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

Euler's formula and classification of surfaces:

 Many books on topology will do, but this book does a very nice job:

• John H. Conway, Heidi Burgiel, and Chaim Goodman-Strauss, The Symmetries of Things, A K Peters, 2008

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