Fall 2005

**History/Overview/Survey Articles**

- N. Alon, Algebraic and probabilistic methods in Discrete Mathematics, in: "Visions in Mathematics, Towards 2000", (N. Alon et. al. eds.), Birkhäuser, 2000, pp. 455-470.
- N. Alon, Spectral techniques in graph algorithms, Lecture Notes in Computer Science 1380 (C. L. Lucchesi and A. V. Moura, Eds.), Sringer, Berlin, 1998, 206-215.
- N. Alon, Randomness and pseudo-randomness in Discrete Mathematics, Proc. of the 2 European Congress of Mathematics, Progress in Mathematics 168 (1998), 1-14.
- Noam Nisan and Amnon Ta-Shma. Extracting Randomness: A Survey and New Constructions. JCSS 1999
- Amnon Ta-Shma's Dissertation, Refining Randomness Hebrew University 1996
- Peter G. Doyle and J. Laurie Snell Random Walks and Electric Networks. A probably more up-to-date version is here
- David Xiao, "The Evolution of Expander Graphs", AB Thesis, Harvard University, 2003.
- Nati Linial, "Expanders, eigenvalues and all that", Invited Talk, NIPS, Dec 2004.
- Sara Robinson, "Computer Scientist Finds Small-Memory Algorithm for Fundamental Graph Problem", SIAM News, Volume 38, Number 1, January/February 2005.
- L. Lovász: Random Walks on Graphs: A Survey [in: Combinatorics, Paul Erdõs is Eighty, Vol. 2 (ed. D. Miklós, V. T. Sós, T. Szõnyi), János Bolyai Mathematical Society, Budapest, 1996, 353--398.]
- Peter Sarnak, What is an expander, Notices of the AMS, Vol 51 (7), 2004.
- Mark Jerrum's page has many related links.

**Related classes and notes**

- CS369E: Expanders in Computer Science (Spring 2005), a class taught at UChicago taught by Cynthia Dwork and Prahladh Harsha.
- Michael Nielsen's notes on expanders (2005)
- CS 225: Pseudorandomness (Spring 2004), a course by Salil P. Vadhan
- Randomized Algorithms (2004), a course by Dana Randall
- 15-859(M): Randomized Algorithms (2004), a course by Anupam Gupta and Shuchi Chawla
- Amnon Ta-shma's expanders class (2003)
- CMSC858T Randomized Algorithms (Spring 2003), a course by Aravind Srinivasan
- CS 174 Randomized Algorithms (Spring 2003), a course by Luca Trevisan.
- CSE 590VG: Codes and Pseudorandom Objects (Winter 2003), a course by Venkatesan Guruswami
- Randomized Algorithms (Fall 2003), a course by John H. Reif
- Course 67659: Expander graphs and their applications (Spring 2002), a course by Nati Linial and Avi Wigderson
- Essential Coding Theory (2002), a course by Madhu Sudan.
- Randomized Methods in Computation (2001), a course by Oded Goldreich
- Randomized Algorithms (1997), a course by Avrim Blum.

**Representative books on Random Graphs, Probability Theory, Coding Theory,
Switching Networks, Expanders, Algebraic Graph Theory**

- Doyle and Snell, Random Walks on Electronic Networks, MAA, 1984. [Now available for free.]
- Bella Bolobas,
(2nd ed.), Cambridge University Press, Studies in Advanced Mathematics, #73, September 2001.**Random Graphs** - Alon, Noga; Spencer, Joel H.
Second edition. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons, New York, 2000. xviii+301 pp. ISBN: 0-471-37046-0*The probabilistic method.* - Molloy, Michael; Reed, Bruce
. Algorithms and Combinatorics, 23. Springer-Verlag, Berlin, 2002. xiv+326 pp. ISBN: 3-540-42139-4**Graph colouring and the probabilistic method** - Kallenberg, O.
. New York: Springer-Verlag, 1997.**Foundations of Modern Probability** - Rajeev Motwani, Prabhakar Raghavan,
, Cambridge University Press, June 1995.**Randomized Algorithms** - F.J. MacWilliams and N.J.A. Sloane,
**The Theory of Error Correcting Codes**, North-Holland, Amsterdam, 1981. - J. H. van Lint,
**Introduction to Coding Theory**, Springer Verlag, Berlin, 1999. - Chris Godsil, Gordon Royle,
**Algebraic graph theory**, Springer; 1 edition (April 20, 2001) - Norman Biggs,
**Algebraic Graph Theory**, Cambridge University Press; 2 edition (February 3, 1994) - Fan Chung,
**Spectral Graph Theory**(CBMS Regional Conference Series in Mathematics, No. 92), American Mathematical Society (May 1, 1997) - Dragos M. Cvetkovic, Michael Doob, Horst Sachs,
**Spectra of Graphs**, Academic Press; 3rd Revised edition (August 1, 1997) - Joseph Y. Hui,
**Switching and Traffic Theory for Integrated Broadband Networks,**Kluwer Academic Publishers / January 1990 - Frank Hwang,
**The Mathematical Theory of Nonblocking Switching Networks**, World Scientific Publishing Company, 2004 - Ding-Zhu Du and Hung Q. Ngo (editors),
**Advances in Switching Networks**, Network Theory and Applications Series, Vol. 5, Kluwer Academic Publisher (June 2001), 368pp., ISBN 0-7923-6953-X

**Some free books**