Subject talk:Mathematics

Organization
I have so many suggestions and I have made a few edits in the last few minutes so I just deleted them and am organizing my comments about organization a little better.

It seems to me that the "Related subjects" should be retitled. They are not related to math. They ARE math. "Mathematical subjects" is a better title. And, these should be the main part of the page, on the left. The books on the left now are more of the books that are not very important, not main topics (algebra, real analysis, calculus), not well developed. These are the books that should be off to the side and the main part of the page should be the main books that are most important and most developed.

Also, the "Related subjects" part is not well organized to begin with. Topology, calculus, mathematics study guides, ... . This is essentially in random order. Something like alphabetical order, or in order by prereqs or something, but there appears to be no order at all. And, it would be nice if books inside each subject are also better organized in some way. And, it would be nice if I could click on a little + and open up the topology books and see those but still be on the same page and I could click on the same for calculus and whatever else and have them all open at the same time. I don't know how to do this in Wiki at all.

On a different but related note, it would be nice if the books were organized a bit more by level. For example, yes Algebra 1 and Abstract Algebra are both "algebra" but they are vastly different in level and don't necessarily belong together do they? If I am a high school student looking for help, it should be easier to find the list of high school books that might actually work for me. Is there any such thing?

Also, just an alphabetical list somewhere of all math books would be nice.

Also, why is there no discussion? Where is a place to talk about books that should be developed more and books that should be created and what is highest priority and various suggestions in general for math books? NumberTheorist (talk) 17:33, 10 February 2010 (UTC)


 * Visit Special:Preferences, go to the gadgets page, and check the box for "Sort HTML lists" and hit the save button at the bottom to get alphabetical lists on the subject pages. A newer version of the software to be installed soon will do this automatically. -- Adrignola talk contribs 22:24, 10 February 2010 (UTC)


 * Okay, that answers one of my questions/concerns/comments. But, as far as the rest, I think they are valid, especially the one about "Related subjects".  Yet, I am unable to do anything about it because only a few can edit this stuff. NumberTheorist (talk) 17:02, 11 February 2010 (UTC)


 * Your other concerns: using a plus sign to expand/contract &mdash; try Category:Mathematics for that; viewing books by level &mdash; try Mathematics bookshelf for that.  There are also alphabetical listings of books and listings by the Dewey Decimal system and Library of Congress system as well if you're interested.  You browse through all of them at Card Catalog Office.  Discussions of books in general can be held in the reading room (there isn't enough activity that people would be watching this page, though it would be the ideal location for such discussion).  And "related subjects" is the title given based on the template used to create the page; it used to say "subtopics" before someone made the change to the current title.  The template has been substituted however, so changing it on all the subject pages will be involved; possibly more involved than it's worth. -- Adrignola talk contribs 19:31, 11 February 2010 (UTC)


 * Thanks, this is very helpful. But, if I am just a new user to this and I want to find books by level, how am I supposed to know where to look?  Could the part at the top of the page which now says "See also: Wikibooks:Mathematics bookshelf." be changed to something more instructive, such as, "For a listing of books by level and topic, see: Wikibooks:Mathematics bookshelf."  It does not have to be exactly that but links should be descriptive and should help me know why I need to click on them.  I shouldn't have to try many different links at random just to find one that might be what I'm looking for, right? NumberTheorist (talk) 21:19, 11 February 2010 (UTC)


 * The changes you have suggested have been applied to the content page corresponding to this talk page. Trying to find a balance between what the bookshelves allow and the convenience of automatic listings on subject pages via categories is something Wikibooks has been striving to achieve for some time now.  It may be far from perfect. -- Adrignola talk contribs 21:41, 11 February 2010 (UTC)


 * Thanks, I appreciate your taking the time to listen and to work on this. NumberTheorist (talk) 21:53, 11 February 2010 (UTC)


 * Sorting books by level seems tricky to me. I ask this question of anyone who I have seen suggest it: How to decide what the "right" order is? Algebra might be taught in highschool in the US, yet might be taught earlier or later in another country. Someone from the US might be fine with Algebra being listed as highschool level, but someone from the UK might expect to see the book listed at another level. How to deal with those differences in a way that will keep the levels meaningful to everyone looking like you? -- dark lama  02:30, 12 February 2010 (UTC)


