I have seen some courses in the university that start with "Topics in this ... Topics in that ...", I have also seen some books that use that word "Topics in Algebraic Graph Theory", "Topics in Structural Graph Theory", so, I've been thinking, what is the difference beetween a book of "Algebraic Graph Theory" and one of "Topics in Algebraic Graph Theory"?, What is the meaning of the word "Topic" in academia context?

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    Also "Special Topics" – Azor Ahai -him- Sep 10 '20 at 17:13
  • I suggest this Question belongs not to Academia, but to English Language Learners. If you insist "Algebraic Graph Theory" and any kind of "Topics in Algebraic Graph Theory" are different, can you explain how, please? – Robbie Goodwin Sep 10 '20 at 18:55
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    I think it belongs here, because I am asking about how the concept is applied in this context, not the word itself, in my native language, topics is translated as "topicos" and there are some courses in my university like "Topicos en Teoria cuantica de campos", "Topicos en aquello" and I still really wouldn't know how the word "Tópicos" is used. The meaning of topic in a dictionay is: "a matter dealt with in a text", but I guess in every book there's always a matter dealt in the text, so from the definition it may look like a pleonasm – DieDauphin Sep 10 '20 at 19:36
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    @RobbieGoodwin They would differ in most universities in that one of them is a "Topics" course (yes this is a thing and is exactly what it sounds like: it covers a collection of variable topics chosen by the instructor that can vary rather than having a fixed syllabus). – Morgan Rodgers Sep 10 '20 at 20:01
  • @RobbieGoodwin I don't know what algebraic graph theory is, but a "Topics in Language Acquisition" would probably delve into a professor's favorite research topic, for example how bilingual English/Spanish kids learn English and Spanish syntax. – Azor Ahai -him- Sep 11 '20 at 20:41

"Topics in" usually means that the content is

  • not meant to be introductory (i.e., the reader is assumed to already have some prior familiarity with the subject), and

  • not meant to cover "all the important things", but can focus on a selection of (well) topics the author is interested in.

For example, a "Topics in Representation Theory" course can afford to skip both the basic properties of finite group representations (as it is not introductory) and focus (e.g.) on quiver and Hopf algebras. Often, books will have more precise titles than "Topics in...", but lecture notes often take their titles from those of the classes, which are often intentionally vague so they don't have to be changed every year depending on the lecturer. For a department, calling a class "Topics in Algebra" is an easy way to offer a course that will be on something different each year without the trouble of having to rename it every year.

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    To elaborate on the last point, the department will often rotate the local specialists in subject X through the "Topics in X" course from year to year, with each of them teaching their favored perspective. So you might want to ask who is teaching it this year and what they plan to do. – David E Speyer Sep 10 '20 at 17:56
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    This answer matches my experience, but it also has a corollary that's often important. Ordinarily, a student cannot take the same class more than once for credit. But that rule doesn't apply to topics courses because (even) university administrators understand that such a course will be about different topics in different semesters. – Andreas Blass Sep 10 '20 at 23:04
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    It may also mean that the course will not progress linearly through things that build on one another, but rather cover disparate, self-contained aspects of the broader subject. – CCTO Sep 11 '20 at 14:46
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    It also means the lecturer doesn't have a good idea of what they're going to teach yet ... – Allure Sep 11 '20 at 20:52
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    At least at my university "topics in ..." refers to advanced discussion of a field not typically covered in the regular curriculum. This could include things like research writing, game design, recent innovations in algorithms, probabilistic algorithms, and other such topics. There's usually a "rotation" of these topics with occasional introduction of something new. Admittedly these are typically "filler" courses for graduates that have taken the core set of graduate classes in order to meet the ~35 credit hours of in-seat course requirements before starting dissertation work. – user117751 Sep 12 '20 at 5:00

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