Mathematics

The Master of Science (MS) in Mathematics program is generally completed within two years. Students take up to 30 academic credits consisting of graduate coursework and research seminars. There are three paths toward the degree: (a) comprehensive examination in graduate material, (b) comprehensive examination and research project, supervised by a faculty, completed during one semester, (c) research thesis, supervised by a faculty, often organized around an effort to complete an original journal article.

• Complete 30 credit hours subject to the following restrictions:
  • At least 20 credit hours of course and seminar work must be earned in residence at Clarkson
  • At least 16 hours must be earned in the Department of Mathematics as courses and seminars numbered above MA 505, with at most one of these credits coming from seminar.
  • Among the courses, one course must be MA 521 Classical Complex Analysis, MA 522 Classical Real Analysis or MA 578 Numerical Analysis, and two other courses must be at the 500 or 600 level. The remainder of the coursework must be approved by the advisor in collaboration with the Graduate Committee Chair.
  • Have an overall grade point average of at least 3.00 in their course work.

Fulfill one of the following:

• Write a thesis under the guidance of a faculty member. The thesis is to be an original or expository study of some area or problem and shall represent 6 to 10 credit hours. The topic of the thesis must be approved by the graduate committee and thesis advisor in advance. As required by University regulations, the thesis must be examined by a committee of at least three Clarkson faculty appointed by the chair of the department.
• Pass two qualifying exams described under the requirements for the PhD degree. The choices must be approved by the student's advisor and the graduate committee.
• Pass one exam from either of the categories (I or II) listed in the PhD requirements, plus complete a special project. A description of the proposed project must be approved in advance by the student's advisor and the graduate committee. When the project is completed, it must be approved by the graduate committee. Completion will carry 3 to 9 hours at the discretion of the student's advisor.
• Typical duration of a MS program is 2 years.

The PhD in Mathematics consists of 90 credits above a bachelors degree. These credits are taken in coursework, seminar and project work to fulfill the PhD requirement. The program consists of extensive coursework completed in the first 2-3 years of the program, followed by the development of the original research dissertation under the direction of one of our faculty members.

PhD candidates take at least 39 credit hours of approved course work (30 of which may be those taken for the MS degree). As required by University regulations, the course work must contain a minimum of fifteen hours in his/her major area, a minimum of nine hours in a minor area, and a minimum of six hours of work outside the department. Cross registered graduate level courses from other institutions are acceptable. The major area and minor area will be identified by the candidate's advisor and must be approved by the graduate committee.

• Have an overall grade point average of at least 3.00 in their course work.
• By the end of the second semester (not including summer) every PhD student must pass a General Comprehensive Exam. The purpose of this exam is to determine whether or not a student possesses the fundamental knowledge and skills to pursue PhD level research and course content. The topics cover Calculus, Differential Equations, Linear Algebra, Real Analysis, Probability, and Statistics. The exam is offered in August, January, and May. By the fourth semester (summer not included) every PhD student must pass two additional written Comprehensive Examinations. One exam will be from Category I and one from Category II below. The choices must be approved by the student's advisor and the graduate committee. In the event that a student has not satisfied these conditions within the time limit allowed, the student must petition the graduate committee in order to continue studies.
  • Category I: (Pure Math) Real Analysis, Complex Analysis, Sets and Topology, Numerical Analysis.
  • Category II: Matrix Theory and Computations, Partial Differential Equations and Boundary Value Problems, Ordinary Differential Equations, Probability and Measure Theory, or Statistics. Acquire at least six hours of seminar credit. A seminar is a course in which the student is expected to make presentations to the class. This is in addition to the minimum of 39 credit hours of approved course work in (i) above. One hour of seminar credit may be earned by either attending a regular scheduled seminar and making one presentation, or attending all colloquia for one semester and giving one presentation at a Department of Mathematics Seminar.
• Have made a formal presentation of a proposed thesis topic to his/her Thesis Committee (see part (vi)) within one year of passing their Comprehensive Exam (part iii). The topic must be acceptable to the committee.
• Write and defend (to their Thesis Committee) a dissertation which embodies the results of their original research. In association with this work, the student must obtain at least 21, but no more than 45, hours of thesis credit. The Thesis Committee consists of at least five Clarkson faculty members of whom at least one is from another department.
• Complete a total of 90 hours graduate credit. The satisfaction of these requirements will be certified by the Thesis Committee.
• Typical duration of the PhD program is 5-6 years.

