How to do research on mathematics? Everyday mathematics is used in some shape or form to help us calculate, analyze, and understand the outcome of quantitative problems in many fields—architecture, agricultural science, art and graphic design, architecture, computer science, environmental science, finance and economics, geological science, science and engineering, and real-life situations. The nature of mathematics entails a high level of thinking and problem solving to investigate a problem through the collection, interpretation, and measurement of data—using different methods, such as algebra, geometry, trigonometry, and calculus—and applying theories, including logic and probability. In the end, the resulting data or statistical outcome can explain a new phenomenon or a common problem in a way that others can hopefully understand. Whether writing a research paper on a famous mathematician, the origin of some important mathematical theory, or a complex mathematical problem, a host of credible research by leaders in the field and sources recommended by librarians await you in print and electronic form to provide the documentation or answers that you are seeking.

**Selected Subject Headings**

Listed below is a sample of a few broad Library of Congress subject headings—made up of one word or more representing concepts under which all library holdings are divided and subdivided by subject—which you can search under and use as subject terms as well when searching online library catalogs for preliminary and/or additional research, such as books, audio and video recordings, and other references, related to your research paper topic. When researching materials on your topic, subject heading searching may be more productive than searching using simple keywords. However, keyword searching when using the right search method (Boolean, etc.) and combination of words can be equally effective in finding materials more closely relevant to the topic of your research paper.

## Suggested Research Topics in Math

- Algebra
- Business Mathematics
- Calculus
- Fractions
- Functions
- Game Theory
- Mathematics—Philosophy
- Set Theory
- Topology
- Women in Mathematics

**Selected Keyword Search Strategies and Guides**

Most online library indexes and abstracts and full-text article databases offer basic and advanced “keyword” searching of virtually every subject. In this case, combine keyword terms that best define your thesis question or topic using the Boolean search method (employing “and” or “or”) to find research most suitable to your research paper topic.

If your topic is “the importance of mathematics in the world,” for example, enter “importance” and “mathematics” with “and” on the same line to locate sources directly compatible with the primary focus of your paper. To find research on more specific aspects of your topic, alternate with one new keyword at a time with “and” in between (for example, “advancements and mathematics,” “contributions and mathematics,” “influence and mathematics,” etc.).

For additional help with keyword searching, navigation or user guides for online indexes and databases by many leading providers—including Cambridge Scientific Abstracts, EBSCO, H.W. Wilson, OCLC, Ovid Technologies, ProQuest, and Thomson Gale—are posted with direct links on library Web sites to guides providing specific instruction to using whichever database you want to search. They provide additional guidance on how to customize and maximize your search, including advanced searching techniques and grouping of words and phrases using the Boolean search method—of your topic, of bibliographic records, and of full-text articles, and other documents related to the subject of your research paper.

**Selected Source and Subject Guides**

As part of your preliminary research to find appropriate resources for your topic, information source and research guides are available through most public and academic libraries and are keyword searchable through your library’s online catalog (to search and locate guides, enter your “subject” followed by these keywords one search at a time: “information sources,” “reference sources,” and “research guide”). Printed guides available for this subject area include

* Guide to Information Sources in Mathematics and Statistics*, by Martha A. Tucker and Nancy D. Anderson, 348 pages (Westport, Conn.: Libraries Unlimited, 2004)

* Mathematics Education Research: A Guide for the Research Mathematician*, by Curtis McKnight et al., 106 pages (Providence, R.I.: American Mathematical Society, 2000)

In addition to these sources of research, most college and university libraries offer online subject guides arranged by subject on the library’s Web page; others also list searchable course-related “LibGuides” by subject. Each guide lists more recommended published and Web sources—including books and references, journal, newspaper and magazines indexes, full-text article databases, Web sites, and even research tutorials—that you can access to expand your research on more specific issues and relevant to your subject.

**Selected Books and References**

#### Dictionaries

* The Concise Oxford Dictionary of Mathematics*, by Christopher Clapham and James Nicholson, 4th ed., 528 pages (Oxford and New York: Oxford University Press, 2009)

This revised fourth edition of applied mathematics and statistics features more than 3,000 entries, arranged in alphabetical order and illustrated with charts, diagrams, and graphs, covering technical mathematical terms, from Achilles paradox to zero matrix. Includes free access to regularly updated online version of the book.

