The Master of Science in Mathematics
The Program
The master's degree in mathematics encompasses the basic graduate curriculum in mathematics, and also offers the opportunity of some more specialized training in an area of interest. A typical master's program will involve a basic analysis course, linear algebra, complex variables, basic probability, possibly courses in ordinary and partial differential equations, and choices from other courses usually taken in the first and second years of graduate study, such as algebra, applied mathematics, and financial mathematics courses. Since most of the courses may be credited toward doctoral studies, the master's degree may be a stepping stone to an eventual Ph.D degree.Information
about admission on a non-degree basis is HERE.
A candidate for the master's degree in mathematics must fulfill the following departmental requirements:
- 36 points of credit, and the grade of at least B in the written comprehensive examinations, or,
- 32 points of credit, and a master's thesis, completed under the supervision of a faculty member and approved by the department.
Under both options, students may be able to transfer up to 8 points of credit (usually equivalent to two CIMS courses) from other academic institutions.
M.S. students who receive the grade of A in the Written
Comprehensive Examinations may apply to the Ph.D. program. The
application will be considered by the Mathematics Fellowship
Committee. The Committee will take into consideration the overall
performance of the student in the M.S. program.
As part of the application process, the student will also be
required to prepare and give a presentation on a mathemaical topic in
front of a specially appointed faculty committee. The
presentation
should take place during the semester in which the written examinations
were taken.
Receiving the grade of A in the written examinations and giving a
presentation does not in itself constitute an offer of admission to the
Ph.D. program, nor an offer of financial support.
Coursework
The master's degree in mathematics encompasses the basic graduate curriculum in mathematics, and also offers the opportunity of some more specialized training in an area of interest. A typical master's program will involve a basic analysis course, linear algebra, complex variables, basic probability, possibly courses in ordinary and partial differential equations, and choices from other courses usually taken in the first and second years of graduate study, such as algebra, applied mathematics, basic probability and mathematical statistics. Since most of the courses may be credited toward doctoral studies, the master's degree may be a stepping stone to an eventual Ph.D. degree.
Students are required to take six of the courses listed below:
Group IMATH-GA 1410 Introduction to Math Analysis I (fall)
MATH-GA 1420 Introduction to Math Analysis (spring)
MATH-GA 2430 Real Variables (fall)
MATH-GA 2450 Complex Variables I (fall)
MATH-GA 2460 Complex Variables II (spring)
Group II
MATH-GA 2110 Linear Algebra I (fall, spring, summer)
MATH-GA 2120 Linear Algebra II (spring, summer)
MATH-GA 2901 Basic Probability (fall, spring, summer)
Group III
MATH-GA 2010 Numerical Methods I (fall)
MATH-GA 2120 Numerical Methods II (spring)
MATH-GA 2043 Scientific Computing (fall, spring)
MATH-GA 2130 Algebra I (fall)
MATH-GA 2310 Topology I (fall)
MATH-GA 2350 Differential Geometry I (fall)
MATH-GA 2470 Ordinary Differential Equations (spring)
MATH-GA 2110 Partial Differential Equations (spring)
MATH-GA 2701 Methods of Applied Math (fall)
Students are required to take at least 2 courses from Group I, at least 2 courses from Group II, and at least 2 courses from Groups I, II, and III, provided that at least one course is from Group III.
The Written Comprehensive Examinations
Students choosing the first option, must pass, with the grade of B, the three-part Written Comprehensive Examination administered by the Department twice a year, in early September and early January. Most master's students tend to take exam toward the end of their graduate studies.
The examinations, in advanced calculus, complex variables and linear algebra, may include some of the following material:
Advanced Calculus: Real numbers. Functions of 1 variable: continuity, mean-value, differentiability, maxima and minima, integrals, fundamental theorem of calculus, inequalities, estimation of sums and integrals, elementary functions and their power series. Funtions of several: partial derivatives, chain rule, MacLaurin expansion, critical points, Lagrange multipliers, inverse and implicit function theorems, jacobian, divergence and curl, theorems of Green and Stokes.
Complex Variables: Complex numbers, analytical functions, Cauchy-Riemann equations, Cauchy's integral and applications, power series, maximum principle, Liouville's theorem, elementary functions and their conformal maps, bilinear transformation, classification of singularities, residue theorem and contour integration, Laurent series, Rouche's theorem, number of zeros and poles.
Linear Algebra:Vector spaces, linear dependence, basis, dimension, linear transformation, inner product, systems of linear equations, matrices, determinants, ranks, eigenvalues, diagonalization of matrices, quadratics forms, symmetric and orthogonal transformations.
Cooperative preparation is encouraged, as it is for all examinations. Students may also find the following books helpful:
Buck, Advanced Calculus; Courant and John, Introduction to Calculus and Analysis; Strang, Linear Algebra; Churchill, Complex Variables and Applications.
Master's Thesis
Students choosing the second option will work on a master's thesis under the supervision of a mathematics faculty member acting as their thesis advisor. In certain cases involving interdisciplinary research, a second advisor outside the Department of Mathematics may be approved by the Director of Graduate Studies. A proposal outlining the program for the thesis will be submitted to the Director of Graduate Studies for approval. Upon completion, a master's thesis must be approved by the thesis advisor and a second reader of his/her choice.
Academic Standards
To continue registering for courses in the Department of Mathematics, a student must be in a good academic standing, fulfilling the following requirements:
- Students must maintain an average of B or better (3.0) in their first 12 credits. Students failing to achieve this will not be permitted to continue in the program. Students cannot obtain an M.S. degree unless they have maintained an overall average of at least B.
- Students will be allowed no more than four no-credit grades, withdrawals, or unresolved incomplete grades during their academic tenure, and no more than two such grades in the first six courses for which they have registered.
- Credit will be given for up to two core courses taken elsewhere, subject to the normal GSAS restrictions on transfer of credit and the approval of the Program Coordinator. At least 30 course points must be taken at New York University.
An M.S. application can be downloaded at www.nyu.edu/gsas/admissions; the Graduate School of Arts and Sciences strongly prefers that you apply online at www.nyu.edu/gsas/online.
For any questions contact us at:
E-Mail: admissions@math.nyu.edu
E-Mail: arnon@cims.nyu.edu
Web page: http://www.math.nyu.edu