# Anurag Agarwal

## Associate Professor

School of Mathematical Sciences

College of Science

585-475-7531

Office Hours

[Spring 2023:] MONDAY and FRIDAY 12:00PM to 12:50PM. If there is a real need, then I can meet by appointment and/or via ZOOM as well.

Office Location

Office Mailing Address

GOS-3216

# Anurag Agarwal

## Associate Professor

School of Mathematical Sciences

College of Science

## Education

BS, MS, Indian Institute of Technology (India); Ph.D., State University of New York at Buffalo

585-475-7531

Areas of Expertise

algebraic number theory

combinatorics

cryptography

graph theory

## Select Scholarship

Published Article

Agarwal, A., M. Lopez, and D.A. Narayan. “Representations for complete graphs minus a disjoint union of paths.”

*Journal ofCominatorial Mathematics and Cominatoral Computing*, 72 (Feb 2010): 173-180. Print. «Agarwal, A. and J.E. Marengo. “The Locus of the Focus of arolling parabola.”

*The College Mathematics Journal*, 41.2 (March 2010): 129-133. Print. «Agarwal, S. and A. Agarwal. “Investigating the nature of knowledge of mathematics required for teaching of functions.”

*Proceedings of theInternational Conference of Education, Research and Innovation*, 2009-10. Print. «Formal Presentation

Agarwal, Anurag. “Representation Numbers and Prague Dimension of Graphs.”

*MAA Seaway Section Meeting*. Plattsburgh, NY. 15-16 Oct. 2010. Presentation.## Currently Teaching

MATH-190

Discrete Mathematics for Computing

3 Credits

This course introduces students to ideas and techniques from discrete mathematics that are widely used in Computer Science. Students will learn about the fundamentals of propositional and predicate calculus, set theory, relations, recursive structures and counting. This course will help increase students’ mathematical sophistication and their ability to handle abstract problems.

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-367

Codes and Ciphers

3 Credits

This course will introduce, explain and employ both the classical and modern basic techniques of cryptography. Topics will include the Vignère cipher, affine ciphers, Hill ciphers, one-time pad encryption, Enigma, public key encryption schemes (RSA, Diffie-Hellman, El-Gamal, elliptic curves), and hash functions. The course will include an introduction to algebraic structures and number theoretic tools used in cryptography.

MATH-371

Number Theory

3 Credits

This course provides an introduction to the study of the set of integers and their algebraic properties. Topics include prime factorization and divisibility, linear Diophantine equations, congruences, arithmetic functions, primitive roots, and quadratic residues.

MATH-412

Numerical Linear Algebra

3 Credits

This course covers numerical techniques for the solution of systems of linear equations, eigenvalue problems, singular values and other decompositions, applications to least squares, boundary value problems, and additional topics at the discretion of the instructor.

MATH-441

Abstract Algebra I

3 Credits

This course covers basic set theory, number theory, groups, subgroups, cyclic and permutation groups, Lagrange and Sylow theorems, quotient groups, and isomorphism theorems. Group Theory finds applications in other scientific disciplines like physics and chemistry.

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-671

Number Theory

3 Credits

This course is an introduction to the standard results and techniques of number theory. Topics include divisibility, congruences, Diophantine equations, Moebius inversion, quadratic reciprocity, and primitive roots. Cryptography and other applications will be discussed. Projects may be required.

MATH-771

Mathematics of Cryptography

3 Credits

This course is an introduction to the mathematical problems and techniques that serve as a foundation for modern cryptosystems. The topics include: classical cryptosystems computational number theory, primality tests, finite fields, private and public key encryption scheme (RSA, El-Gamal), and applications such as digital signatures, one way functions, and zero knowledge proofs. Use of elliptic curves in cryptography will also be covered.

MATH-790

Research & Thesis

0 - 9 Credits

Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.

MATH-799

MATH GRADUATE Independent Study

1 - 3 Credits

Independent Study