 * That is a good question, but now that Adrignola has shown me around here, I see that the Mathematics bookshelf already has the books organized in a great way, both by level and by topic. And, it doesn't call them high school math, it just calls it introductory mathematics.  In looking at it, perhaps the organization could be done slightly better but it's very good and I'm happy with it.  At least right now, that seems like a better page than this one but this is the way things are done I guess.  NumberTheorist (talk) 02:47, 12 February 2010 (UTC)

Hello, I looked around a bit and one thing I noticed is the book Combinatorial Topology. It has nothing except a few chapter titles and some red links. And, the chapter titles that are given are all things already covered in the book Topology. And, it looks like the guy who created it created it over 3 years ago and hasn't touched it since. So, I can't think of a single reason to keep this page. It should be deleted. But, I don't know how to request such a thing. NumberTheorist (talk) 17:36, 12 February 2010 (UTC)


 * Requests for deletion is your best bet. -- Adrignola talk contribs 18:35, 12 February 2010 (UTC)

Shift the burden of content creation to students
I have found that although there is a nice framework in place, that there is a serious lack of content. It seems to me that the best way to improve (and add to) the content available on open education sites is to have a few students currently enrolled in "real life" versions of courses work under an "open education" mentor as they go along. After all, who better to create material than students who actually just went through the process of learning it!? They will know best what is important and what is not important to facilitate their understanding. It is incredibly time consuming to produce/improve content in parallel with a post-school life. However, during an "in-school" life, this exercise is mutually beneficial - generating material is one of the best ways to help the student really learn the material (if you can't explain it, you don't know it!), prepare for exams, etc. At the same time, they could let WikiBooks know which topics were explained unsatisfactorily, which topics could have benefited from additional images, etc. It seems to me that it would only take one or two iterations (less than a year!) to produce some incredible material.

I really believe in the idea that "teaching is the best way to learn". By shifting the burden of creating educational resources onto freshly taught students, we are leveraging a huge, capable labor population. If a person is not enrolled in a real course, it is significant extra workload for them to create content for WikiVersity. However, if a student is taking a course, rather than spend the week before an exam staring at a book, they could be summarizing concepts, etc on WikiBooks, both helping them prepare for an exam as well as generating useful content for the world to share.

I am particularly interested in high school level technical topics (mathematics, physics, etc). It seems that with thousands of schools and millions of students, it should be easy to get ~5 interested students from every course imaginable. Then in only one or two semesters (with good mentors!), we could have an amazing foundation that could then be refined by future semesters of the same type of students.

Let me know if you agree with this and if you have any suggestions of how to recruit this type of student.

Daviddoria (talk) 16:10, 25 June 2010 (UTC)


 * Hi, I have been a bit distracted this week. In principle it is a fine idea, and there are a few books that have come about as classroom projects.  The difficulty is in getting the word to students, and getting their course instructors on board.  Being a teacher myself the idea of requiring my students to submit their work under an open license, it may be that today, or someday down the road the would like their work to be exclusively their own.  But once they have clicked submit here they have lost that opportunity.  On the other hand, giving class credit for contributing here would make sense to me if it was one of several options the students could choose from.


 * My idea for recruiting students is to develop our top level material. If we have a really top notch calculus book, freely available, then many students will come around as they prepare for their AP exams.  While they are here they will probably browse around, look at the algebra books or computer science, history etc and realize there is a lot they can add.  Particularly with mathematics people can usually contribute at a level below what they are studying for.  So my hope always was if we had a few nice, but fairly advanced books this would propagate down to improve our less advanced books.  But who knows, maybe this doesn't work because people are always looking forward. Thenub314 (talk) 10:43, 6 July 2010 (UTC)

Finding the top Maths Books
A casual visitor arriving here and wondering if there are any featured (completed) maths books could easily not find them. As far as I can see, to find the other featured maths book they have to drill down to find Formal Logic, and they won't find the wikijunior maths books at all.

