Help:Using textbook references
In many Groupprops, articles, particularly basic definition articles and articles on standard terminology, there is a subsection titled Textbook references in the References section. This section is penultimate, coming before the External links section.
This article describes how you can use textbook references.
Forward search: from wiki to book
Suppose you encounter a definition or fact on the wiki, and want to read more about it. The Textbook references section gives links to books where the definition or fact is given. Here's how a typical textbook reference section for a definition page looks:
Page name: Nilpotent group
Textbook references section reads:
- Abstract Algebra by David S. Dummit and Richard M. Foote, 10-digit ISBN 0471433349, 13-digit ISBN 978-0471433347, More info, Page 190 (formal definition, along with lower central series and upper central series)
- Groups and representations by Jonathan Lazare Alperin and Rowen B. Bell, ISBN 0387945261, More info, Page 103 (definition introduced in paragraph, along with lower central series and upper central series)
- A Course in the Theory of Groups by Derek J. S. Robinson, ISBN 0387944613, More info, Page 122 (formal definition, in terms of central series)
- An Introduction to Abstract Algebra by Derek J. S. Robinson, ISBN 3110175444, More info, Page 174 (formal definition, in terms of central series)
- Algebra (Graduate Texts in Mathematics) by Thomas W. Hungerford, ISBN 0387905189, More info, Page 100 (definition introduced in paragraph)
- Topics in Algebra by I. N. Herstein, More info, Page 117 (definition introduced based on exercises 13-14, that implicitly define lower central series and upper central series, and precedes exercise 15)
Here's how a given textbook reference is to be read:
- It begins with the name of the book and author, along with ISBN number and a link to more information. Clicking on the ISBN number leads to a page that gives links to the pages for online booksellers for the given book.
- There's a superscript link for more information. This'll take you to the book clip page, which'll allow you to get a quick idea of what the book is, as well as check out what are the terms defined, facts proved and facts stated in the given book. It also gives information like: what are the places where this book is used as a course reference, and what material on the wiki is closely related to content in the book.
- This is followed by the page number, chapter or section where the definition or fact statement is given. Parenthetically, further information about the kind of information is provided. For instance, the first reference, above, to the book by Dummit and Foote, says that the term is defined along with upper central series and lower central series. Note that page numbers, chapters and sections, as well as the specific language in the book, may vary with edition.
Here's how the references section looks for the fact article normality is not transitive.
- Abstract Algebra by David S. Dummit and Richard M. Foote, 10-digit ISBN 0471433349, 13-digit ISBN 978-0471433347, More info, Page 88, Exercises 22(a) and (b) (part (a) asks for the case where we're intersecting only two subgroups)
- Topics in Algebra by I. N. Herstein, More info, Page 53, Problem 4 (stated only for intersection of two subgroups)
- An Introduction to Abstract Algebra by Derek J. S. Robinson, ISBN 3110175444, More info, Page 45, Exercise 2
Note that along with the page number and exercise numbers, the information in parentheses gives an idea of the specific circumstances of the way the fact is stated in the book.
In addition to this, the automatically generated Facts at the bottom of the page, give a list of all the books where the given term is referenced, defined, stated, or proved. The convention followed is:
- If there's any textbook reference for the given term or fact, the given term is considered to be referenced in the given textbook.
- If the term is defined in the given book, it is listed as defined in the given textbook.
- If the fact is stated (not necessarily proved) in the given book, it is listed as stated in the given textbook. This includes facts that are stated in exercises and riders.
- if the fact is stated and proved in the given book, it is listed as proved in the given textbook.
Backward search: from book to wiki
Locating the book on the wiki
There are two ways of doing this:
- Locate the page for the book using Category:Books.
- Type the ISBN number of the book in the search area. For instance, for the book by Dummit and Foote, type "ISBN 0471433349" in the search bar. This'll give you the hit for Book:DummitFoote.
- Search using the authors, or other criteria. You can limit the search to books by ticking the "Book" namespace in search (learn more at Help:Searching Groupprops).
Learning more from the book page
The book page should give general information about:
- The contents, structure and organization of the book
- Places where the book is used as a course material or reference text
- Information and material on the wiki that is closely related to the book
Locating specific information in or about the book
Every book page has a box on top with links to pages that list the terminology defined, facts stated, facts proved, and all stuff referenced in the book. Using these links, you should be able to:
- Get a flavor of the kind of content in the book, by seeing what terms are defined, what facts are stated, and what proofs are given.
- Locate a specific fact that is stated in the book, on the wiki. Since these pages display only those facts tha tare stated in the given book, you have a narrower range within which to search.
Note that the language specifically used in the book is not duplicated on the wiki. So, searching using specific text in the book is unlikely to be effective.
Semantic search: make sophisticated queries about book content
Semantic search works well for a number of more sophisticated queries about books. You can make semantic search queries at the page Special:Ask. Here are some examples:
- Suppose you want a complete list of basic definitions in group theory, that have been referenced in the book by Dummit and Foote. Then the query to be typed in is:
[[Category:Basic definitions in group theory]][[Referenced in::Book:DummitFoote]]
- Suppose you want to find out what things occurs both in the book by Alperin and Bell, and in the book by Dummit and Foote. The query for that is:
[[Referenced in::Book:DummitFoote]][[Referenced in::Book:AlperinBell]]
- Suppose you're interested in a list of those facts that are stated in a particular book, say, the book by Alperin and Bell. Then you can do:
- Suppose you're interested in a list of those facts that are proved in a particular book, for instance, Dummit and Foote. Then you can do:
Again, multiple queries of this sort can be combined. So you can find out all the facts that were stated in one textbook, proved in another, and that are of a particular kind (for instance, subgroup property implications).