Department of Mathematics and Statistics

Mathematica is a comprehensive software tool for mathematics.

• It performs symbolic and numerical calculations.
• It produces advanced plots and graphics for mathematical visualization.
• It has a programmable interface that allows for extensive exploration of mathematics.

Many Haverford students use Mathematica in their math coursework, and students frequently use Mathematica in research projects—not only in the math department, but also in other quantitative disciplines, like economics and physics.

• Mathematica is available in every computing lab at Haverford.
• Haverford students can download a version of Mathematica for use on their own computers (Windows or Macintosh). Detailed installation instructions are available on the IITS Mathematica page. (Bryn Mawr students should visit BMC: Software Downloads.)
• Faculty and staff who want to run Mathematica on campus or at home should contact dlippel [at] haverford.edu (David Lippel) or rmanning [at] haverford.edu (Rob Manning).
• A Linux version of Mathematica is available; contact dlippel [at] haverford.edu (David Lippel) for more information.

• Learning to use Mathematica

  There are many fine video tutorials for Mathematica. First-time users should start by watching the first few videos in the Hands-on Start to Mathematica. You should experiment with Mathematica as you watch these tutorials.

  Complete documentation is available at the Mathematica Documentation Center, which includes many How-To Topics.

• Getting help

  • Students should contact the computing prodesk [at] haverford.edu (ProDesk) for questions about installing Mathematica.
  • Questions about using Mathematica can be asked in the Math Question Center.
  • Ask David Lippel by dlippel [at] haveford.edu (e-mail) or during his math computing office hours

LaTeX is a document preparation system for mathematics and other technical material. It's the world standard for producing papers in math. Learning to use LaTeX is essential for Haverford Math majors. David Lippel is available for LaTeX consultations during his Computing Office hours, and at other times by appointment.

Overview

The usual process for producing a document with LaTeX is as follows.

1. You use a "front end" program to create and edit a file that contains the LaTeX code for the document. Let's say this file is called mypaper.tex. It consists of a mix of English and LaTeX commands. The recommended front end programs are TeXworks for Windows and TeXShop for Mac OS.
2. Once you have typed a sufficient fragment of mypaper.tex, you press a button in the front end program that invokes the "back end" programs (LaTeX and TeX) which produce a typeset output file called myfile.pdf. The front-end program also launches a pdf viewer so that you can see the output file.
3. Return to Step 1 to continue work on the document.

LaTex on Campus

• KINSC H204(IITS lab). Windows computers. Front end: TeXworks, available in the Start Menu in the folder MikTex 2.9.
• KINSC H012 (Math Department Lab) and H215. Macs. Front end: TeXShop.

Getting LaTeX on Your Own Computer

The following TeX distributions provide a full LaTeX system by bundling together front-end programs with all the back-end programs and support packages you'll need.

• Macintosh: The standard TeX distribution for OS X is MacTeX. It includes the TeXShop front end in the folder/Applications/TeX. The installation is straightforward: simply run the MacTeX installer package. For further information, see the LaTeX on Macintosh pdf.
• Windows: The standard TeX distribution for Windows is MikTeX. Under normal circumstances, you should install the "Basic" MikTeX system. This installs the most commonly used TeX packages; more exotic packages will be downloaded automatically as needed. MikTeX includes the TeXworks front end. (Look under MikTeX 2.9 in the Start Menu.) See the LaTeX on Windows pdf for further information.
• Linux, etc.: The standard TeX distribution for Unix and Unix-like operating systems is TeX Live. The easiest way to get Tex Live is to find it in the package repository of your OS distribution. The TeXworks and Texmaker front ends are available for Linux. It is also possible to use your favorite Unix editor to produce LaTeX source files; for example, GNU emacs together with the auctex package (already included in many emacs distributions) provides a full-featured front end.

Learning LaTeX

One of the best ways to learn LaTeX is to examine and modify a sample LaTeX source file.

• Here is Curtis Greene's sample file:

  • LaTeX source file: papershell2010.tex.
  • PDF output file: papershell2010.pdf.
  • Sample graphics file: myfile.pdf. To see how to embed a pdf graphic into a LaTeX document, download myfile.pdf, put it in the same folder as papershell2010.tex, and then typeset papershell2010.tex.

• And here is Elizabeth Milicevic's sample file:

  • LaTeX source file: IntroTeX2012.tex.
  • PDF output file: IntroTeX2012.pdf.
  • Sample graphics file: TeXfigure.pdf. Read the source file for instructions on how to modify it to include this figure.

Beginning users should consult the The Not So Short Introduction to LaTeX, or George Graetzer's Short Course. Web videos to accompany the "Short Course" are here.

For users with some experience:

• The LaTeX Wikibook is a good source of information.
• LaTeX and TeX are mature programs that have been around a long time. (They predate the internet, if you can imagine that!) Yet, they have also changed significantly over time. Thus, there is a lot of obsolete information about LaTeX and TeX on the web. Unfortunately, when you do an undirected web search to get information, this obsolete information often comes up. It helps to know about the following authoratitive web sites:
  • The TeX Users Group (TUG). TUG maintains an introductory page for TeX/LaTeX and a list of TeX Resources on the Web.
  • The Comprehensive TeX Archive Network (CTAN).
• The document An essential guide to LATEX 2e usage: Obsolete commands and packages is an excellent guide for discriminating the "right" and "wrong" ways to do something in LaTeX.
• If you are looking for the command to produce a particular symbol, try one of the two resources below.
  • DeTeXify is a web service that finds LaTeX commands matching any symbol that you sketch with your mouse. It's the quickest way to find the right command for that tricky symbol you are looking for.
  • The Comprehensive LaTeX Symbol List contains over 5900 symbols. Start with Section 1.2, "Frequently Requested Symbols", and then search the index.
• Various books are available in the Math Lounge and the Math computer lab, including Math Into Latex by George Grätzer.

