### This Program

The master’s degree in mathematics encompasses the fundamental graduate curriculum in mathematics, additionally to provides the chance of more specialized learning an market. An average master’s program requires fundamental courses in solid analysis, complex analysis and straight line algebra, adopted by other fundamental courses of instruction for example probability, scientific computing, and differential equations. Based on their mathematical interests, students can realize your desire to think about more difficult graduate courses in pure and applied mathematics.

Specifics of admission round the non-degree basis is **HERE** .

A candidate for the master’s degree in mathematics must match the following departmental needs:

- 36 points of credit, and the grade of no under B within the written comprehensive examinations, or,
- 32 points of credit, along with a master’s thesis, completed underneath the supervision in the faculty member and approved with the department.

Under both options, students might transfer around 8 points of credit (usually similar to two CIMS courses) business educational institutions.

### Coursework

Students are required to consider eight courses (24 credits) using this list. All courses in Group I, two courses from Group II, and two additional courses from Group II or Group III needs to be taken. Substitute classes are listed in the final outcome.

Group I (Mandatory Preparation)

MATH-GA 1410 Overview of Math Analysis I (fall)

MATH-GA 2450 Complex Variables I (fall)

MATH-GA 2110 Straight line Algebra I (fall, spring, and perhaps summer time time time)

MATH-GA 1002 Multivariable Analysis (spring)

Group II (Fundamentals)

MATH-GA 1420 Overview of Math Analysis II (spring)

MATH-GA 2460 Complex Variables II (spring)

MATH-GA 2120 Straight line Algebra II (spring)

MATH-GA 2901 Fundamental Probability (fall, spring, summer time time time)

MATH-GA 2043 Scientific Computing (fall, spring)

MATH-GA 2470 Ordinary Differential Equations (spring)** Group III** (more difficult core graduate courses)

MATH-GA 2010 Record Methods I (fall)

MATH-GA 2020 Record Methods II (spring)

MATH-GA 2130 Algebra I (fall)

MATH-GA 2310 Topology I (fall)

MATH-GA 2210 Number Theory (spring)

MATH-GA 2350 Differential Geometry I (fall)

MATH-GA 2490 Partial Differential Equations (fall) MATH-GA 2701 Means of Applied Math (fall)

MATH-GA 2702 Fluid Dynamics (fall)

MATH-GA 2550 Functional Analysis (fall)

MATH-GA 2563 Harmonic Analysis (spring)

MATH-GA 2911 Probability: Limit Theorems I (fall)

MATH-GA 2902 Stochastic Calculus (fall, spring and summer time time time)

DS-GA 1002 Record and Mathematical Methods (fall)

MATH-GA 2430 Real Variables (one-term) is a substitute for MATH-GA 1410 and 1420 Overview of Math Analysis I and II.

MATH-GA 2451 Complex Variables (one-term) is a substitute for MATH-GA 2450 and 2460 Complex Variables I and II.

MATH-GA 2111 Straight line Algebra (one-term) is a substitute for MATH-GA 2110 and 2120 Straight line Algebra I and II.

Another one-term course might be taken carrying out a first term from the equivalent two-term course, but might not be taken carrying out a equivalent two-term sequence is finished. Resolution of conflicts will need the applying within the Director of Graduate Studies.

Just the credits within the completed courses will count toward the amount.

Be aware that master’s and non-degree students in their newbie of study generally aren’t allowed a subscription for virtually any Advanced Topics courses. In further semesters, students are permitted a subscription for such courses with permission of both course instructor along with the Director of Graduate Studies for the M.S. Program.

### The Written Comprehensive Examinations

Students choosing the initial option, must pass, with the grade of B, the 3-part Written Comprehensive Examination administered using the Department two occasions yearly, noisy . September and also the month from the month of the month of january. Most master’s students have a very inclination to think about exam toward the final outcome in the graduate studies.

Students are allowed to just accept written examinations two occasions, without any special permission. Another and final attempt might be granted using the Department round the situation-by-situation basis.

The examinations, in advanced calculus, complex variables and straight line algebra, can include a few in the following material:

**Advanced Calculus:** Real figures. Functions of a single variable: continuity, mean-value, differentiability, maxima and minima, integrals, fundamental theorem of calculus, inequalities, estimation of sums and integrals, elementary functions additionally for their power series. Funtions of several variables: partial derivatives, chain rule, MacLaurin expansion, critical points, Lagrange multipliers, inverse and implicit function theorems, jacobian, divergence and curl, theorems of Eco-friendly and Stokes.

**Complex Variables:** Complex figures, analytical functions, Cauchy-Riemann equations, Cauchy’s integral and applications, power series, maximum principle, Liouville’s theorem, elementary functions additionally for their conformal maps, bilinear transformation, classification of singularities, residue theorem and contour integration, Laurent series, Rouche’s theorem, amount of zeros and rods.

**Straight line Algebra:** Vector spaces, straight line dependence, basis, dimension, straight line transformation, inner product, systems of straight line equations, matrices, determinants, ranks, eigenvalues, diagonalization of matrices, quadratics forms, symmetric and orthogonal transformations.

Cooperative preparation is inspired, as it is for people examinations. Students might also identify the next books useful:

Buck, *Advanced Calculus* Courant and John, *Overview of Calculus and Analysis* Strang, *Straight line Algebra* Churchill, *Complex Variables and Applications*.

### Master’s Thesis

Students selecting the 2nd option relies on a master’s thesis underneath the supervision in the mathematics faculty member becoming their thesis consultant. Sometimes involving interdisciplinary research, another consultant outdoors the Department of Mathematics might be approved with the Director of Graduate Studies. An offer outlining this program for the thesis will most likely be printed for that Director of Graduate Studies for approval. When completed, a master’s thesis needs to be approved with the thesis consultant another readers of his/her choice.

### Academic Standards

To help keep registering to courses within the Department of Mathematics, students needs to be within the good academic standing, fulfilling the next needs:

- Students must maintain typically B or better (3.) in their first 12 credits. Students failing to accomplish this won’t be allowed to help keep within the program. Students cannot have the M.S. degree unless of course obviously clearly they’ve maintained an over-all average getting no less than B
- Students will most likely be permitted a maximum of four no-credit grades, withdrawals, or unresolved incomplete grades within their academic tenure, and a maximum of two such grades within the first six classes for they’ve registered.
- Credit is going to be deliver to roughly two core courses taken elsewhere, vulnerable to the traditional GSAS limitations on alteration of credit along with the approval within the Program Coordinator. No under 30 course points needs to be taken at New You can College.

An M.S. application accessible at internet.nyu.edu/gsas/admissions the Graduate School of Arts and Sciences strongly prefers using online at internet.nyu.edu/gsas/online.

For virtually any questions call us at:

*Department of Mathematics**Courant Institute of Mathematical Sciences**251 Mercer Street**New You can, NY 10012-1185**Tel. (212) 998-3238**Fax (212) 995-4121*