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Dear Prospective Applicant,

Thank you for your interest in graduate studies in the Department of Mathematics at UCLA. Applications are accepted for Fall quarter matriculation only. The application deadline is December 15. Application review process begins in late December; to ensure full consideration, applications should be complete, with all supporting material submitted, by that time.

You must submit the UCLA Graduate Admissions Application (see http://www.gdnet.ucla.edu/gasaa/admissions/applicat.htm) You must submit also the Application Fee for the UCLA Graduate Admissions Application. Instructions for this payment are given online. As part of the Graduate Division Application, you will be required to submit:

• Transcripts (scans and originals)
• GRE General and Math Subject test scores
• Statement of purpose
• Letters of Recommendation (see online UCLA application)
• List of Mathematics Courses taken
• Applicants whose native language is not English must take the TOEFL exam and submit their TOEFL score.

Each applicant must select an area (pure or applied) and a field of interest as part of the application. The two areas have slightly different course requirements but both allow for flexibility to take many combinations of courses and qualifying exams throughout the department. Students can ask to switch areas or fields after starting the program if their interests change.

1. A bachelor's degree or its equivalent, to be completed by the time of matriculation, with a minimum B (3.0 on a 4.0 scale) GPA in undergraduate junior/senior years and in post baccalaureate work.

   Applicants for the MA program must have a 3.2 GPA in upper division math courses; applicants for the PhD program must have a 3.5 GPA in upper division math courses. Applicants with a Master's degree must maintain a 3.6 GPA.

   Prospective students do not need to have an undergraduate mathematics major, but must complete at least 12-quarter, or 8-semester courses in substantial upper division mathematics. Comparable Upper Division Courses at UCLA:

   • Algebra 110AB: Ring of integers, integral domains, fields, polynomial domains, unique factorization. Groups, structure of finite groups.
   • Linear Algebra 115AH: Abstract vector spaces, linear transformations, and matrices; determinants; inner product spaces; eigenvector theory.
   • Analysis 131ABH: Rigorous introduction to foundations of real analysis; real numbers, point set topology in Euclidean space, functions, continuity. Derivatives, Riemann integral, sequences and series of functions, power series, Fourier series.
   • Differential Geometry 120A: Curves in 3-space, Frenet formulas, surfaces in 3-space, normal curvature. Gaussian curvature. Congruence of curves and surfaces. Intrinsic geometry of surfaces, isometrics, geodesics, Gauss/Bonnet theorem.
   • Ordinary Differential Equations 135AB: Systems of differential equations; linear systems with constant coefficients, analytic coefficients, periodic coefficients, and linear systems with regular singular points; existence and uniqueness results; linear boundary and eigenvalue problems; two-dimensional autonomous systems, phase/plane analysis, stability and asymptotic behavior of solutions.
     
   • Applied Numerical Methods 151AB: Introduction to numerical methods with emphasis on algorithms, analysis of algorithms, and computer implementation issues. Solution of non-linear equations, numerical differentiation, integration, and interpolation. Numerical solution of differential equations.
     

   
   
2. Three letters of recommendation with preferably all, but always at least 2, from mathematicians who are familiar with the student's work.
3. The GRE General and Math Subject tests. For results to reach us in time, the General test should be taken by October and the Math Subject test by November.

Useful Links:

For more information, contact the Math Dept. Graduate Advisor, gradapps@math.ucla.edu.
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