* Encyclopedic Dictionary of Mathematics*, 2nd ed., edited by Mathematical Society of Japan and Kiyosi Ito, 4 vols. (Cambridge, Mass.: MIT Press, 1987)

This unique four-volume encyclopedia of applied mathematics features 450 articles, including 70 new articles since its first edition, published in 1977, covering such categories as algebra; group theory; number theory; Euclidean and projective geometry; differential geometry; algebraic geometry; topology; analysis; complex analysis; functional analysis; differential, integral, and functional equations; special functions; numerical analysis; computer science and combinatorics; probability theory; statistics; mathematical programming and operations research; mechanics and theoretical physics; and the history of mathematics.

* The Facts on File Dictionary of Mathematics*, 4th ed., by John Daintith and Richard Rennie, 262 pages (New York: Checkmark Books, 2005)

This dictionary covers mathematical terms and concepts—some 320 entries in all—fully illustrated, including lists of Web sites and bibliographies of sources.

* The Penguin Dictionary of Mathematics*, 4th ed., edited by David Nelson, 496 pages (London and New York: Penguin Books, 2008)

Everything from algebra to number theory and statistics to mechanics is thoroughly covered in this updated reference encompassing more than 3,200 cross-referenced entries from all branches of pure and applied mathematics. Also includes biographies of more than 200 major figures in mathematics.

#### Encyclopedias

* CRC Concise Encyclopedia of Mathematics*, 2nd ed., by Eric W. Weisstein, 3,252 pages (Boca Raton, Fla.; London: Chapman & Hall/CRC, 2003)

This revised and expanded second edition—adding 1,000 pages of new illustrated material since its first edition—broadly covers mathematical definitions, formulas, figures, tabulations, and references on the subject.

* Encyclopaedia of Mathematics*, 11 vols., 5,400 pages (Dordrecht, Netherlands, and Boston: Reidel; Norwell, Mass.: Kluwer Academic Publishers, 1989–94; New York: Springer, 2005– )

This major unabridged 11-volume reference with index, hailed as “the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today,” contains more than 7,000 cross-referenced entries covering all aspects of mathematics, including mathematical definitions, concepts, explanations, surveys, examples, terminology and methods, and more. In 2007, two new supplements—the first since the series was first published—were issued containing nearly 600 new entries in each written by experts in the field.

* Encyclopedia of Mathematics Education*, by Louise Grinstein and Sally I. Lipsey, 700 pages (New York: Routledge Falmer, 2001)

Designed for elementary, secondary, and post-secondary educators, this single-volume lists more than 400 alphabetically arranged entries covering all areas of mathematics education, including assessment, curriculum, enrichment, learning and instruction, and more.

* Encyclopedia of Statistical Sciences*, 2nd ed., edited by Samuel Kotz, et al., 16 vols., 9,686 pages (New York: Wiley, 2005)

Revised reference set expanded to 16 volumes and written by 600 experts detailing every area of statistical sciences, including its origin, new trends, and changes, and such areas as statistical theory and methods and application in biomedicine, computer science, economics, engineering, genetics, medicine, the environment, sociology, and more.

#### Guides and Handbooks

* Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences*, 2nd ed., by Ivor Grattan-Guiness, 2 vols., 976 pages (Baltimore, Md.: Johns Hopkins University Press, 2003)

This illustrated two-volume set features 176 concise articles divided into 12 sections covering the development, history, cultural importance, problems, and theories and techniques of math and its execution in related sciences, including astronomy, computer science, engineering, philosophy, and social sciences, from its early beginnings through the 20th century. Features annotated bibliographies of sources with each article.

* Figures of Thought: Mathematics and Mathematical Texts*, by David Reed, 208 pages (London and New York: Routledge, 1994)

This single reference traces the history and evolution of mathematics and the work of famous mathematicians throughout history, including Dedekind, Descartes, Grothendieck, Hilbert, Kronecker, and Weil and an understanding of their approaches to mathematical science.

* Guide to Information Sources in Mathematics and Statistics*, by Martha A. Tucker and Nancy D. Anderson, 368 pages (Englewood, Colo.: Libraries Unlimited, 2004)

Praised as a “useful resource for college librarians and those just getting started in mathematics and statistics research,” this revised edition encompasses how to locate and access hundreds of print and electronic sources on mathematical sciences from 1800s to date.