Two possible solutions:
 * 1) The left hand panel could show not only books in Mathematics but also all subcategories.
 * 2) (less good) Show counts for all subcategories, so we can see that there are two featured maths books.

I think it's a significant problem. To get more editors we need more readers. To get more readers we need more people to find the good/completed books. JamesCrook (talk) 12:10, 5 November 2010 (UTC)


 * No, this is a top level category and the reader will be overwhelmed if all books in subcategories were shown. We have 2,300 books and less than a dozen top-level subject categories.  That would also defeat the effort put into categorizing them in anything but mathematics.  What needs to be done is to get all the books out of Category:Mathematics and into more specific categories.  Then this page can use root subject instead of subject page, which as you can see at Subject:Humanities allows manual specification of all the featured books in subcategories and just shows featured books and subcategories. – Adrignola talk 12:59, 5 November 2010 (UTC)

Possible new sub-categories
JamesCrook (talk • contribs) 19:45, 5 November 2010 (UTC)
 * High School Mathematics Extensions - K12 mathematics
 * Set Theory - Discrete mathematics
 * Category Theory - Category theory (other books in this category might have titles like 'Homological Algebra' and 'Functors' and 'Diagram Chasing'). Possibly there is a technical problem in a book title also being a category?  In which case rename Category:Category Theory to Category:Mathematical Category Theory could be a solution.  Or maybe sentence case solves it?
 * Famous Theorems of Mathematics - Mathematics history (would include biography)
 * Fermat's Last Theorem - Discrete mathematics (Number theory)
 * Mathematics Worksheet - Mathematical collections
 * Number Theory - Discrete mathematics (Number theory)
 * History of Mathematics - Mathematics history
 * Mathematics Handbook - Mathematical collections
 * Problems in Mathematics - Mathematical collections
 * There's only one book in Subject:Topology, so maybe it could be moved and subjects condensed. Subject pages and their respective categories should be sentence case to avoid conflicts with books using title case.  Don't know whether there's any preference on either "mathematics collections" or "mathematical collections".  Please work with Thenub314 on these categories as I'm no expert. – Adrignola talk 19:49, 5 November 2010 (UTC)
 * OK. Thanks for your help.  I'll hold off on doing more on this until I hear from Thenub314.JamesCrook (talk) 20:00, 5 November 2010 (UTC)
 * Just a note: the book's category itself should have the same categories as those placed inside the Subjects template on the root page, so that the collection of the book's pages moves along with the book's title pages in the categories. I know we're esoteric with things here so please bear with it. – Adrignola talk 20:11, 5 November 2010 (UTC)


