Here are some references for the material covered in class.

Geometry of curves:

- Marcel Berger,
*A Panoramic View of Riemannian Geometry*, Springer, 2003 - Manfredo P. Do Carmo,
*Differential Geometry of Curves and Surfaces*, Prentice Hall, 1976

Random walks:

- William Feller,
*An Introduction to Probability Theory and Its Applications*, Wiley, 1950 - Christian Remling, Notes on Random Walks based on Feller, Chapter III

Elliptic curves:

- Joseph H. Silverman and John Tate,
*Rational Points on Elliptic Curves*, Springer-Verlag, 1992 - J. S. Milne,
*Elliptic Curves*, BookSurge Publishing, 2006 (see also www.jmilne.org)

Permutation groups:

For permutation basics, any book on abstract algebra or group theory will do, such as:

- I. N. Herstein,
*Topics in Algebra*, Wiley, 1975 - David S. Dummit and Richard M. Foote,
*Abstract Algebra*, Prentice Hall, 1991

- An online 15-puzzle: http://www.archimedes-lab.org/game_slide15/slide15_puzzle.html
- Aaron F. Archer, "A Modern Treatment of the 15 Puzzle,"
*American Mathematical Monthly***106**(1999), pp. 793-799. Available at JSTOR if you are on campus (or you can log into the OU library's website and go from there).

Knot theory:

- Colin C. Adams,
*The Knot Book*, American Mathematical Society, 2004

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