Master of Science in Mathmatics (MSM)

General

All pertinent regulations set forth in the Graduate Studies Bulletin and the Bulletin of the College of Natural Sciences and Mathematics must be observed. The student must consult the departmental Director of Graduate Studies prior to beginning his/her graduate program so that proper records may be established within the department. It is the student's responsibility to be informed about current degree requirements. It is the joint responsibility of the student and the student's advisor to maintain communications and to track the student's progress toward meeting those requirements. The departmental Director of Graduate Studies will serve as interim advisor for the purposes of initiating a course of study until an advisor is selected.

Prerequisites

The prerequisite for admission to the Master's Degree program is the equivalent of an undergraduate major in mathematics as defined at this University. Students not meeting this requirement may, at the discretion of the Chairman of the Department, be admitted to the program conditionally until the deficiency is removed. Courses taken to remove deficiencies may not be counted as part of the Master's Degree program. For students uncertain of their preparation, the following courses (some of which may count for elective credit) are strongly recommended: MATH 4331-4332 (for any Analysis courses); MATH 4333 (for Algebra); MATH 4337 (for Topology); MATH 4377-4378 (for all advanced subjects).

MSM Core Courses

At least 15 hours from the following Master's Degree Core Courses are to be completed, with a one-year sequence in two of the following three areas.

• Area I
  Functions of a Real Variable (MATH 6320;6321)
  Complex Analysis (MATH 6322;6323)
  Functional Analysis (MATH 7320;7321)
  
• Area II
  Modern Algebra (MATH 6302;6303)
  Algebraic Topology (MATH 6340;6341)
  Point Set Topology (MATH 6342;6343)
  
• Area III
  Differential Equations (MATH 6324;6325)
  Partial Differential Equations (MATH 6326;6327)
  Numerical Analysis (MATH 6370;6371)
  Probability Models and Mathematical Statistics (MATH 6382;6383)

Options

There are two options available for obtaining an M.S. in Mathematics:

• Plan I - Thesis
  A minimum of 30 semester hours is required. These hours include 6 semester hours of Master's Thesis credit and a minimum of 24 semester hours in course work. These 24 semester hours must consist of 18 semester hours of courses in mathematics at the 6000 level or above and 6 semester hours of courses in mathematics at the 4000 level or above. No more than 3 of the 24 hours may be in special problems.The Master's Thesis is to be accomplished by agreement between them student and the student's advisor. After all course work and the thesis are completed and all other degree requirements are satisfied, an oral and/or written examination over the candidate's background will be conducted by the thesis committee. Questions for this examination may be drawn from the student's courses and thesis. Once the thesis has been accepted by the committee, a final corrected version must be submitted to the College by the student.
  
  
• Plan II - Tutorial
  A minimum of 36 semester hours is required. These hours must include 6 semester hours in Master's Tutorial credit and a minimum of 30 semester hours in other course work. Of these 30 hours at least 21 must be in regularly scheduled mathematics courses at the 6000 level or above. Not more than 6 of the 30 may be in special problems. With departmental approval, up to 9 hours of the 30 may be at the 4000 level in mathematics. With departmental approval, 6 semester hours may be taken in a minor in a related field (in courses at the 4000 level or above).The Master's Tutorial is to be accomplished by agreement between the student and the student's advisor. If the tutorial consists of a project, it should be as demanding as a thesis, however, a formal defense and submission to the College are not required. The tutorial requirement may be satisfied by participating in regularly scheduled classes, if this is the decision of the student and advisor. The advisor is required to place on file in the department office a statement which summarizes the contribution of the student in the Master's Tutorial.

Master of Science in Applied Mathmatics (MSAM)

Introduction

The Department of Mathematics of the University of Houston offers a Master of Science in Applied Mathematics. The intent of this program is to provide students with training in mathematics appropriate for many professional mathematical positions in industry. Recent graduates are employed in the aerospace, engineering, energy, actuarial and financial industries, as well as in biostatistics, and as teachers in high schools and community colleges.

The UH faculty in applied mathematics and computational sciences is internationally recognized for research achievement and teaching. We have excellent computing resources and the university library has an outstanding mathematics collection.

Students take two one-year sequences of core courses chosen from the areas of mathematical analysis, numerical analysis, applied and computational mathematics, and probability and statistics. They also take electives and complete a tutorial project. The tutorial typically involves studying and writing a report on a specific topic involving the application of mathematics, with the guidance of a faculty member.

The mathematics department has a network of terminals and workstations available for use by graduate students. Students who do not already have experience with scientific computing and/or programming languages will be able to learn the necessary topics through courses or tutorials.

For the convenience of students, core courses for the program are generally taught between 4pm and 7pm on Mondays through Thursdays. More specific details on courses are given below.

Admission to the Program

To be admitted to the program, a student must have completed a baccalaureate degree with a 3.0 GPA over the last 60 hours of course work and have a good background in mathematics. A student need not have majored in mathematics to be admitted. It is expected, however, that the student has completed at least 9 hours of mathematics at the junior or senior level, preferably in courses such as advanced linear algebra, analysis, differential equations, and probability and statistics. When these requirements are not met, students may be admitted on a conditional basis and have the opportunity to acquire the necessary background.

Program Requirements and Electives

All pertinent regulations set forth in the Graduate Studies Bulletin and the Bulletin of the College of Natural Sciences and Mathematics must be observed. Currently the requirements for the M.S. degree in Applied Mathematics are that a student complete 30 credit hours of courses at the University of Houston with an average grade of B (that is a 3.0 GPA) and no more than 3 grades below C+. A student must:

• Successfully complete (C or higher) two out the following four basic course sequences:
  MATH 6360;6361: Applicable Analysis,
  MATH 6370;6371: Numerical Analysis,
  MATH 6377;6378: Basic Tools for the Applied Mathematician; Basic Scientific Computing(see CMO below),
  MATH 6382;6383: Probability and Statistics,
  MATH 6366, 6367: Optimization.
  
• Successfully complete another 6 credit hours of courses at the 6000 or 7000 level in the mathematics department.
  
• Pass another 6 hours of elective course work approved by the Director of Graduate Studies. The elective courses need not be taken in the Mathematics department and may include some senior (4000) level undergraduate courses.
  
• Complete a tutorial project under the supervision of a faculty member. Students working on this project sign up for MATH 6315 and 7315: Master's Tutorial.

Within these requirements, students are encouraged to pursue their own interests. In particular, the subject matter of the tutorial project is often related to a student's professional work. It is usually less formal than a thesis but it is expected that the topic chosen will be treated thoroughly and in depth. To pass Math 7315, a student writes a project report which must be approved by his/her supervisor and a summary of the project must be provided to the Director of Graduates Studies.

The Department of Mathematics is developing a number of options within the MSAM. So far we have two options: the Computational Mathematics Option (CMO), and the Financial Mathematics Option (FMO).