1. Chapter 1: “Reading” Working with the Literature Copyright Bruno Buchberger 2004 No parts of this file may be copied or stored without written permission.

2. The Role of the Literature Categories of Documents Bibliographic Data Working with the Literature –Searching Literature –Reading Papers –Documenting

3. Questions: What do you do if your paper is rejected? How do you search for literature on “the Galois groups of origami constructions”? Under which keywords to you look for “non-linear equations”? What is the difference between an editor, a publisher, and a referee? What do you do if you are asked to write a referee report for a paper? How do you find out whether a paper of 1992 was further pursued?

4. How do you find out whether a journal article is available in your library? Do articles in conference proceedings count as “publications”? Will journals become obsolete with the future advances of the web? How long does it take to find out whether a paper is relevant for your research? Is the following reference OK: “N. Nakatani. On Fibonacci Numbers. Technical Report, 2004 “ ? Is the following citation OK: “For the resolution method, see [Miller, Mayr 2004]” ?

5. The Role of the Literature own thinking consulting the literature

6. Categories of Documents Books Journal Articles Conference Proceedings Articles Collection Articles Technical Reports Please see the lecture notes for details. authorship, contents, originality, quality control, organization and production, access, reputation. “books” “papers” “publications” “refereed publications”

7. The organization of journals: author publishing company editor and ed board anonymous referee reader Please see the lecture notes for details.

8. Anonymous peer refereeing: A corner-stone of modern science. An non-trivial invention (~ 1650). An ingenious invention: the purifying effect of anonymous criticism. Independent of belief, religion, race, sex, nationality, age, authority, politics, … The essence of “scientific” literature independent of the “medium”. The basis of “democracy”. A gift for the authors.

9. A refereeing “algorithm”: saves time of referees helps authors authors can help referees Read abstract, conclusion, intro. In scope? no Reject. yes Report.

10. Read paper superficially Clarity? no Reject. yes Importance? no Reject. yes Report.

11. Difficulty? no Reject. yes Originality? no Reject. yes Report.

12. Sufficient details? no Reject. Goto “presentation?” Revise. Intuitively correct? no yes Report.

13. Read and check paper in detail Correctness? no Reject. yes Presentation? no Revise. yes Accept. Report.

14. The Role of the Literature Categories of Documents Bibliographic Data Working with the Literature –Searching Literature –Reading Papers –Documenting

15. Bibliographic Data for unique identification of literature documents for getting hold of documents  completeness ! Please see the lecture notes for details.

16. The Role of the Literature Categories of Documents Bibliographic Data Working with the Literature –Searching Literature –Reading Papers –Documenting

17. Working with the Literature: Search

18. Research Index, see citeseer.ist.psu.edu/cs "CompuMath Citation Index " (CMCI), see www.isinet.com/products/citation/specialty/cmci search for math / CS search engines “forward search” is possible! A literature search “algorithm”: Given: a “topic” Find: all relevant literature on the topic. Web Search engines Citation indices Please see the lecture notes for details.

19. cites AB The fundamental relation between papers: backward search forward search

20. Authors are happy if you ask about their papers! Ask colleagues. Use available papers. Use reference lists for backward search.

21. authors’ index keyword (subject index) thesauri are a problem! example: AMS Subject Classification Scheme. the documentation of math is not problem oriented! Use libraries.

22. An experiment: search for “equations”: for linear equations (over fields), search under the keyword "linear algebra" for linear equations (over the integers), search under the keyword "number theory" for nonlinear equations (over fields), search under the keyword "algebraic geometry" for numerical methods for equations solving (in the real and complex numbers), search under the kewyord "numerical mathematics" for nonlinear equations over the integers, search under the kewyord "recursive function theory" ("algorithm theory, or even "metamathematics"). for differential equations, search under the keyword "differential equations“.

