AIM Written Preliminary Exams Written examinations are offered in the following areas twice a year (first week of September and January): Differential Equations and Linear Algebra. Reference texts include: W. E. Boyce and R. C. DiPrima, Elementary Differential Equations. R. Haberman, Applied Partial Differential Equations with Fourier Series and Boundary-Value Problems (Chapters 1-4). G. Strang, Linear Algebra and its Applications. Advanced Calculus and Complex Variables. Reference texts include: J. Stewart, Multivariable Calculus. K. Ross, Elementary Analysis: The Theory of Calculus. J. W. Brown and R. V. Churchill, Complex Variables and Applications. Probability and Discrete Mathematics. Reference texts include: S. Ross, A First Course in Probability. R. P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction. J. Kleinberg and É. Tardos, Algorithm Design. The written examinations are each three hours long. A student must pass two of these written examinations within 13 months of entering the AIM PhD program in order to be eligble to proceed in the program. The examinations are designed to test the background mathematical knowledge that every student will need to succeed in the program and will cover work at the advanced undergraduate level. Students have a maximum of thirteen months (that is, three attempts) to pass two of the written examinations. A schedule of upcoming examination dates and some recent examination papers can be found by following this link: AIM Preliminary Examinations Questions? If you have any questions about the AIM program or admission, please contact us at the following address or e-mail below. Please include "AIM PROGRAM" in the subject line of any e-mail inquiry. AIM Program Department of Mathematics University of Michigan Ann Arbor, MI 48109-1043 USA 734.615.3439 or 734.764.7436 E-mail: math-grad-admissions@umich.edu