# University of Vermont

## 2011-12 Online Catalogue

### Mathematics (Bachelor of Science)

#### Overview

The mathematics curriculum is quite flexible. It is designed to provide a sound basic training in mathematics that allows a student to experience the broad sweep of mathematical ideas and techniques, to utilize the computer in mathematics, and to develop an area of special interest in the mathematical sciences.

In addition to the Bachelor of Science degree described here, the Department of Mathematics and Statistics also offers a Bachelor of Arts degree in the College of Arts and Sciences. A faculty advisor from Mathematics will assist students in determining which degree program best suits their individual needs and plans. Some of the career plans for which a well-designed major in mathematics can provide ideal preparation are highlighted below.

#### General Requirements

- Requirements for All Undergraduate Degree Students
- Mathematics and Statistics Requirements for the Bachelor of Science

#### Specific Requirements

#### Recommendations for Major Courses

In consultation with their advisor, students should choose an area of interest within the mathematics major and plan a coherent program that addresses their interests in mathematics and its applications. This area might be one of those listed below, or it might be another area suggested by the student. As a guide, students interested in one of the areas would typically take at least three courses in that area, including all of the courses marked with an asterisk (*). In addition, students should take courses from at least two other areas. Because of its centrality in mathematics, students should make sure that they take at least one course listed under Classical Mathematics. In following these recommendations, a course listed in more than one area is meant to be counted only once.

##### Classical Mathematics

Classical mathematics encompasses those areas having their roots in the great traditions of mathematical thought, such as geometry and topology, mathematical analysis, algebra and number theory, and discrete mathematics. Courses in this area include the following: MATH 141, MATH 151, MATH 173, MATH 236, MATH 240, MATH 241*, MATH 242, MATH 251*, MATH 252, MATH 255, MATH 257, MATH 260, MATH 264, MATH 273, MATH 331, MATH 353.

##### Applied Mathematics

Applied Mathematics involves the use of mathematical methods to investigate problems originating in the physical, biological, and social sciences, and engineering. Mathematical modeling, coupled with the development of mathematical and computational solution techniques, illuminates mechanisms which govern the problem and allows predictions to be made about the actual physical situation. Current research interests of the faculty include biomedical mathematics, fluid mechanics and hydrodynamic stability, asymptotics, and singular perturbation theory. Courses in this area include the following: MATH 230*, MATH 236, MATH 237*, MATH 238, MATH 240, MATH 272, MATH 273, MATH 274.

##### Computational Mathematics

Computational mathematics involves both the development of new computational techniques and the innovative modification and application of existing computational strategies to new contexts where they have not been previously employed. Intensive computation is central to the solution of many problems in areas such as applied mathematics, number theory, engineering, and the physical, biological and natural sciences. Computational mathematics is often interdisciplinary in nature, with algorithm development and implementation forming a bridge between underlying mathematical results and solution of the physical problem of interest. Courses in this area include the following: MATH 173, MATH 230, MATH 237*, MATH 238, MATH 274, STAT 201.

##### Theory of Computing

The mathematical theory of computing deals with the mathematical underpinnings allowing effective use of the computer as a tool in problem solving. Aspects of the theory of computing include: designing parallel computing strategies (graph theory), analyzing strengths and effectiveness of competing algorithms (analysis of algorithms), examining conditions which ensure that a problem can be solved by computational means (automata theory and computability), and rigorous analysis of run times (complexity theory). Courses in this area include the following: MATH 173, MATH 223, MATH 224*, MATH 243, MATH 273, MATH 325, CS 346, CS 353.

##### Mathematics of Management

Mathematics of Management involves the quantitative description and study of problems particularly concerned with the making of decisions in an organization. Problems are usually encountered in business, government, service industries, etc., and typically involve the allocation of resources, inventory control, product transportation, traffic control, assignment of personnel, and investment diversification. Courses in this area include the following: MATH 173, MATH 221*, MATH 222, MATH 230, MATH 236, MATH 273, STAT 141 or STAT 211, STAT 151 or MATH 207, STAT 224, STAT 241, STAT 253.

##### Actuarial Mathematics

Actuaries use quantitative skills to address a variety of risk related problems within financial environments. A unique feature of the actuarial profession is that a considerable amount of the formal training is typically completed after graduation "on-the-job."

The Society of Actuaries is an international organization that regulates education and advancement within the profession. Candidates may earn designation as an Associate of the Society of Actuaries (ASA) by satisfying three general requirements. These are: (1)

The*Preliminary Education Requirements,*PE; (2)*the Fundamentals of Actuarial Practice Course,*FAP; and (3) the*Associateship Professionalism Course,*APC. The multiple component FAP is based on an e-learning format, and can be pursued independently. After completing the PE and at least one of the FAP components, candidates are eligible to register for the one-half day APC.*Preliminary Education Requirements*consist of (1) prerequisites (2) subjects to be validated by educational experience (VEE), and (3) four examinations. While at the university, students can satisfy the prerequisites, the VEE courses, and the first two preliminary examinations. The following courses are recommended as preparation for the specific requirements.**Prerequisites.**Calculus MATH 21,MATH 222, and MATH 121, Linear algebra MATH 124, Introductory accounting (BSAD 060, BSAD 061), Business law (BSAD 017, BSAD 018), and Mathematical statistics (STAT 261, STAT 262). These are topics that will assist candidates in their exam progress and work life but will not be directly tested or validated.**Subjects Validated by Educational Experience.**Economics (EC 011,EC 012), Corporate Finance ((BSAD 180, BSAD 181), and Applied Statistical Methods (STAT 221, STAT 253). Candidates will demonstrate proficiency in these subjects by submitting transcripts.**Preliminary Examinations.**Exam P - Probability (STAT 151, STAT 251), Exam FM - Mathematics of Finance (BSAD 180,BSAD 181). Other applicable departmental courses include: Statistics for Business STAT 195, Statistical Analysis via Computers STAT 201, Applied Regression Analysis STAT 225, Survival Analysis STAT 229, Categorical Data Analysis STAT 235, Nonparametric methods STAT 237, Combinatorics MATH 173, and Operations Research (MATH 221, MATH 222).
##### Probability and Statistical Theory

Probabilistic reasoning is often a critical component of practical mathematical analysis or risk analysis and can usefully extend classical deterministic analysis to provide stochastic models. It also provides a basis for statistical theory, which is concerned with how inference can be drawn from real data in any of the social or physical sciences. Courses in this area include the following: MATH 222, MATH 241, MATH 242, (STAT 151 or MATH 207), STAT 241, STAT 252a, STAT 252b, STAT 261, STAT 262, STAT 270.

#### Recommendations for Allied Field Courses

Students should discuss Allied Field courses with their advisor and choose ones which complement their mathematical interests. Students with certain mathematical interests are advised to emphasize an appropriate Allied Field as indicated below and take at least six credits in courses numbered 100 or above in that field.

##### Applied Mathematics:

Allied Field (1), (2), (3), (4), (6) or (9).

##### Computational Mathematics:

Allied Field (4) or (5).

##### Mathematics of Management:

Allied Field (7). Students interested in Mathematics of Management are advised to include Economics EC 011 and EC 012 in their choice of Humanities and Social Sciences courses, and to include Business Administration BSAD 060 and BSAD 061 in their choice of Allied Field courses. Those wishing to minor in Business Administration should contact the School of Business Administration and also take Business Administration BSAD 173 and two other courses chosen from Business Administration Field Courses.

#### Affiliations

- Colleges and Schools: College of Engineering and Mathematical Sciences. College of Arts and Sciences.
- Departments and Programs: Mathematics and Statistics Department.