 * I think some fine tuning could be very useful. Some ideas that come to mind is that the choice of the term "Mathematical Collections" might be useful, because of things like Collections, some people might be expecting a list of books that have pedia press ready collections.
 * Somehow we would like to get across more the mental idea of a book that is simply a list of problems, (judging from the list of books suggested for that category. What jumps to my mind is "Mathematics workbooks", what do you think?
 * I would personally like to see the books listed for "Discrete mathematics (Number theory)" be listed simply under "Number theory", since things like p-adic fields aren't discrete but are part of number theory.
 * While "Topology" and "Category theory" have only one book in them it is a bit difficult to know what to do. On the one hand subjects are not useful if we let them get diluted to the point that every subject only has one book, on the other hand it is very tempting to classify the subjects as mathematicians usually internally classify the subfields of mathematics.  There is some small hope more stuff is coming, for example User:TakuyaMurata/Topological groups might be a nice seed for a book in Topology (and algebra) if Taku could be convinced to move it into the main space, but I haven't seen him around for many months and it might be a long (possibly infinite) time before his return.  Overall I would say leave these as seperate for now, but if they must be merged merge Topology into Geometry and Category theory into Algebra. Thenub314 (talk) 04:08, 9 November 2010 (UTC)
 * You've missed the KEY issue, which is to depopulate books out of the top level category (Subject:Mathematics). We should even strive to only have books in the 'leaf' categories.  Then we don't get featured books being hidden.  See Subject_talk:Mathematics for motivation.  JamesCrook (talk) 16:19, 9 November 2010 (UTC)
 * Ah, I did miss the that section above, and jumped right to reading this. I would prefer not to use  which if I understand correctly depends on a hand written list of Featured books and so takes us a back a step toward the old bookshelf system.  (Of which I was a fan, so take the criticism with a grain of salt.)
 * Also, as a strategy when patrolling new books, if I am unsure which is the best sub-subject to put them in I place them in the top level subject. Then hopefully someone more knowledgeable then myself can move them along to the best place. This might mean I have been inadvertently making some books disappear from the subject pages... I will have to hunt through and make sure there are no such hidden books.  That is concerning, and something I would like to avoid on this page.  It would seem sensible to me to have every subject page have a list of books in that subject even if no books should appear in that subject.  New authors who are unfamiliar with our system always might add  and if we used  we would be relying on page patrollers to spot this as a mistake, and correct it.
 * To be honest I have long wanted to dispose of the templates entirely and design a something that was closer in spirit to the old Math bookshelf, but using dynamic lists. It would be easy to create a category for Featured mathematics books, place the featured books in in an have the books not be displayed in a dynamic list and add a spot them without depopulating the top level. (Generally speaking I think depopulating the top level is a good idea, but I see it just as a separate categorization issue.) The thing that stopped me for proceeding further was a disagreement about the concept of categorizing books by level.  After I had created Category:University level mathematics books, I was hoping to create category's for primary and secondary level as well, but there was a bit of a disagreement if this could be done in any sensible way. If I recall correctly Darklama felt the idea just couldn't work (for reasons I can describe if your interested).  And basically him and I were the only two people interested in the problem at the time, so I sidelined the project of redoing the subject page until there were a few more people about to determine consensus.  If your interested we could attempt to depart from using a preset template for the mathematics subject page. It might be worth glancing at the old Mathematics bookshelf Thenub314 (talk) 18:02, 9 November 2010 (UTC)


 * As for miscategorization, that's something we have to check no matter what as incorrect or excessive categorization is still possible. Yes, a "featured mathematics books" category could be used instead, though books aren't featured so often that it would be any less time compared to adding a list item and it would be necessary to look in the underlying code to see that that category is used since the featured book template can't add that automatically.  My personal feelings are that I like the unified look of the subject pages which I feel makes things look more professional.  It doesn't surprise me that some (not just you, Thenub) have been fond of the idea of a patchwork for the subject pages because in the past people had been of the mind that they could differ in appearance.  But that just reminds me of the sad fact that we have a very small project-wide community and instead consist of cohorts of people centered around individual books and subject areas.  Beyond that the single page display of all books in a subject area doesn't scale.  – Adrignola talk 19:43, 9 November 2010 (UTC)

Depopulating Top Level Category
I do not want to have my time wasted at this stage by a carefully considered reopened debate over bookshelves vs subject pages, even though the grass on the other side does look somewhat greener to me too. I want to solve this problem now and without a lot of effort. In maths what we have is broken. The logic book is not easily found. I think the templates are usable, and they look good or better than good. I don't mind the very small risk of a whole textbook dropping through a crack in the system through relying on a manual update. We all want to depopulate the top level - so let us do that as a first step. Beyond that - I too would like to use the kind of classification that universities would use, even for one book categories. When and if we have a problem with quantity of second level subjects we will address it then. We need 'Number Theory', 'Mathematics History' and possibly 'wikijunior maths'. We need the various level-of-difficulty classifications and to put books in more than one category if appropriate. Can we get back to discussing what new second level subjects to create to depopulate the top level and then get on with it?JamesCrook (talk) 21:27, 9 November 2010 (UTC)


 * I have created the Number theory and Mathematics history category. Probably we should also create a wikijunior mathematics section, but this is secondary to deciding what to do about High School Mathematics Extensions.  Is "K-12 Mathematics" a bit too americanized? (Says the American fellow to the Irish gentleman.)  This one of the major complaints when I tried to categorize things by level before. Thenub314 (talk) 22:53, 9 November 2010 (UTC)


 * English gent (who lives in Ireland) thinks K-12 is better term here than secondary school. Any teacher looking for educational resources will/should know what K-12 means (or be able to use google to find out).  Be bold!


