Course Prerequisites

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

  1. 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
  2. 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)
  3. 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)
  4. Algebra (Math 510): Please review the undergraduate algebra material. Textbook for Fall 2012 and 2013: Rotman: Advanced Modern Algebra (2nd edition)
  5. 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 - or just google Sigmon MATLAB Primer). Textbook for Fall 2011 and 2013: Datta: Numerical Linear Algebra and Applications (2nd edition).  
  6. 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"
  7. 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 Lp 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"

Textbooks for Fall 2013
(Please double-check the information with the department before purchusing) Math 502a Proskurowski Numerical Linear Algebra & Applications (2nd) SIAM
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: August 17, 2011