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Master of Science in Mathematics

The program 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, the students are expected to have broad knowledge and fundamental understanding of probability theory, real analysis, and modern algebra. Depending on the concentration they choose students gain deeper understanding of advanced mathematics or 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.

The Master of Science in Mathematics consists of four core courses and six electives and offers an optional concentration in Discrete Mathematics and Cryptography. The total credit requirement for the program is 30 credits. Students 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. 

Program Educational Objectives:

  1. 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.
  2. 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.
  3.  Demonstrate broad-based skills and understanding of problem solving, ethics, social awareness, communication, and teamwork to excel as recognized leaders in their profession.

Program Educational Outcomes:

  Upon completion of the program, student should be able to:

  1. 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.
  2. Demonstrate a comprehensive understanding of mathematical analysis, modern algebra, and advanced probability theory.
  3. 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.
  4. Clearly communicate mathematical concepts orally and in writing.
  5. Understand professional behavior and the ethics of using and quoting results.
  6. Work efficiently in collaboration with others.

 Program Outcomes specific to the concentration in Discrete Mathematics and Computation:

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

Mathematics Requirements

Common Core Courses

MA 605Foundation of Algebra I

3

MA 540Introduction to Probability Theory

3
Or
MA 611Probability

3

MA 635Functional Analysis I

3

MA 606Foundation of Algebra II

3
Or
MA 636Functional 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 503Discrete Mathematics for Cryptography

3
MA 526Foundations of computation and computational complexity

3

MA 544Numerical Linear Algebra for Big Data

3
Or
MA 552Axiomatic Linear Algebra

3

MA 564Mathematics of post-quantum cryptography

3
MA 565Quantum Algorithms

3
MA 567Computational Algebraic Geometry

3
MA 620Introduction to Network and Graph Theory

3
CS 579Foundations 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 503Discrete Mathematics for Cryptography

3
MA 526Foundations of computation and computational complexity

3
MA 541Statistical Methods

3
MA 544Numerical Linear Algebra for Big Data

3
MA 550Introduction to Lie Theory

3
MA 552Axiomatic Linear Algebra

3
MA 564Mathematics of post-quantum cryptography

3
MA 565Quantum Algorithms

3
MA 567Computational Algebraic Geometry

3
MA 606Foundation of Algebra II

3
MA 611Probability

3
MA 612Mathematical Statistics

3
MA 620Introduction to Network and Graph Theory

3
MA 627Combinatorial Analysis

3
MA 623Stochastic Processes

3
MA 636Functional Analysis II

3
MA 637Mathematical Logic I

3
MA 638Mathematical Logic II

3
MA 649Intermediate Differential Equations

3
MA 650Intermediate Partial Differential Equations

3
MA 651Topology I

3
MA 652Topology II

3
MA 681Complex Analysis with Applications

3
MA 717Algebraic Topology

3
MA 727Theory of Algebraic Numbers

3
MA 752Advanced Topics in Algebra

3
MA 800Special Problems in Mathematics (MS)

1-6
MA 810Special Topics in Mathematics

1-3
MA 900Thesis in Mathematics

1-10
CPE 695Applied Machine Learning

3
CS 570Introduction to Programming, Data Structures, and Algorithms

3
CS 579Foundations of Cryptography

3
CS 600Advanced Algorithm Design and Implementation

3
CS 601Algorithmic Complexity

3
CS 693Cryptographic Protocols

3
PEP 553Quantum Mechanics and Engineering Applications

3
PEP 557Quantum 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.