 * My apologies. I have gone ahead and emptied out the top level subject and gone over to .  If we do thinker with the page (and I hope we do!) we ultimately we should stick very close in color scheme, layout, etc.  As Adrignola correctly points out consistency is desirable, as it comes across as more professional.  I didn't mean to reopen the subject/bookshelf discussion, only that I always wanted to tinker with the Subject:Mathematics and its sub-subjects to include information about which level a book is intended for.  I suppose I had more in mind substituting the template directly and tweaking what is there already.  By the way, are there any objections to renaming "Mathematical collections" to something like "Collections of problem in mathematics"?  I would really like it to be clear that we are talking about collections of problems, instead of anything else. Thenub314 (talk) 23:53, 9 November 2010 (UTC)


 * Looks good, but don't forget to recategorize the book's category so it moves with the root page. I took care of that for any that were missed; no worries.  I also added formatting consistency for the categories, links to Wikipedia subjects for any that had some, and protected the new subjects.  "Collections of problems in mathematics" is quite wordy.  Could we get by with "mathematics problems"? – Adrignola talk 00:34, 10 November 2010 (UTC)
 * Nice catches, thanks! As you know I am not so great with these sort of details. I could live with "Mathematics problems".  Another option I that is less wordy that I like is  "Mathematics workbooks" but my gut tells I may be alone in liking that title.  Thenub314 (talk) 02:00, 10 November 2010 (UTC)


 * That may actually be better in my opinion. – Adrignola talk 02:19, 10 November 2010 (UTC)

Fine Tuning
Thanks for the re-org to depopulate the top level. It's good.

I envisaged 'Mathematical Collections' as for anything that was a miscellany. It just happened that the majority were problem sets. I didn't think 'Solutions to Hartshorne's Algebraic Geometry' belonged in it. Ideally SHAG belongs in Subject:Algebraic Geometry, but putting it in both Subject:Algebra and Subject: Geometry would do for now. The 'Mathematics Handbook' has now disappeared, which is good - and reduces the need for a miscellany category. 'Mathematics workbooks' implies that there are solutions (good) as well as problems. I guess that is good. Thenub314, if you would like to change over to that I'm fine with it, at least until we have more maths books. I'm also fine with no change. What matters to me is that the top stays depopulated. JamesCrook (talk) 00:05, 11 November 2010 (UTC)

Size of this list
Having now looked at Subject:Books_by_subject and compared mathematics to other top level subjects, we have too much at our second level. Here's a proposed shift down of some of our second level items:

Keep at second level:


 * Applied mathematics
 * Pure mathematics (new)
 * K-12 mathematics
 * Mathematical collections
 * Mathematical references
 * Mathematics history
 * Mathematics study guides

Now at third level (under Pure mathematics)
 * Algebra
 * Calculus
 * Category theory
 * Discrete mathematics
 * Elementary arithmetic
 * Geometry
 * Mathematical analysis
 * Mathematical logic
 * Number theory
 * Topology

JamesCrook (talk) 23:32, 11 November 2010 (UTC)