* A History of Mathematics: An Introduction*, 3rd ed., by Victor J. Katz (Boston: Addison-Wesley, 2009)

This updated third edition provides a historical and world perspective of mathematics—its early and modern history, its evolving techniques, and contributions to the art of mathematics from throughout the Western and non-Western world.

* INSTAT, International Statistics Sources: Subject Guide to Sources of International Comparative Statistics*, by M. C. Fleming and J. G. Nellis, 1,080 pages (London: Routledge, 1994)

Unprecedented in its coverage, this A-to-Z guide details statistical data sources on business, economics, and social sciences topics, including agriculture, employment, energy, environment, finance, health, manufacturing, population, and wages. A subject index to all topics is included.

**Selected Full-Text Article Databases**

**ArticleFirst** (Dublin, Ohio: OCLC FirstSearch, 1990– )

Full-text articles and citations to more than 16,000 journals in all subjects, including science, technology, and others; also known as OCLC ArticleFirst Database.

**ESBCOHost Academic Search Elite** (Ipswich, Mass.: ESBSCO Publishing, EBSCOHost, abstracting/indexing: 1984– , full text: 1990– )

A Web index of full-text articles from more than 1,250 journals, plus abstracts and citations from 3,200 journals covering general science, the social sciences, and more.

**JSTOR** (Ann Arbor, Mich.: Journal Storage Project, 1800s—latest 3 to 5 years)

A Web archive of important scholarly journals, some in full text, including more than 37,000 articles from The American Mathematical Monthly (1894–2004), since the 1800s in economics, finance, and mathematical sciences.

**ScienceDirect** (St. Louis, Mo.: Elsevier Science, 1995– )

Leading science database on the Web with full-text access to more than 9.5 million articles from more than 2,500 scientific, mathematical, technical, and social science journals.

**Web of Science** (Philadelphia: Thomson Scientific, 1840– )

Contains detailed bibliographic records to more than 8,700 worldwide scientific journals and publications, with full-text articles from more than 250 scientific journals from 1840 to date; allows searching of material from other related databases, including Science Citation Index (1900– ), Social Sciences Citation Index (1956– ), Arts & Humanities Citation Index (1975– ), Index Chemicus (1993– ), and Current Chemical Reactions (1986– ).

**Wilson Select Plus** (Bronx, N.Y.: H.W. Wilson Co., WilsonDisc/OCLC FirstSearch, 1994– )

On the Web, indexes and abstracts full-text articles from 2,621 journals, magazines, and newspapers covering such subjects as science, humanities, education, and business.

**Selected Periodicals**

* Acta Mathematica Sinica* (Tokyo, Japan: Springer-Verlag Tokyo/Chinese Mathematical Society, 1936– )

This English-translated version of the popular quarterly journal published by the Chinese Mathematical Society since 1936 (originally titled, Journal of Chinese Mathematical Society, until it was renamed in 1952) publishes authoritative reviews of current citations with abstracts to articles from current and past issues searchable in such online databases as Academic OneFile, Current Abstracts, Current Contents/Physical, Chemical and Earth Sciences, International Abstracts in Operations Research, Journal Citation Reports/Science Edition, Mathematical Reviews, Science and Technology Collection, Science Citation Index Expanded, SCOPUS, TOC Premier, and Zentralblatt MATH.

* American Journal of Mathematics *(Baltimore, Md.: Johns Hopkins University Press, 1878– )

As “the oldest mathematics journal in the Western Hemisphere,” published since 1878, this academic journal, one of the most respected and celebrated in its industry, publishes pioneering mathematical papers and articles about all areas of contemporary mathematics. Articles are indexed and abstracted in the following electronic databases: CompuMath Citation Index, Current Contents/Physical, Chemical and Earth Sciences, Current Mathematical Publications, General Science Index, Index to Scientific Reviews, Math-SciNet, Mathematical Reviews, Science Citation Index, Social Science Citation Index, and Zentralblatt MATH. To browse journals by subject or title, or search past issues, visit http://www.press.jhu.edu/journals/american_journal_of_mathematics/.

* Annals of Applied Probability* (Beachwood, Ohio: Institute of Mathematical Statistics, February 1991– )

First published in February 1991, this scholarly journal publishes important and original research covering all facets of contemporary applications of probability. Electronic access to all issues of the journal is available through JSTOR (issues older than 3 years from the current year).

