constructs that lack continuity." would be decent. @harej 04:21, 4 October 2009 (UTC)
 * I'm not sure. "Lack continuity" is a little ambiguous, and the discreteness restriction applies primarily to the objects of study themselves, not just to the functions operating on them.  In any case, to say "discrete math is math about discrete objects" isn't really tautological, if you think about it, as long as "discrete objects" are properly explained. Which I think they are at present. — Radagast3 (talk) 04:39, 4 October 2009 (UTC)

relations —Preceding unsigned comment added by 59.164.188.179 (talk) 18:51, 4 December 2009 (UTC)

Continuous topics in Theoretical computer science and other areas
The sentence: "Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in all branches of computer science". I've highlighted the word "all" because I think it is misleading to say discrete mathematics is used in all areas but omit to mention the existence of continuous analog computation. It gives the impression that all computation is discrete.

The article should mention that information theory and computer science and the other areas include continuous processes and continuous signals, and not give the misleading impression that these subjects are solely concerned with discrete objects.

Plenty references describe the use of differential equations and continuous dynamical systems to model analog computation: e.g. Analog computation with continuous ODEs MS Branicky - Proc. IEEE Workshop Physics and Computation, 1994, or Analog computation with dynamical systems, HT Siegelmann, S Fishman - Physica D: Nonlinear Phenomena, 1998 Bethnim (talk) 09:21, 22 March 2010 (UTC)
 * "It gives the impression that all computation is discrete." Ultimately, it is, unless you really think P = NP. Tijfo098 (talk) 06:04, 25 March 2011 (UTC)

"Further reading" section
The "Further reading" section, as it stands now, is a mishmash of fundamental texts and not-so-memorable books. I have attempted to prune it, reducing the list to just half a dozen of undoubtedly great texts, but my edit has been reverted. May we discuss here a policy, or an explicit list, in order to avoid that anybody adds his preferred book? I suggest, at the very least, the criterion that at least one of the authors is the subject of a WP article. Other opinions? If not, in the next few days I will delete exactly the items failing this criterion. Goochelaar (talk) 08:35, 1 August 2011 (UTC)


 * I don't have a strong opinion on this, but I think deleting possible references on the grounds of such a relatively mechanistic criterion might not be helpful. The article is clearly at a very basic level, so even the mishmash list is a helpful addition to it, as far as I can tell (I'm not into discrete maths, though). If you care about the article, maybe you try and add a few more specific references to the text, thus moving some "Further reading" items to the reference list? Jakob.scholbach (talk) 10:04, 1 August 2011 (UTC)

I agree with Goochelaar. The list contains too many elementary texts that are all basically isomorphic to each other. There are zillions of them, many better known than some of these. I think 3-4 general elementary texts would be enough (my vote is Biggs, Graham et al, and Matousek et al), plus serious general handbooks like Rosen. McKay (talk) 07:03, 2 August 2011 (UTC)

I agree with Jakob.scholbach. For a very basic article such as this, the further reading list should contain a significant number of elementary texts and readings. I think the general elementary texts suggested by McKay (Biggs, Graham et al, and Matousek et al), plus several other elementary readings, should be included. Discreto (talk) 07 August 2011 (UTC)


 * Sorry for not having taken part to the discussion any more, and thanks for all the opinions and edits. I believe the bibliography is somewhat better now. Goochelaar  (talk) 23:11, 7 August 2011 (UTC)

Somewhat misleading
This article makes no mention of the fact that DM is basically the name of an introductory course mostly used in North America, and maybe the UK. In fact the definition of the the field as including a whole bunch of other fields (instead of being the introductory course to them) does not appear to be actually sourced. 86.127.138.234 (talk) 11:43, 11 February 2015 (UTC)

Also sentences like "Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, programming languages [...]" strongly imply that DM is a field of research that somehow influenced something else, which actually isn't the case. It's rudiments of those fields that get put under freshman-level DM umbrella course. 86.127.138.234 (talk) 11:48, 11 February 2015 (UTC)


 * I don't think the article is misleading. While it's true that discrete mathematics is often an introductory course in university math programs, the article is not about the course. It's about the entire field of discrete mathematics as a whole. I'm going to go ahead and remove the misleading tag. If anyone disagrees with me, then we can discuss it further here. Thanks, wia (talk) 23:03, 23 March 2015 (UTC)


 * It's more than just undergraduate coursework: Discrete Mathematics (journal). -- 120.19.193.37 (talk) 12:11, 13 July 2016 (UTC)


 * Definitely looks like (an active) field of research to me. Metaquanta (talk) 22:15, 28 August 2018 (UTC)

The sentence in the beginning, '... discrete mathematics has been characterized as the branch of mathematics dealing with ...', is, IMHO, misleading. The problem is the phrase, 'branch of mathematics'. For precalculus, the article describes it as a course or courses. I don't think discrete math is a recognized branch or field of math, just as precalc is not a branch of math. — Preceding unsigned comment added by 173.95.166.98 (talk) 20:48, 6 August 2020 (UTC)

Discrete Feynman diagrams and quantum matrices
The main article doesn't mention enough the use of D.M. in Feynman diagrams and quantum matrices. — Preceding unsigned comment added by 2.84.221.55 (talk) 19:32, 2 February 2016 (UTC)

Assessment comment
Substituted at 19:55, 1 May 2016 (UTC)

The "definition" given in lead section is esoteric gibberish that uses vague pictures and metaphors but is actually meaningless
What does it mean for real numbers, graphs, integers etc to "vary rather smoothly" or not? What does it even mean for numbers or graph to "vary"? These are visual images but without real sense.

Did it mean that in any open interval between two real numbers there is always a real number? Rational numbers have this property too, yet are they considered continuous? The only remotely acceptable definition mentioned in the article is that discrete math is related to countable sets. If, as the article admits, there is no exact definition of the term "discrete math", then it is better not to give one than to be enigmatic.