Mathematical Sciences

Summary of the Mathematical Sciences Track

The Department of Mathematics and the Program in Applied Mathematics jointly developed the Professional Master¹s Degree in Mathematical Sciences in an effort to capitalize on the world-renown resources, facilities, and faculty of both units. The degree is interdisciplinary by nature and is intended specifically for individuals intending to make careers in industry, commerce, and the public sector.

Guiding Principles

The degree program has been designed to give students both depth and breadth in the mathematical sciences, and at the same time expose you to research and training experiences that will equip you for a variety of jobs in non-academic settings. It should be emphasized that the Professional Master's Degree in Mathematical Sciences is a true graduate level degree and students are expected, and required, to take on the challenge of advanced graduate level courses in the mathematical sciences.

Courses of study are designed according to the following principles:

• Flexibility: Close personal advising of each student to design, within broad guidelines, the best program of study to suit your academic and professional needs and interests.

• Depth: The course-work requirements will ensure that the student has a reasonably deep knowledge of one or more areas of mathematics.

• Breadth: The program of study will consist of a coherent collection of disciplinary courses, and a minimum of two out-of-discipline courses to ensure cross-disciplinary breadth. Overall, the chosen program should have a thematic basis reflecting the student's interests and intended career goals.

• Computing Skills: Today's employers expect and require a high level of computational skills, and the program of study must ensure that graduates are able to meet the computational challenges they are presented with.

• Communication Skills: Good written and verbal communication are essential. Students must be able to finish a project on time and present the results both orally and in writing.

• Professional Skills: In addition to traditional academic activities, the degree program expands the student's professional skills by requiring an internship, the taking of business courses, and participation in other cohort experiences.

The degree is made up of at least 33 units consisting of course work, chosen according the guiding principles, a Master's project or thesis, and a colloquium series. In addition students are required to undertake a summer internship or an equivalent training experience.

Course work is selected as follows:

• Disciplinary courses: Typically five or six mathematics courses, consisting of:
  1. Depth requirement: Students are expected to complete a two semester sequence of one of the designated core courses and (at least) one semester of another. Illustrative examples of how to organize this are given in the sample courses of study below. Core courses include:
     1. Algebra (Math 511a,b)

     2. Analysis (Math 523a,b) or Principles of Analysis (Math 527 a, b)*

     3. Numerical Analysis (Math 575 a, b)

     4. Methods of Applied Mathematics (Math 583a,b)

     5. Probability Theory (Math 563 a, b)**

     6. Stochastic Processes (Math 565a, b)**

     7. Theoretical Statistics (Math 567a, b)**

     * The two analysis sequences have a slightly different emphasis. Math 523, which is designed for students in the Mathematics PhD program, has a slightly more theoretical flavor whereas Math 527, which is designed for students in the Applied Mathematics PhD program, is slightly more applications oriented.

     ** These courses are usually only offered on an alternate year basis and students intending to take any of these courses must take this into account when designing their program of study (which is typically 2 years).

     Students should note that course work should consist of 500 level (i.e. graduate) courses. A number of courses listed in the Graduate Catalogue are "dual-listed", meaning that they are offered as joint 400/500 courses. The use of such courses in designing the disciplinary part of the program (i.e. the mathematics courses) is strictly limited and requires the approval of the student's advisor. Cases where such dual listed courses are permitted, e.g. Math 543 (Theory of Graphs and Networks), are usually a consequence of the equivalent graduate level courses having extensive prerequisites.

  2. Breadth requirement: three or four more thematically related mathematics courses, or approved equivalents from other departments. Students can explore various mathematical themes including:

     • Algebra

     • Coding Theory

     • Graph Theory

     • Combinatorics

     • Probability

     • Computer Science

     • Numerical Analysis & Modeling

     • Queuing Theory

     • Numerical PDEs

     • Stochastic Processes

     • Real Analysis

     • Statistics

     • Regression & Multivariate Analysis

• Cross-disciplinary courses: Typically two courses from outside Mathematics, chosen with considerable flexibility, but thematically related to the choice of disciplinary courses. Some of the units students can chose coursework from include:

  • Physics

  • Computer Science

  • Molecular and Cellular Biology

  • Chemistry

  • Geosciences

  • College of Engineering and Mines

  • College of Agriculture and Life Sciences

  • College of Science

  • Optical Sciences Center

• Research Tutorial Group (Math 586): This one unit course is required for most incoming students.

