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There is no textbook required for the course. Lecture notes are available for the current term as well as selected lecture notes from a previous term. Reference textbooks for each topic are listed in the table below.

Linear Programming Schrijver, A. Theory of Linear and Integer Programming . Chichester: John Wiley & Sons, 1998. ISBN: 0471982326.

For the Ellipsoid, 3 references are (the latter 2 contain a few mistakes):

Groetschel, M., L. Lovasz, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization. Berlin, New York: Springer-Verlag, 1993, chapter 3. ISBN: 0387567402. [The standard reference on the ellipsoid. The most complete and precise description.]

Chvatal, V. Linear Programming. New York: W. H. Freeman & Company, 1983, appendix. ISBN: 0716715872. [An easy to read description without all the details.]

Korte, B. H., and J. Vygen. Combinatorial Optimization. Berlin, Heidelberg, New York: Springer-Verlag, 2002, chapter 4. ISBN: 3540431543. [A detailed description.]

For Interior-point Algorithms, a good reference is:

Roos, C., T. Terlaky, and J. -Ph. Vial. Theory and Algorithms for Linear Optimization: An Interior Point Approach. Chichester: John Wiley & Sons, 1997. ASIN: 0471956767.
Network Flows Ahuja, R. K., T. L. Magnanti, and J. B. Orlin. Network Flows: Theory, Algorithms, and Applications. Englewood Cliffs, NJ: Prentice Hall, 1993. ISBN: 013617549X.
Data Structures For both Splay Trees and Dynamic Trees:

Sleator, and Tarjan. "Self-adjusting Binary Search Trees." Journal of the ACM 32, no. 3 (July, 1985): 652-686. ISSN: 0004-5411.
Approximation Algorithms Vazirani, V. Approximation Algorithms. Berlin: Springer-Verlag, 2001. ISBN: 3540653678.

Hochbaum, D., ed. Approximation Algorithms for NP-Hard Problems. Boston: PWS Publishing Company, 1997. ISBN: 0534949681.

Sanjeev Arora's Euclidean TSP paper. Journal of the ACM 45, no. 5 (September, 1998). New York, NY, USA: ACM Press. ISSN: 0004-5411.
Number-Theoretic Algorithms Lov'asz, L. "An Algorithmic Theory of Numbers, Graphs, and Convexity." In CBMS Regional Conference Series in Applied Mathematics (SIAM, 1986). Philadelphia, PA: Society for Industrial and Applied Mathematics, 1986. ISBN: 0898712033.

Bach, E., and J. Shallit. Algorithmic Number Theory. Vol. 1. Cambridge, MA: MIT Press, August 26, 1996. ISBN: 0262024055.