Here are some academic prerequisites for certain frequently taken first year courses:

- Differential Geometry (Math 535a):
**Familiarize yourself with the material in chapters 1-3 in the book Michael Spivak: "Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus."**

*Textbook for Fall 2011:*Warner: Foundations of Differentiable Manifolds & Lie Groups - Real Analysis (Math 525a): The textbook is usually
Gerald B. Folland: Real Analysis Modern Techniques and Their
Applications (2nd edition). To prepare for the course,
please read W. Rudin: "Principles of Mathematical
Analysis" (also affectionately known as "Baby Rudin"), especially the
chapters on compactness, Riemann integral, sequences and series of
functions. Also please read the Chapter 0 in the Folland's book
(The Language of Set theory, orderings, cardinality, more about well
ordered sets, the extended real number system, metric
spaces). This material is needed but not covered in the class Math
525a.

*Textbook for Fall 2011, 2012, 2013:*Gerald B. Folland: Real Analysis Modern Techniques and Their Applications (2nd edition) - Probability (Math 507): This is a measure theory based
probability
class. It
can be taken concurrently with Math 525a; however it would be best to
read during summer the last chapter (Measure Theory) in Rudin's
Principles book (see above).

*Textbook for Fall 2011, 2012 and 2013:*Durrett: Probability: Theory and Examples (4th edition)

- Algebra (Math 510): Please review the undergraduate algebra
material.
*Textbook for Fall 2012 and 2013:*Rotman: Advanced Modern Algebra (2nd edition) - Numerical Analysis (Math 502): Please review linear algebra.
Also, please
learn basics of Matlab (a good book under $20 is K. Sigmon and T. A.
Davis, MATLAB Primer, Sixth Edition, Chapman and Hall/CRC, Boca Raton,
FL, 2002; free version of the second edition is available at http://math.ucsd.edu/~driver/21d-s99/matlab-primer.html
- or just google Sigmon MATLAB Primer).
*Textbook for Fall 2011 and 2013:*Datta: Numerical Linear Algebra and Applications (2nd edition). - Applied Probability (Math 505): This is a probability class which
is
not based on measure theory. Background in probability is slightly
helpful, but
not necessary.

*Textbook for Fall 2011, 2012 and 2013:*Grimmett and Stirzaker: "Probability and random process" - Partial Differential Equations (Math 555a): Most of the class
does
not need the measure theory, so it can be taken during the first
year. There is a bit of Fourier transform and L
^{p}spaces needed when Sobolev spaces are discussed, but this can be learned/reviewed without difficulty.

*Textbook for Fall 2011 and 2013:*L.C. Evans: "Partial Differential Equations"

(Please double-check the information with the department before purchusing) Math 502a Proskurowski Numerical Linear Algebra & Applications (2nd) SIAM Textbooks for Fall 2013

Math 505a Berger Grimmett and Stirzaker: Probability & Random Process (3rd) Oxford Univ

Math 507a Kukavica Durrett: Probability (4th) Cambridge U. Press

Math 509 Zhang none

Math 510a E. Friedlander Rotman: Advanced Modern Algebra (2nd) AMS

Math 525a Haydn Folland: Real Analysis (2nd) Wiley

Math 530a Ma (multiple texts)

Math 532 Arratia Bryant: Aspects of Combinatorics

Math 540 Lauda Hatcher: Algebraic Topology Cambridge U. Press

Math 541b Nguyen Casella: Statistical Inference (2nd) Thomson

Math 555a Ziane Evans: Partial Differential Equations (2nd) AMS

Math 570a Sacker Naylor/Sells: Operator Theory in Science & Engr (2nd ed) Springer-Verlag

Math 574 Fulman Horn/Johnson: Matrix Analysis Cambridge U. Press

Math 578b Waterman: Introduction to Computational Biology CRC Press

Math 610 Malikov none

Math 605 Asok none

Math 650 Piterbarg Ramsay: Statistical Sleuth (2nd) Thomson

Math 705 Lototsky none

Math 710 E. Friedlander none

Math 725 Kukavica none

Math 740 Bonahon none

Last update: