Master of Science in Mathematics

The Master of Science in Mathematics prepares students for careers in mathematical sciences or those computer science related fields where a deeper knowledge of mathematical foundations is required. It accommodates individuals with varying academic backgrounds and career objectives, including students interested in pursuing a Ph.D. in the mathematical sciences. The program offers an optional concentration in Discrete Mathematics and Cryptography. Upon completion of the program, students are expected to have broad knowledge and fundamental understanding of probability theory, real analysis, and modern algebra. The students gain a deeper understanding of advanced mathematics and applications of discrete mathematics to computer science and develop awareness of the interplay between mathematical disciplines and their relevance to science, computer science and engineering.

Concentrations

To gain a deeper understanding of advanced mathematics and applications of discrete mathematics to computer science, and particularly cryptography, the students are encouraged to pursue the concentration in:

Discrete Mathematics and Cryptography

Program Objectives

The program prepares students to:

apply analytical skills necessary to formulate and solve complex mathematical problems that are of contemporary relevance in the fields of pure mathematics, discrete mathematics, or related fields such as computer science.
apply mathematical skills and knowledge to facilitate career advancement in education, industry, or to pursue more advanced study such as a Ph.D. degree in mathematics or mathematics-related fields.
demonstrate broad-based skills and understanding of problem solving, ethics, social awareness, communication, and teamwork to excel as recognized leaders in their profession

Program Outcomes

By the time of graduation, students will be able to:

identify, formulate, and solve broadly defined mathematical and or scientific problems by applying their knowledge of mathematics and other technical topics to mathematics related fields.
demonstrate a comprehensive understanding of mathematical analysis, modern algebra, and advanced probability theory.
demonstrate their understanding of current research in at least one of the concentration areas, or some other related mathematical discipline by presenting the corresponding literature and performing research on related projects.
clearly communicate mathematical concepts orally and in writing.
understand professional behavior and the ethics of using and quoting results.
work efficiently in collaboration with others.

Concentration in Discrete Mathematics and Computation Program Outcomes

By the time of graduation, students will be able to:

demonstrate a comprehensive understanding of discrete mathematics including graph theory, modern algebra and their applications to computer science.
demonstrate a comprehensive understanding of foundations of classical computation and complexity theory, and classical and “quantum resistant” cryptographic protocols and their implementations.
implement relevant algorithms in programming languages such as C++ and Python.

Degree Requirements

The program is a 30-credit degree program. Students are required to complete:

4 core courses (12 credits)
6 electives (18 credits)

Students who choose to pursue the concentration in Discrete Mathematics and Cryptography are required to select at least 3 courses from the concentration in Discrete Mathematics and Cryptography electives list.

Common Core Courses

MA 605	Foundations of Algebra I	3

MA 540	Introduction to Probability Theory	3
	Or
MA 611	Probability	3

MA 635	Functional Analysis I	3

MA 606	Foundation of Algebra II	3
	Or
MA 636	Functional Analysis II	3

Concentration in Discrete Mathematics and Cryptography Elective Courses

Students who choose to pursue the optional concentration in Discrete Mathematics and Cryptography must select at least three courses from the following list:

MA 503	Discrete Mathematics for Cryptography	3
MA 526	Foundations of computation and computational complexity	3

MA 544	Numerical Linear Algebra for Big Data	3
	Or
MA 552	Axiomatic Linear Algebra	3

MA 564	Mathematics of Post-Quantum Cryptography	3
MA 565	Quantum Algorithms	3
MA 567	Computational Algebraic Geometry	3
MA 620	Intro Network & Graph Theory	3
CS 579	Foundations of Cryptography	3

MA 526: CS 601 is acceptable in place of MA 526.

Only one of MA 544 and MA 552 can count as an elective course towards the concentration.

Elective courses for the program

MA 503	Discrete Mathematics for Cryptography	3
MA 526	Foundations of computation and computational complexity	3
MA 541	Statistical Methods	3
MA 544	Numerical Linear Algebra for Big Data	3
MA 550	Introduction to Lie Theory	3
MA 552	Axiomatic Linear Algebra	3
MA 564	Mathematics of Post-Quantum Cryptography	3
MA 565	Quantum Algorithms	3
MA 567	Computational Algebraic Geometry	3
MA 606	Foundation of Algebra II	3
MA 611	Probability	3
MA 612	Mathematical Statistics	3
MA 620	Intro Network & Graph Theory	3
MA 627	Combinatorial Analysis	3
MA 623	Stochastic Processes	3
MA 636	Functional Analysis II	3
MA 637	Mathematical Logic I	3
MA 638	Mathematical Logic II	3
MA 649	Intermediate Differential Equations	3
MA 650	Intermediate Partial Differential Equations	3
MA 651	Topology I	3
MA 652	Topology II	3
MA 681	Complex Analysis with Applications	3
MA 717	Algebraic Topology	3
MA 727	Theory of Algebraic Numbers	3
MA 752	Advanced Topics in Algebra	3
MA 800	Special Problems in Mathematics (MS)	1 - 6
MA 810	Special Topics in Mathematics	1 - 3
MA 900	Thesis in Mathematics	1 - 10
CPE 595	Applied Machine Learning	3
CS 570	Introduction to Programming, Data Structures, and Algorithms	3
CS 579	Foundations of Cryptography	3
CS 600	Advanced Algorithm Design and Implementation	3
CS 601	Algorithmic Complexity	3
CS 693	Cryptographic Protocols	3
PEP 553	Quantum Mechanics and Engineering Applications	3
PEP 557	Quantum Information and Quantum Computation	3

Students may choose MA 900 - Thesis in Mathematics for six credits as one of their electives to work on a specific project with an advisor. Enrolling in MA 900 is subject to approval by the program coordinator.