Algebra/Algebraic Geometry - Master's Degree

Masters Degree in Mathematics of Cryptography and Communications

We are in the process of applying for a new Masters Degree. Here is a draft of the application.

The MSc in Mathematics of Cryptography and Communications is a highly focussed two year degree giving instruction into some of the mathematics behind modern secure information and communications systems. The programme of study specialises in mathematics relevant for public key cryptography, coding theory and information theory.

The MSc is for students who want to learn more about the mathematics which underlies modern secure information and communications systems. After obtaining this degree students would be well prepared to begin doctoral studies in the area or for a technical (possibly R&D) role in the communications industry.

Degree Requirements:

36 credits of graduate courses are required.

Required Courses:

1. MTH 571: Algebra I 4 credits
2. MTH 572: Algebra II 4
3. MTH 577: Computational Algebra I 4
4. MAT 631: Introduction to Cryptography 3
5. MTH 673: Coding Theory I 3

Three of the following courses

MAT 575: Elliptic curves in cryptography 3
MTH 576: Algebraic Curves 3
MTH 578: Computational Algebra II 4
MTH 671: Commutative Algebra 4
MTH 670: Algebraic Number Theory 4
MAT 672: Algebraic Geometry 4

A maximum of 9 credits of the following:

MTH 695: Special Topics in Cryptography 3
1. MTH 694: Seminar in Mathematics of Communications 2
2. MAT 699: Thesis Research 3-6

The course MTH 694 can not be taken more than twice. At most 6 credits can be taken of MTH 699.

Schedule

Schedule of Algebra/Algebraic Geometry/Cryptography is as follows:

The course MTH 694 runs every semester.

Suggested plan of study

Plan A:

For students coming in an odd year

- MTH 571: Algebra I (4)
- MTH 631: Introduction to Cryptography (3)
- MTH 575: Elliptic curves in Cryptography (3)
- MTH 577: Computational Algebra I (4)
- MTH 671: Commutative Algebra (4)

- MTH 572: Algebra II (4)
- MTH 673: Coding theory (3)
- MTH 576: Algebraic Curves (3)
- MTH 578: Computational Algebra II
  or MAT 672: Algebraic Geometry (4)
- MTH 670: Algebraic Number Theory (4)

Plan B:

For students coming in an even year.

- MTH 571: Algebra I (4)
- MTH 577: Computational Algebra I (4)
- MTH 631: Introduction to Cryptography (3)
- MTH 575: Elliptic curves in Cryptography (3)
- MTH 694: Seminar in Communications (2)

- MTH 572: Algebra II (4)
- MTH 578 or MTH 670 or MTH 672 or MTH 695 (4)
- MTH 694: Seminar in Communications (2)
- MTH 673: Coding Theory (3)
- MTH 576: Algebraic Curves (3)
- MTH 695 or MTH 699 (3)

Degree options

In order to graduate the student needs to choose one of the following options:

- Master's Exam. The exam contains two parts:
  - Algebra Exam: The algebra part which covers material from MTH 571-572
  - Specialty exam: Choose one of the following sequences
    - Elliptic curves, Algebraic curves
    - Coding Theory
    - Computational Algebra I, II

Both parts of the exam are written and last 5-hours each. They are offered three times a year and administered by the advising committee of the program. Each student can take the exam only twice. Transferring students who have taken these courses elsewhere are free to take the exams when they arrive at OU.

- Thesis option: The student can choose the thesis option instead of the exam options. All classes of the program other then MTH 571, 572 are project oriented. The student must decide during the Fall of the second year if he/she wants to follow the thesis option. Projects during class will provide plenty of opportunities to write a thesis
- A thesis advisor must be chosen in agreement with the program's advising committee. The thesis must fulfill all requirements of the Graduate School at Oakland University.

Advisory Committee

Any changes to this program have to be approved by the Advisory Committee. The advisory committee has as members 3-4 world experts in the area and 2 faculty members from Oakland University. One of the members of the Advisory Committee who is a faculty member at OU will serve as graduate advisor for the program.

Employment Opportunities and Alumni

A student who graduates from the program has two main career paths: to work as a cryptography expert in industry or to continue a career path in academia and continue studies for a PhD in Mathematics or Computer Science.

Our program gives a very strong background in both theoretical mathematics and programing skills. We intend to help our alumni with employment opportunities in industry, NSA, government agencies etc. Students who choose to pursue PhD studies in cryptography can do so at Oakland University of in other universities throughout the world.