23. data types method types problem types EQUATIONS BOOLEAN ALGEBRAS ELIMINATION SOLUTION OF BOOLEAN EQUATIONS BY ELIMINATION Mathematics as a 3-D space

24. e.g. Mathematical Reviews e.g. Current Mathematical Publications bibliographies /= literature surveys Consult review journals, contents journals, bibliographies.

25. Iterate i.e. form the symmetric, transitive closure of the “A cites B” relation (i.e. iterate forward, backward search) and prune irrelevant items at each step until the literature set stabilizes.

26. prune: by reading title and abstract  title and abstract are enormously important the decision not to read a paper is very important

27. Advice: Be embedded into the research community: local national regional global

28. The Role of the Literature Categories of Documents Bibliographic Data Working with the Literature Searching Literature –Reading Papers –Documenting

29. Working with the Literature: Read Two opposing aspects: –analyze quickly the essential contents of a paper –understand and check details.

30. A “algorithm” for quick reading: Given: a paper. Find: the relevant contents. Read (in this order) title and abstract reference list conclusion introduction and literature review Please see the lecture notes for details.

31. Clarify and formulate in your own words the essential problems treated the new contribution to their solution For each problem, proceed by “Gerber’s Rule”: –What is given? –What has to be found?

32. Look to concrete problem instances. What is given and what has to be found in the example? How would you solve the problem? What do you know about known solutions in the literature? What is specific about the problem, i.e. what distinguishes the problem from other, similar problems? What is the specific difficulty of the problem? How could the problem be specified formally? What might be the specific contribution of the paper to the solution of the problem (even if you did not yet see the details presented in the paper)? Is the problem and its solution relevant for your topic?

33. Understand and check the relevant details. knowing terminology and results in the area getting the intuitions behind the formal details checking the formal details

34. For (getting the intuitions and) checking the formal details: Complete mastery of the formal methodology of mathematics (“reasoning”) is necessary, see Chapter “Thinking”. This can be learned!

35. The Role of the Literature Categories of Documents Bibliographic Data Working with the Literature Searching Literature Reading Papers –Documenting

36. Working with the Literature: Document Complete documentation of the literature used in your paper is obligatory: –For making the paper completely understandable. –For giving intellectual credit to the results used.

37. Steps: documentation during work the reference list citing the literature review (bibliographies)

38. Documentation during work: a list of all references (ordered alphabetically by authors) with complete bibliographic data and keywords.

39. The reference list: completeness of bibliographic data uniformity.

40. Citing: Cite all papers which you use in your paper. Cite the papers in which the results appeared for the first time. Cite sufficiently many papers for making your paper understandable. Do not include papers into the reference list which you did not use in your paper. Be careful with self-citations.

41. Literature review: May go by authors. Should be summarized in a “statement of originality”. In addition, individual citations in the text will often be necessary. Bibliographies are different: Are independent of one’s own paper, go by “topic” (preferably, by “problems”), see lecture notes.

42. Literature work: is essential is a pleasure must be professional must minimize the effort of the potential readers. Summary

43. Check: Can you answer the initial questions?

44. Questions: What do you do if your paper is rejected? How do you search for literature on “the Galois groups of origami constructions”? Under which keyword to you look for “non-linear equations”? What is the difference between an editor, a publisher, and a referee? What do you do if you are asked to write a referee report for a paper? How do you find out whether a paper of 1992 was further pursued?

45. How do you find out whether a journal article is available in your library? Do articles in conference proceedings count as “publications”? Will journals become obsolete with the future advances of the web? How long does it take to find out whether a paper is relevant for your research? Is the following reference OK: “N. Nakatani. On Fibonacci Numbers. Technical Report, 2004 “ ? Is the following citation OK: “For the resolution method, see [Miller, Mayr 2004]” ?

46. Exercise: choose (a very limited) topic (advice: a “problem”) search the relevant literature read the relevant papers (to the point where you can determine the relevance and essential contributions of the papers) document the result of the literature search. My office hour: Mo, Oct 11 and Oct 18, 14-16 h.