Clayton Shonkwiler

Home Research Teaching Art, etc. Links

CSU Math Links

• Undergraduate Information
• Seminars
• Department Calendar
• CSU Math homepage

Former Departments

• UGA Math Department
• Haverford Math Department
• Penn Math Department
• Sewanee Math Department

Tables of Knot Invariants I Maintain

• Stick Number — The best stick number upper bounds I know of for all prime knots through 10 crossings. See also all prime knots through 16 crossings for which the exact stick number is known.
• Superbridge Index — The best superbridge index bounds I know of for all prime knots through 10 crossings. See also all prime knots through 16 crossings for which the exact superbridge index is known.

Mathematical Software I Use

• KnotPlot — Self-described as “the World’s most elaborate knotting software”.
• Magma — Computational algebra system.
• Mathematica — Powerful symbolic and numerical computing environment.
• plcurve — Ted Ashton, Jason Cantarella, Harrison Chapman, and Tom Eddy’s C library for handling polygonal space curves.
• pyknotid — Python modules for identifying knots.
• Regina — Software for low-dimensional topology.
• SageMath — Free, open-source mathematics software system based on Python.
• SnapPy — Python-based software for studying knots, links, and hyperbolic 3-manifolds.
• stick-knot-gen — Tom Eddy’s Python scripts for generating and identifying random stick knots.
• Wirt_Hm_Suite — Homomorphisms from knot groups to Coxeter groups.

Online Math Resources

• arXiv — The math preprint server.
• DLMF — The NIST Digital Library of Mathematical Functions.
• ETC — Clark Kimberling’s Encyclopedia of Triangle Centers.
• functions.wolfram.com — Wolfram’s mathematical functions site.
• Google Scholar — Google’s scholarly works-oriented search and profiles.
• Inverse Symbolic Calculator — Very useful for turning decimal numbers into exact expressions.
• Knot Atlas — Important resource for knot and link theory.
• KnotInfo — Definitive table of knot invariants.
• Mathematics Genealogy Project — I’m a mathematical descendent of Leibniz, Euler, Gauß, Dirichlet, and many others.
• MathOverflow — A place to ask questions.
• MathSciNet — Mathematical Reviews and other useful stuff.
• Mathworld — Wolfram’s math encyclopedia.
• Michael Shamos’ Catalog of Real Numbers — Nice complement to the Inverse Symbolic Calculator.
• Oberwolfach Photo Collection — Extensive collection of current and historical photos of mathematicians.
• OEIS — The Online Encyclopedia of Integer Sequences.
• Wikipedia — Surprisingly reliable for mathematical topics.