Depending on whether a topic has already been decided (i.e. search terms to describe the area of interest) or not, a thesis writer can start investigating the general landscape by consulting an encyclopedia or an introductory text on the area of interest. Browsing would be the way to go if you are still open to suggestions.
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Math 399 : Library Resources for Math Thesis Writers (HC)
Where to Start?
Browsing - for idea generation:
Books
Browsing is most useful when there is a finite number of items to sort through. For example, by going to the right section of the books stacks, you can browse books grouped together by the same subject. All math works fall under the general LC class QA. Some rough divisions as follows:
QA5 Dictionaries and encyclopedias
QA95 Mathematical recreations
QA150-255 Algebra
QA241-246 Number Theory
QA273 -280 Probabilities. Mathematical Statistics
QA299.6 - 433 Analysis
QA440 - 699 Geometry. Trigonometry. Topology.
QA801 -939 Analytic Mechanics
Journals
Here are some fun, accessible journals that publish insightful expositions written to inform readers who are new to a topic. Some titles will have current developments in math research, history of math, cultural connections with math and math education and learning. Many book reviews are found here, as well as humor, puzzles and art.
The Mathematical Intelligencer
Bulletin (new series) of the American Mathematical Society
Holdings:
(Bryn Mawr College) Available from 1891-present.
(Haverford College) Available from 1891-present.
(Swarthmore College) Available from 1891-present.
Publisher: [Providence, R.I.] : American Mathematical Society,
Journal of recreational mathematics
Holdings:
(Bryn Mawr College) Available from 2003-present except most recent 6 month(s).
(Haverford College) Available from 2003-present except most recent 6 month(s).
(Swarthmore College) Available from 2003-present except most recent 6 month(s).
Publisher: [Amityville, NY, etc.] Baywood Pub. Co. [etc.]
Mathematics magazine
Holdings:
(Bryn Mawr College) Available from 1947-present.
(Haverford College) Available from 1947-present.
(Swarthmore College) Available from 1947-present.
Publisher: Pacoima, Calif. : Mathematics Magazine,
Notices of the American Mathematical Society
Holdings:
(Bryn Mawr College) Available from 1995-present.
(Haverford College) Available from 1995-present.
(Swarthmore College) Available from 1995-present.
Publisher: [Providence, R.I.] : The Society,
Websites
Math Forum - Internet Math Library
A directory of useful websites grouped in categories familiar to mathematicians. Click on the Library Home page to see more resources classfied for user types, levels (K-12, College) and purpose (education, research).
MAA's Basic Library List
See a list of the most useful and classic books in all math topics.
Search - to find information on a known topic:
Encyclopedias, Handbooks and Dictionaries
Many handbooks serve as overviews of a topic and are available for checkout. For example, individual volumes of the Encyclopedia of mathematics and its applications series are listed as individual volumes and are shelved in regular stacks. To find these, do a keyword search in Tripod, using the expression: (encyclopedia or handbook or dictionary) and mathematics. Substitute your own topic keyword as appropriate, e.g. for a handbook on combinatorics, do a keyword search with (encyclopedia or handbook or dictionary) and combinatorics. Browse through the list. While examining particularly good hits, click on the subject heading to see more in the same classification.
Britannica online
Including Britannica's entire encyclopaedic database, articles not yet in the print Britannica encyclopedia. Current Coverage. Math topics cover related ideas and mathematicians.
The Online Encyclopaedia of Mathematics
From official description: "Terms alphabetically. This online edition comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics. The Encyclopaedia of Mathematics is updated on a regular basis.
MathWorld
Official Description: "MathWorldTM is the web's most extensive mathematical resource, provided as a free service to the world's mathematics and internet communities as part of a commitment to education and educational outreach by Wolfram Research, makers of Mathematica." Many interactive and animated pages for numerous math topics.
Wikipedia
Quite a useful collection. Use as springboard for inspiration but corroborate with authoritative sources with known authors with proper credentials and affiliation.
Databases - to find articles & books
Front for the Mathematics ArXiv
Excerpted from the site iFAQ :"The mathematics arXiv was formed from a number of smaller mathematical archives, with some in the arXiv system and some elsewhere, at the beginning of 1998. The system as a whole has over 200,000 articles in physics, over 20,000 in mathematics, and over 2,000 in computer science. The ultimate goal is to distribute all new research literature in all three disciplines worldwide, to store it permanently, and to keep it freely available...This includes not only formal new results, but also summaries, survey articles, expositions, informal notes, and software, as long they are somehow useful for other research mathematicians."
MathSciNet
Provider: AMS
This is the web interface to access the database Mathematical Reviews. It provides citations to the world's mathematical literature including journal articles, conference proceedings, and books. Topics covered include all aspects of mathematics, statistics, and related areas. Cover 1940-present.
For how to use this effectively, see
One way to get background information on a topic is to look for overviews. Find them by combining a MSC classification code search (e.g. 12-01 for Instructional exposition material in Field Theory and polynomials) and a topic keyword (e.g. "Galois Theory") to bring up overviews in Galois Theory.
For how to use this effectively, see
Using the Mathematics Literature, edited by Kristine K. Fowler. New York,NY, Marcel Dekker, 2004, (on reserve)
See instructions on how to search here, taken from the above reference, pp40-42.