• What Makes a Successful Candidate?
  Typical successful applicants have an undergraduate or a Master’s degree in mathematics, applied mathematics, statistics, or a related quantitative discipline. While the balance of topics in any student’s background may vary, we expect that applicants will have had an excellent foundation in undergraduate mathematics, including experience with proof-based courses, coding in at least one programming language such as MATLAB, Python, Julia, R, etc., and fluency in written and spoken English. Prior research experience is not a requirement, but it definitely helps in making a strong case for the student to be accepted.
   
• Dates & Deadlines
  Your application will be accepted at any time, although new students are accepted only for the Fall and Spring semesters. Please complete the application at least 2 months, and up to 10 months in advance of the start of the semester. Once an application file is submitted, the faculty review takes at least one month to complete.
   
• TA & RA Positions
  If you are additionally applying for a TA or RA position please see additional deadlines. Reviews for admission and for a TA or RA position are separate, with the TA/RA process significantly more competitive due to a very limited number of available spots. Past successful applicants to TA/RA positions have had significant undergraduate research experience (e.g. participating in semester-long or year-long research projects, potentially co-authoring a publication), and some experience in teaching, whether as a tutor for college-level courses or an undergraduate teaching assistant. In most such cases, recommendation letters and statements of purpose gave the committee a good understanding of the content of research/teaching experience, and the degree to which students were involved.
   
• Research Fit/Topics
  It is critical that the evaluation committee understands how specifically a student may fit in the research program at Clarkson; statements that say “I will do whatever it takes/work on whatever topic” are typically not helpful – instead, we encourage the applicants to describe a smaller set of research topics for which they believe they are well prepared and which may keep their interest for the next 5 years.
   
• No Minimum GPA/GRE Score Required
  There are no GPA, GRE, or other scales/cutoffs that we use to accept/disqualify applicants; rather, the committee evaluates holistically the set of skills and experiences applicants bring with them.

• Statement of Purpose. Statements of purpose give our Department the best understanding of why you want to join the program, in terms of your research goals and the Clarkson experience. Typical length is around 1 typed page, not to exceed 2 pages. While some applicants write in a literary style, this is not needed.
  At least one paragraph should be devoted to what research excites/interests you, and how it connects to research programs of our faculty. Think about who you might like to work with, and why Clarkson is a good fit for you as you write. The faculty names should also then be entered under the relevant question in the form you fill in during the application process. This paragraph is commonly the most useful part of the entire statement.
  Another paragraph should be devoted to highlighting anything in your background (education, work or life experience) that makes you exceptionally well-suited for graduate school. Additionally, if anything is unusual in your background, for example you changed schools mid-degree, have grades on your record that are inconsistent with academic excellence, or are trying to switch from another specialty to mathematics, please devote some space in the statement to explain it, highlighting it as a strength of yours or for explaining why it is not a weakness (anymore).
  In all that you write, write in terms specific to your interests/experience, rather than in general terms. For example, describing your research interest as “I can work on any problem given by the faculty” is not very useful, as it does not provide much information about how you are different from other applicants.
• Letters of Recommendation. Recommendation letters are crucial to a successful application. Ask individuals who can say something positive about your research, coursework, and other school-related activities. Try to get a diverse pool of letter writers, so that we can hear about the full breadth of your undergraduate/Master's experience. The letters should come primarily from academic faculty, commenting on your scholarly abilities and suitability for graduate studies. Non-academic recommenders, e.g., employment supervisors, typically do not carry as much weight unless the position is somehow related to your academic ambitions. Personal references from friends and family, commenting either on scholarly ability or character traits, are not useful and should be omitted.
• Curriculum Vitae. CV should summarize your academic preparation, with emphasis on any teaching and research experience.
• Transcripts. Please make sure that the scans are well organized and clearly legible. The Department does not maintain a list of necessary undergraduate courses, however, successful applicants will have been exposed to topics in calculus, matrix analysis and linear algebra, proof-based calculus, differential equations, and probability and statistics. 
• GRE (General). Optional for those with MS or BS degrees in mathematical sciences (mathematics, applied mathematics and statistics); for others it is required but waivers will be considered on a case by case basis. You may request a GRE waiver by emailing graduate@clarkson.edu after completing all other components of the application.
• English Proficiency Test. Knowledge of English is verified by completing a TOEFL, IELTS, or Duolingo English Test. If you are from US, Canada, UK, Ireland, Australia, New Zealand or any English-speaking Caribbean countries, or you have completed a undergraduate or graduate degree in the countries listed, you may request a waiver by e-mailing gradintl@clarkson.edu after completing the rest of your application.

There are no specifics for MS program applicants. If you already have a certain career path in mind, e.g., using your MS degree as a stepping stone to an eventual Ph.D. program, or trying to enter a specific industry, please elaborate in your statement of purpose.