## Select Scholarship

R.Felea, FIOs with cusp singularities and open umbrellas, Journal of Pseudo-Differential Operators and Applications volume 12, no 38 (2021).

R.Felea, R. Gaburro, A. Greenleaf, C. Nolan, Microlocal analysis of Doppler SAR, Inverse Problems and Imaging, vol 13, no 6, 2019, 1283-1307.

G.Ambartsoumian, R. Felea, V. Krishnan, T. Quinto, C. Nolan A class of singular FIOs in SAR imaging II: transmitter and receiver with different speeds, SIAM J of Math Analysis, Vol 50, no 1, 2018, 591-621.

MATH-181

Project-Based Calculus I

4 Credits

This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals.

MATH-182

Project-Based Calculus II

4 Credits

This is the second in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates.

MATH-231

Differential Equations

3 Credits

This course is an introduction to the study of ordinary differential equations and their applications. Topics include solutions to first order equations and linear second order equations, method of undetermined coefficients, variation of parameters, linear independence and the Wronskian, vibrating systems, and Laplace transforms.

MATH-241

Linear Algebra

3 Credits

This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course.

MATH-341

Advanced Linear Algebra

3 Credits

This is a second course in linear algebra that provides an in-depth study of fundamental concepts of the subject. It focuses largely on the effect that a choice of basis has on our understanding of and ability to solve problems with linear operators. Topics include linear transformations, similarity, inner products and orthogonality, QR factorization, singular value decomposition, and the Spectral Theorem. The course includes both computational techniques and the further development of mathematical reasoning skills.

MATH-381

Complex Variables

3 Credits

This course covers the algebra of complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy's integral theorem and integral formulas, Taylor and Laurent series, residues, and the calculation of real-valued integrals by complex-variable methods.

MATH-431

Real Variables I

3 Credits

This course is an investigation and extension of the theoretical aspects of elementary calculus. Topics include mathematical induction, real numbers, sequences, functions, limits, and continuity. The workshop will focus on helping students develop skill in writing proofs.

MATH-432

Real Variables II

3 Credits

This course is a continuation of MATH-431. It concentrates on differentiation, integration (Riemann and Riemann-Stieltjes integrals), power series, and sequences and series of functions.

MATH-495

Undergraduate Research in Mathematical Sciences

1 - 3 Credits

This course is a faculty-directed project that could be considered original in nature. The level of work is appropriate for students in their final two years of undergraduate study.

MATH-498

Independent Study in Mathematical Sciences

1 - 3 Credits

This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.

MATH-633

Measure Theory of Elements and Functional Analysis

3 Credits

This course will provide a general introduction to Lebesgue measure as applied to the real numbers, real-valued functions of a real variable, and the Lebesgue integral of such functions. It also covers topics in functional analysis relevant to application of measure theory to real-world problems. Students will be expected to read and understand proofs, and to demonstrate their understanding of topics by writing their own proofs of various facts.

MATH-742

Partial Differential Equations II

3 Credits

This is a continuation of Partial Differential Equations I and deals with advanced methods for solving partial differential equations arising in physics and engineering problems. Topics to be covered include second order equations, Cauchy-Kovalevskaya theorem, the method of descent, spherical means, Duhamels principle, and Greens function in higher dimensions.

MATH-799

MATH GRADUATE Independent Study

1 - 3 Credits