Help @MathCenter

Mathematics graduate students who are TAs hold office hours in RE-129. Any TA can help with any course they have some knowledge about, when they are not busy with students in their assigned courses. Make sure you use this great resource!

Software help

If you decide to use Macaulay2, you might want to consult a chapter by Bernd Sturmfels from a book on Macaulay2.
Information on how to use Mathematica/Maple for computations with Gröbner bases may be found in Appendix C of the textbook.
(Note: Maple packages tend to be rather slow in comparison with a dedicated system such as Macaulay2.)

Help with typing math: TeX, etc.

You are encouraged to type your assignments. You can access LaTeX in the computer labs; more information and help can be found on this departmental page. Note: for Macs, I recommend TeXShop.
You might also consider using the what-you-see-is-what-you-get text editor TeXmacs; it makes it unnecessary for you to learn the LaTeX typesetting language while producing output of comparable quality. The program is freely downloadable, available for various platforms, able to import and export LaTeX files, and offers a plugin for Macaulay 2.

Math 431/530: Computational Algebraic Geometry // Applied/Computational Algebra

Course material

Textbook The goal is to cover at least the first four chapters of the book Ideals, Varieties, and Algorithms, An Introduction to Computational Algebraic Geometry and Commutative Algebra, Third Edition, by David Cox, John Little, and Donal O'Shea, Springer, New York, 2007.

Note: the authors of the book have a web page with errata, software links, etc.

Software Some of the assignments in this course will involve the use of computer algebra systems. No previous experience with computer programming is assumed, but I expect that you are able and willing to familiarize yourself with the use of the program of your choice.

You are welcome to use a general-purpose program such as Mathematica or Maple (which can do algebra, calculus, graphics, and so on). If you prefer, you may also use Singular, Macaulay2, CoCoA or Sage. These free software systems are explicitly designed to support computations in algebraic geometry and commutative algebra. All these systems are available for most platforms (Unix, Linux, Mac OS X, Windows, etc.).

The instructor's software of choice for this course will be Macaulay2.

Additional Here are some reference books / other reading materials. These could be updated mid-semester; any updates will be announced.
  • William W. Adams and Philippe Loustaunau, An Introduction to Gröbner Bases, Graduate Studies in Mathematics 3, American Mathematical Society, Providence, RI, 1994. Available through library i-share
  • Thomas Becker and Volker Weispfenning, Gröbner Bases: A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics 141, Springer, New York, 1993. Available through library i-share
  • Ralf Fröberg, An Introduction to Gröbner Bases [electronic resource], Wiley, New York, 1997. e-copy available from Galvin library (via i-share).
  • Gröbner bases: statistics and software systems, T. Hibi (editor), Springer 2013. e-copy available from Galvin library.
  • Klaus Hulek, Elementary Algebraic Geometry, American Mathematical Society, Providence, RI, 2003. available through library i-share
  • David Cox, John Little, and Donal O'Shea, Using Algebraic Geometry, Graduate Texts in Mathematics 185, Springer, New York, 2005. e-copy available from Galvin library.
  • Hal Schenck, Computational Algebraic Geometry, London Mathematical Society Student Texts 85, Cambridge University Press, Cambridge, 2003. e-copy available from Galvin library (via i-share).
  • Bernd Sturmfels, Solving Systems of Polynomial Equations, CBMS Regional Conference Series in Mathematics 97, American Mathematical Society, Providence, RI, 2002. e-copy available from Galvin library (via i-share).
  • Niels Lauritzen Concrete Abstract Algebra: From Numbers to Gröbner Bases, Cambridge University Press, Cambridge, 2003. available through library i-share
  • Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen and William Traves, An Invitation to Algebraic Geometry, Undergraduate Texts in Mathematics, Springer, New York, 2000. available through library i-share