In general, to use the MSC (Mathematics Subject Classification), select "Search MSC" from the "Other Tools" tab at the top right of the main page. From here, select a classification such as 11 Number Theory. Press "Search" and a list of sections for the classification will display including 01. Section 01 is labeled "Instructional exposition". Click on the icon to the right of the 11-01 and everything in MathSciNet with that classification will display. Similarly, every major MSC subject class of xx has special sections xx-01 (instructional exposition), xx-02 (research exposition) and xx-03 for historical documents.
An example using MSC 12 is shown below.
12-00 
(1973-now) General reference works (handbooks, dictionaries, bibliographies, etc.)
(1973-now) General reference works (handbooks, dictionaries, bibliographies, etc.) 12-01 (1973-now) Instructional exposition (textbooks, tutorial papers, etc.)
(1973-now) Instructional exposition (textbooks, tutorial papers, etc.) 12-02 (1973-now) Research exposition (monographs, survey articles)
12-03 (1973-now) Historical (must also be assigned at least one classification number from Section 01)
(1973-now) Research exposition (monographs, survey articles) 12-03
(1973-now) Historical (must also be assigned at least one classification number from Section 01) One way to get background information on a topic is to look for overviews. Find them by combining a MSC classification code search (e.g. 12-01 for Instructional exposition material in Field Theory and polynomials) and a topic keyword (e.g. "Galois Theory") to bring up overviews in Galois Theory.
Zentralblatt MATH Database
Zentralblatt MATH is the world's most complete and longest running abstracting and reviewing service in pure and applied mathematics. The Zentralblatt MATH Database contains more than 2.0 million entries drawn from more than 2300 serials and journals and covers the period from 1868 - present by the recent integration of the Jahrbuch database (JFM).
The entries are classified according to the Mathematics Subject Classification Scheme (MSC 2000).
Subject coverage:
Pure mathematics (e.g. algebra, logic, topology, geometry, analysis) , probability theory, statistics, mathematical physics, classical, solid and fluid mechanics, numerical mathematics, mathematical programming, theoretical computer science and automata theory, systems theory, control, operations research, economics, information and communication, circuits, coding, cryptography, applications in biology, chemistry, sociology, psychology.
The entries are classified according to the Mathematics Subject Classification Scheme (MSC 2000).
Subject coverage:
Pure mathematics (e.g. algebra, logic, topology, geometry, analysis) , probability theory, statistics, mathematical physics, classical, solid and fluid mechanics, numerical mathematics, mathematical programming, theoretical computer science and automata theory, systems theory, control, operations research, economics, information and communication, circuits, coding, cryptography, applications in biology, chemistry, sociology, psychology.
Search Engines
Google Scholar
This taps scholarly resources such as referreed math journals, preprints, society websites and faculty websites. The results are ranked by the number of citations and the reputation of the citing source. You can configure the preference to link to Tripod so that you can immediately link to the full text of the article or find the call number of a book if we have it. Often if you see another link that says something like "Group of 5", it offers you more ways to find the same item. See search tips from Google - a few minute can save you lots of time.
Scirus
This is a free search engine from Elsevier, the publisher giant. It links to peer-reviewed journals, notably journals from ScienceDirect, ArXiv.org eprints, SIAM math journals, MIT Open Courseware and millions of other websites with substantive information. Upon getting a set of answers, you can elect to refine your topic further by choosing various aspects of the topic, located on the right sidebar.
Lateral thinking - use Citation Indexes
Citation indexes expose the citations of an article, allowing for backward tracing through list of works cited and forward tracing to find articles that have cited it. By following these citation relationships, the researcher is able to follow developments of an idea, discover new ways of thinking about a certain topic and discover retractions or corrections of the original article.Citeseer and Web of Science are both citation indexes, the former gathering material from the open web and employs autonomous citation indexing with no human intervention; and the latter, indexing selected journals in the traditional press.
CiteSeer
Particularly useful for folks interested in the computing side of math. CiteSeer is a scientific literature digital library and search engine that focuses primarily on the literature in computer and information science. CiteSeer can show the citation statistics and the context of citations to a given paper, allowing a researcher to quickly and easily see what other researchers have to say about an article of interest.
Web of science
Provider: ISI
Find out who cites whom and why they do. Citation searching often provides unexpected connections between ideas in disparate subjects. Web of Science provides access to the Social Sciences Citation Index, Science Citation Index, and Arts and Humanities Citation Index. Search for scholarly articles in any discipline, or for articles that cite a known author or work. Science citation index coverage: BMC: 1955-present; HC: 1972-present; SC: 1984-present.
Notices of the American Mathematical Society
Lots of information useful to the mathematics major - from accessible articles to state of math education to doctoral program information. Also information on upcoming conferences and career news on this site.
Open Source Math Software:
SAGE
General and Advanced Pure and Applied Mathematics
Use SAGE for studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.
Use SAGE for studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.
Reserve Books for Math 399:
Find out what have been set aside for Thesis Writers
Haverford Math Theses Archive
This is a list of math theses through the years, sorted in reverse chronological order. The theses are available for use in the library. They are shelved behind the Z call number in the journals compact shelving.