• Computing courses: Students are expected to have a high level of computational proficiency and will be expected to take the courses necessary to achieve this.

• Business courses: Students are required to take at least one of the two business courses (B AD 510: Business Fundamentals for Scientists and MIS 578: Project Management) especially designed for the Professional Master's degrees by the Eller College of Management at the University of Arizona. Students with no business background normally take the B AD 510 course first and are encouraged (but not required) to take the more advanced MIS 578 course.

• Industrial Colloquium Series: Students are required to attend and participate in a special weekly colloquium series with students from the other Professional Master's Degree Programs to hear and meet invited speakers.

• Internship: An internship in industry, a national laboratory, or some other setting outside the University during the first or second summer, is an essential part of the degree. Alternatives to traditional internships will be designed for students who are already employed in industry.

• Thesis/Final Project: Either a 3-unit project or a 6-unit MS thesis: in either case students are required to complete the project in a timely fashion and give both an oral presentation and a written thesis/project document.

• Graduation requirements: The degree has the attractive feature of not requiring a written qualifying examination. However students must fulfil minimum GPA requirements. The Graduate College at the University of Arizona currently only allows the award of A,B,C, D (but not plus/minus) grades to graduate students. Students in the Professional Master's Degree Program in the Mathematical sciences must have a GPA of better than 3.0, both cumulatively and for their mathematics courses. The Graduate College does have a grade replacement option and students may, with instructor and Program director approval, retake a course to improve their grade. If a student's GPA falls below 3.0 they are put on academic probation by the Graduate College. Students with two semesters of academic probation are removed from their degree program

Sample Courses of Study

Below are four examples of the package of courses that might be taken by a student whose interests lie in the directions of: cryptography, numerical analysis and modeling, probability and stochastic processes, and statistics.

• Cryptography

  Math 511a,b - Algebra

  Math 563a - Probability*

  Math 539 - Coding Theory

  Math 543 - Graph Theory

  Math 547 - Combinatorics

  Two courses from Computer Science or Management Information Science

• Numerical Analysis and Modeling

  Math 575a,b - Numerical Analysis

  Math 583a - Methods of Applied Mathematics

  Math 585 - Modeling, or Math 697B - Applied Mathematics Laboratory

  Math 576a,b - Numerical Partial Differential equations , or Math 553A - Partial Differential equations (theory)

  Math 697a - Computational Science

  Two courses from Aeronautical and Mechanical Engineering

• Probability and Stochastic Processes

  Math 523a,b or Math 527a,b - Real Analysis

  Math 547 - Combinatorics

  Math 563a (b) - Probability *

  Math 566 - Theory of Statistics, or Math 561 - Regression and Multivariate Analysis

  Math 568 - Stochastic Processes

  Two courses from Systems and Industrial Engineering or Management Information Science, e.g. Queuing Theory

• Statistics

  Math 567a,b - Theoretical Statistics*

  Math 563a - Probability*

  Math 561 - Regression and Multivariate Analysis

  Math 562 - Time Series Analysis

  Math 571 - Design of Experiments

  Two courses in Bioinformatics and courses in the use of standard statistical packages

Career Opportunities

Combining a solid and broad mathematics knowledge base with high level computational expertise and communication skills provides the necessary tools for rewarding careers in many areas of applications-orientated mathematics. The Professional Master's Degree in Mathematical Sciences helps students build careers incorporating scientific computing and mathematical modeling applicable to fields as diverse as aerodynamics, fluid mechanics, atmospheric and meteorological sciences, bioinformatics, systems engineering, finance, and cryptography.