# 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:**

- 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 Educational Outcomes:**

** ** Upon completion of the program, student should 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.

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

- 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.

## Mathematics Requirements

### Common Core Courses

MA 605 | Foundation 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 | Introduction to Network and 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 | Introduction to Network and 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 695 | 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 |