* Annals of Combinatorics* (Singapore and New York: Springer-Verlag, 1997– )

This journal covers new developments, mathematical breakthroughs and mathematical theories in combinatorial mathematics, particularly its applications to computer science, biology, statistics, probability, physics, and chemistry, as well as representation theory, number theory topology, algebraic geometry, and more. Articles are indexed and fully searchable in Academic OneFile, Current Abstracts, Current Contents/Physical, Chemical and Earth Sciences, Journal Citation Reports/Science Edition, Mathematical Reviews, Science and Technology Collection, Science Citation Index Expanded, and others.

* Foundations of Computational Mathematics* (New York: Springer-Verlag New York, 2001– )

Introduced in January 2001, this quarterly academic journal, published in association with the Foundations of Computational Mathematics, features articles discussing the connections between mathematics and computation, including the interfaces between pure and applied mathematics, numerical analysis, and computer science. Full-text articles from issues since 2001 can be viewed in PDF form at http://link.springer.com/journal/10208.

* Historia Mathematica* (Amsterdam, Netherlands: Elsevier Science B.V., 1974– )

Launched in February 1974, this quarterly periodical of the International Commission on the History of Mathematics of the Division of the History of Science of the International Union of the History and Philosophy of Science covers all aspects of mathematical sciences, including mathematicians and their work, organizations and institutions, pure and applied mathematics, and the sociology of mathematics, as well as all cultures and historical periods of mathematics and its development. The primary aim and focus of each issue is topics in the history of math, including research articles, book reviews, and more. Full-text articles are accessible through ScienceDirect.

* Journal of Mathematics and Statistics* (New York: Science Publications, 2005– )

Published since January/March 2005, this peer-reviewed, open-access international scientific journal presents original and valuable research in all areas of applied and theoretical mathematics and statistics. To view or search back issues, visit http://thescipub.com/jmss.toc.

* Journal of Pure and Applied Algebra* (Evanston, Ill.: Elsevier Science, 1971– )

This monthly journal published in association with Northwestern University’s math department focuses on the development and theories of pure and applied algebra. Also available in microform since its first issue in January 1971, full-text articles from all issues can be searched in Elsevier Science’s ScienceDirect online database.

* The Journal of Symbolic Logic* (Poughkeepsie, N.Y.: Association for Symbolic Logic, 1936– )

Leading scientific journal founded in 1936 by the Association for Symbolic Logic (ASL) containing scholarly work and research on symbolic logic. The journal is distributed with two others published by the ASL: The Bulletin of Symbolic Logic and Review of Symbolic Logic. Full-text access to The Journal of Symbolic Logic (1936–2003) is available via JSTOR.

* Journal of the American Mathematical Society (JAMS)* (Providence, R.I.: American Mathematical Society, January 1, 1988– )

Mathematics journal published quarterly by the American Mathematical Society reporting research in all areas of pure and applied mathematics. Journal articles are indexed in such subscription Web databases as Citation Index—Expanded, CompuMath Citation Index, and Current Contents, Physical, Chemical & Earth Sciences. Since January 1996, JAMS is also accessible online at http://www.ams.org/publications/journals/journalsframework/jams.

* Mathematical Physics, Analysis, and Geometry* (Norwell, Mass.: Kluwer Academic/Plenum Publishing Corp., 1998– )

Scientific journal covering concrete problems of mathematics and theoretical analysis and application of analysis on all math, from geometry to physics, including problems of statistical physics and fl uids; complex function theory; operators in function space, especially operator algebras; ordinary and partial differential equations; and differential and algebraic geometry. Journal is indexed and abstracted in many subject-specific online databases, including Academic OneFile, Current Abstracts, Google Scholar, Journal Citation Reports/Science Edition, Mathematical Reviews, and others.

* SIAM Journal on Applied Mathematics* (Newark, Dela.: Society for Industrial & Applied Mathematics, 1953– )

Published by the Society for Industrial & Applied Mathematics since 1953, this quarterly journal reviews applied mathematics of physical, engineering, biological, medical, and social sciences, including research articles discussing problems and methods pertinent to physical, engineering, financial, and life sciences. Full bibliographic records with abstracts of articles from 1997 to the present can be searched on SIAMS Journals Online at http://www.siam.org/journals/siap.php.

**Selected Web Sites**

**American Mathematical Society** (http://www.ams.org/home/page)

Association of professional mathematicians, headquartered in Providence, Rhode Island, reporting on mathematical research and education, conferences, surveys, publications, scholarship programs, and more.