Research interests of our faculty include algebra, combinatorics, algebraic geometry, topology, mathematical biophysics, calculus of variations, mathematical pedagogy, mathematical economics, and statistics (and the faculty at Bryn Mawr have interests in dynamical systems, harmonic analysis, number theory, as well as some of the topics listed above). Often there are summer research opportunities for students to work with a faculty member on questions pertinent to his/her research program. These summer research projects can lead to joint student-faculty journal publications, and opportunities for students to present their work both on campus and at regional and national mathematics meetings.

We also encourage our students to seek out summer research opportunities elsewhere.  Please talk to a professor and/or the CCPA to get some ideas.

Applying to graduate school in the mathematical sciences is much like applying to college, only you don't need to apply for financial aid since almost all graduate programs admit students with full support (tuition and a modest stipend) in the form of a teaching assistantship or research assistantship. The steps in the process, with suggested months to initiate them, are enumerated below:

• In September, register to take the GRE General Test and the Mathematics Subject Test.
• In October, find graduate programs well matched to your talents and interests.
• In November, ask 3-4 professors for letters of recommendation and apply for fellowships.
• In December/January, send applications to 8-10 graduate programs including a safe school.
• In March, visit your two favorites of the graduate programs that offer you admission.

Graduate Record Examinations

General Test: The GRE General Test plays a similar but less important role in graduate admissions than the SAT I plays in undergraduate admissions. Information about the test is available online at www.gre.org/cbttest.html.

Subject Test: The test that matters at many graduate programs is the Subject Test in Mathematics. Information about this GRE Subject Test is available online at http://www.ets.org. Register by August 22 to take the Subject Test on September 27, and by September 19 to take the Subject Test on October 25. Calculus is 50% of the test, algebra is 25%, and other topics (real analysis, discrete math, general topology, geometry, complex variables, probability and statistics, and numerical analysis) are 25%. 2001!!! Try the practice test!

Graduate Programs

Relative Rankings of Programs:The National Research Council and National Academy of Science ranked graduate programs based on data collected in 2006. Results for graduate programs in mathematics are available at NRC/NAS math rankings and results for graduate programs in probability and statistics are reported at NRC/NAS stat rankings. Another ranking is published annually by U.S. News and World Report in the print and online editions of Best Graduate Schools. Ask Lynne if you wish to borrow a print copy of the 2003 edition. The more highly ranked programs generally have more selective admissions, and their graduates tend to get better job offers. However, if you know the area of mathematics research that most interests you, it is better to attend a graduate program that is strong in that area rather than a more highly ranked program that is weak in that area. The quality of your work in graduate school matters most!

Strengths of Individual Programs: The American Mathematical Society surveys graduate programs in the mathematical sciences annually. The number of graduate students, the number of faculty, the number of degrees awarded broken down by research area, and the number of faculty who have published in the last three years are some of the statistics published annually in Assistantships and Graduate Fellowships in the Mathematical Sciences. If you want to know which graduate programs have a high level of activity in your areas of interest or which graduate programs have a high Ph.D. completion rate, this publication is the place to start. But ultimately, you will want to write to about a dozen programs to request detailed information that is current. Links to the web sites of all U.S. mathematics departments are listed alphabetically on a page at Penn State recommended by Curtis.

Fellowships

Teaching and Research Assistantships: When admitted to a Ph.D. program in the mathematical sciences, prospective graduate students are offered a teaching or research assistantship. The quality and quantity of teaching assisgnments varies considerably from institution to institution. A good program's faculty will closely mentor all teaching assistants and limit the number of hours per week they are expected to devote to teaching duties. Support in the form of a teaching or research assistantship should be guaranteed for at least four years.

National Fellowships: Fellowships offered by government organizations for graduate study in the mathematical sciences include National Science Foundation Graduate Fellowships, National Defense Science and Engineering Graduate Fellowship, and National Physical Sciences Consortium Graduate Fellowships. The application deadline for NSF graduate fellowships is October 30, 2014; the application deadline for NDSEG graduate fellowships is December 12, 2014; and the application deadline for NPSC graduate fellowships is typically November 30.

• Search Tools
  • MathSciNet Full Search: A search engine provided by the American Mathematical Society.
  • Tripod Math Portal
• General Reference
  • AMS Home Page: The American Mathematical Society has an excellent and comprehensive selection of Internet Resources.
  • Caltech'sGuide to Mathematics Resources: Caltech's page lists many places of mathematical interest.
  • Math Departments on the Web: From Penn State, a world-wide list of departmental home pages.
  • GAMS: Guide to Available MathSoftware: This electronic guide is provided by the National Institute of Standards and Technology (NIST).
• Other Resources
  • The Math Forum at Drexel University: Includes "Ask Dr. Math," which is a page for submitting math queries at all levels (K-12 and beyond)
  • Mathjokes

• Guidelines for Collaborating on Math and Stats Homework
• Avoiding Plagiarism in Math