 * I am prefer not creating a "Pure mathematics" subject. The difficulty is that many of the subjects that are then classified under pure mathematics have aspects that are both pure and applied.  I will have to think about the best way to shorten the list.  But is there a reason to do so except keeping up with the Jones's?
 * Well... by your logic we should also abolish the Applied mathematics subject!  If university departments have little difficulty deciding which is which, surely we can split along the lines they use?  For me the most borderline case is 'Calculus' and that is pure.  In a more extreme case, if there is one, we could put a subject under both, just as we put 'Algebraic Geometry' under Algebra and Geometry, even though it is a subject in its own right.  As to 'keeping up with the Jones' - as a mathematician surely you see the merits of a balanced tree :-) ?  More seriously, we have far less content than 'Science' yet take up more space on the subject page.  It is less about competing, more about trying to do the right thing by other subject groups.  If I was designing subjects the whole subject hierarchy would have higher arity at each level and I would reduce the depth - I am happy with much more information per page - but I am not going to go round getting consensus for that and then after that go round changing every subject tree to meet my preference and fixing the templates too to work well with larger lists.  The real issue is technology.  A search-and-sort is more useful than these static lists.  It's kind of futile trying to fix it within the limitations of template generated static lists because it can only get to a certain level of goodness with that approach.  I'd sooner lobby for search-and-sort extensions to the software than lose my time tweaking a system that is not going to improve a lot by tweaking.  What I care about is a certain level of usability.  I think it is a disaster if featured books cannot be found for a particular subject starting from the subject.  It now works for humanities and mathematics but I believe is broken in some other subjects.  I would be most upset if a teacher looking for a mathematics textbook to use at K-12 level cannot find those books starting from mathematics.  At the time of writing this I don't really mind about the finer details of how it is done, whether we split pure and applied or lump them together, whether we have an 'other' catch all at each level, whether we have an escape to a complete book list for a subject, whether we allow or don't allow one book categories and all that kind of thing. JamesCrook (talk) 13:24, 14 November 2010 (UTC)


 * Well I suppose the difference I saw between the Applied mathematics subject and the Pure mathematics subject (as they are currently anyways) is that applied mathematics is mostly only attempting to classify books. With "Mathematical Physics" being an obvious exception.
 * While at the moment when I look at Subject:Mathematical Analysis it has Numerical Methods as a book, which would not normally be considered a book on pure mathematics. Similarly, Crystallography also falls under Subject:Geometry and so is another book which aims to be applied which falls under the category of pure mathematics.
 * I am also concerned that these pages turn out to be more persistent then perhaps they should be, so I always try to ask what will be a good system to use going forward. The idea that troubles me is there parts of algebraic geometry that have a lot to do with coding theory and cryptography, category theory is these days being applied to computer science, etc.
 * One way to handle this is to place the book in both the Category theory subject and the Applied mathematics subject if necessary. But this seems a bit off to me if Category theory itself is under pure mathematics.  Thenub314 (talk) 17:05, 14 November 2010 (UTC)

I realize it has been a year or so, but I turned up to this page looking for the linear algebra book, so I could verify that is appears in the completed category of books, and realized I didn't know how to find it. Overall I would like to move away from the pure mathematics category because it hides everything from view, and buries it too deep. Perhaps it would be better to populate this page a bit more, making this page larger, but the depth to which one needs to dig a bit less. Thenub314 (talk) 20:34, 14 November 2011 (UTC)


 * I completely agree. I have an undergraduate degree in math and a master's in statistics, and I still don't know which subsection to try for a lot of topics. How are most people supposed to understand why (for example) probability, statistics, and modeling theory are to be found under "applied mathematics" but algorithms, logic, and calculus are to be found under "pure mathematics" — especially since the "definitions" of these subdivisions are only to be found on the subpages and not on this page? - dcljr (discuss • contribs) 23:42, 15 November 2012 (UTC)

Needs complete reorganization
As I mentioned in the previous section, I find the current classification scheme almost completely useless. The "Pure mathematics" vs. "Applied mathematics" dichotomy is problematic, to say the least. And "K-12" vs. "University level" isn't much better: why should Calculus be in K-12? Not everyone learns calculus before they get to college. I think a better scheme would use 3 divisions, roughly corresponding to: "before algebra", "algebra and after, but before calculus", and "calculus and after". I know not everything is easily classified according to this scheme, but I think it would be clearer to most people. - dcljr (discuss • contribs) 23:57, 1 May 2013 (UTC)

Towards a PlanetMath Books Exchange
Please lend your support to this Individual Engagement Grant meta:Grants:IdeaLab/PlanetMath_Books_Project proposal I've put together with PlanetMath contributor Raymond Puzio. Inspired by the PlanetMath Exchange project, our aim with this proposal is to improve the PlanetMath platform and make it easy to produce mathematics textbooks -- for export to places like Wikibooks. Your endorsement of the grant proposal would mean a lot! And any comments prior to the Sept. 30, 2013 deadline will help us improve the proposal. --Arided (discuss • contribs) 22:37, 27 September 2013 (UTC)