**American Statistical Association** (http://www.amstat.org/)

This Web site for the nation’s leading professional organization for statisticians and professors provides resources for visitors and members, including association news, membership information, educational opportunities, publications, meetings and events, and outreach programs.

**Euler Archive—Dartmouth College** (http://eulerarchive.maa.org/)

Provides online access to Dartmouth College’s archive of 866 original works of pioneering Swiss mathematician Leonard Euler as well as other original publications and current research.

**MacTutor History of Mathematics** (http://www-history.mcs.st-andrews.ac.uk/history/index.html)

Features searchable historical mathematical topics, biographies of notable mathematicians from AD 500 to present, and an index of famous curves.

**Math Archives** (http://archives.math.utk.edu/)

Online resource covering a wide range of mathematical topics and Internet resources arranged by subject.

**Mathematical Atlas** (http://www.math-atlas.org/)

Gateway collection of articles discussing various mathematical concepts, with links to additional resources in all areas of mathematics.

**Mathematics on the Web** (http://www.mathontheweb.org/mathweb/)

Online mathematical sources maintained by the American Mathematical Society and organized by subject, including article abstracts and databases, as well as bibliographies; books, journals, columns, and handbooks; math history and math topics; information about mathematics departments, institutes, centers, associations, societies, and organizations; and related software and tools.

**Mathematics, Statistics, and Computational Science at NIST** (http://math.nist.gov/)

Site provided by the National Institute of Standards and Technology, offering information on NIST projects, events, and organizations; math software; statistical guides and handbooks; statistical data sets; and more.

**Math Forum** (http://mathforum.org/)

This site, maintained by Drexel University’s School of Education, offers both resources and information on math and math education, along with access to the Internet Mathematics Library, discussion groups, and more.

**Math on the Web** (http://www.mathontheweb.org/mathweb/index.html)

Web portal produced by the American Mathematical Society providing access to mathematical news and information, journals, and reference materials.

**Math World** (http://mathworld.wolfram.com/)

Deemed by its creators as “the Web’s most extensive mathematics resource,” this site includes a searchable math dictionary and encyclopedia, interactive tools, and information on the computational software program Mathematica.

**+plus magazine** (http://plus.maths.org/content/)

Free access to this weekly online magazine featuring the latest mathematical news, articles by leading mathematicians and science writers, a browsable archive, and information on a variety of mathematical applications.

**Probability Tutorials** (http://www.probability.net/)

Online math tutorials explaining probability, definitions, theorems, solutions, and more.

**SIAM: Society for Industrial and Applied Mathematics** (http://www.siam.org/)

Official Web site for the Society for Industrial and Applied Mathematics offering information on books, careers and jobs, conferences, journals, proceedings, and the latest news.

**Zentralblatt MATH** (http://www.zentralblatt-math.org/zmath/en/)

Searchable database of more than 2 million citations with abstracts to books, journals, conference reports, and more, from 1868 to present.

### Careers Related to Mathematics

**Science, Technology, Engineering, and Mathematics Career Cluster** (http://career.iresearchnet.com/career-clusters/science-technology-engineering-and-mathematics-career-cluster/)

Science careers include jobs in biology, chemistry, geology, meteorology, or any other natural, physical, or earth science. Mathematics is the science and study of numbers and how they relate to each other. Engineering and technology encompasses many areas of study, such as aviation, environmental science, and robotics, just to name a few. All of these engineering fields employ unique and sometimes similar methods of research, development, and production to reach practical solutions to problems and questions.

**Mathematics and Physics Career Field** (http://career.iresearchnet.com/career-fields/mathematics-and-physics-career-field/)

Mathematics and physics are closely related natural sciences. Mathematics is the science and study of numbers and how they relate with each other. Physics is the study of the basic elements and laws of the universe.

**Engineering Career Field **(http://career.iresearchnet.com/career-fields/engineering-career-field/)

A lot of brainpower goes into engineering—a lot of knowledge, creativity, thoughtfulness, and pure hard work. Humankind has been “engineering,” so to speak, since we realized we had opposable thumbs that we could use to handle tools. And from that point on we began our ceaseless quest to make, to build, to create tools and systems that helped us live our lives better. There were a lot of mistakes, but engineers and scientists learned from them and built a foundation of engineering laws and principles.