Mathematics B.S.MSC.
All students must meet the Degree and University Requirements.
All students must meet the Catamount Core Curriculum Requirements.
All students must meet the College Requirements.
Mathematics Major
Mathematics permeates every aspect of our daily lives. In support of this, the mathematics curriculum is designed to provide a strong foundation for anyone who is interested in developing their ability to navigate our increasingly quantitative society. All students are introduced to the power and breadth of mathematics and to core ideas and techniques in the discipline. Courses that emphasize written and oral communication of quantitative information increase the value to the student of this mathematical knowledge.
The flexible curriculum enables each student to focus on a particular area of interest. This flexibility is especially important given the widely varying interests and career goals of our students. Students planning on a career in a technical field may choose to focus on courses in applied mathematics. Those planning on graduate school in mathematics or in a closely related field will benefit from the more advanced elective courses needed for graduate-level studies. Those interested in law, business, teaching, or other pursuits have the opportunity to freely sample from all areas according to their interests.
A Bachelor of Arts with a major in mathematics is offered and supervised by the College of Arts and Sciences (CAS). Students opting for this degree require an advisor from the Department of Mathematics and Statistics. Refer to the CAS section of this catalogue for more information.
Concentrations that provide suggested preparation for a student’s career plans are listed in the next section, along with the courses recommended for each concentration.
Regulations
Students pursuing the Bachelor of Science in Mathematical Sciences (Majoring in Mathematics) or the Bachelor of Science degree with a major in Data Science are subject to the Academic Standards in CEMS outlined in this catalogue.
Additional Regulations
No more than three grades of D, D+, or D– in 3000-level (or higher) mathematics (MATH) or statistics (STAT) courses may be used to satisfy “Core Curriculum” and “Major Courses” requirements.
A minimum of 120 credits is required. Students must satisfy all University requirements.
A. Core Curriculum
CEMS 1500 | CEMS First Year Seminar | 1 |
MATH 1234 | Calculus I ^{1} | 4 |
MATH 1248 | Calculus II | 4 |
MATH 2055 | Fundamentals of Mathematics | 3 |
MATH 2248 | Calculus III | 4 |
MATH 2522 | Applied Linear Algebra | 3 |
or MATH 2544 | Linear Algebra | |
MATH 3468 | Anyl in Several Real Vars I | 3 |
MATH 3551 | Abstract Algebra I | 3 |
CS 1210 | Computer Programming I | 3 |
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A student with a MATH 1234 waiver can use it to fulfill the requirement of MATH 1234 in the Core Curriculum. However, at least three extra credits of mathematics numbered above MATH 1242 must be added to the Major Courses requirement.
B. Major Courses
A minimum of twenty-one additional credits in mathematics, statistics, or computer science courses numbered 2000-level or above, excluding MATH 2111 and MATH 2180. At least twelve credits must be in courses numbered 3000-level or above and no more than twelve credits can be taken in computer science.
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 in the Recommendations for Major Courses section below, or it might be another area suggested by the student.
C. Allied Field Courses
Twenty-four credits selected from the following Allied Fields:
- Physical Sciences
- Biological Sciences
- Medical Sciences
- Engineering
- Computer Science (CS 2100 or higher)
- Agricultural Sciences
- Business Administration
- Psychology
- Economics
- Environmental Sciences/Studies
- Natural Resources
Students, in consultation with their advisors, must plan a sequence of Allied Field courses consistent with their professional and personal goals. Students interested in pursuing intensive studies in an area not specifically listed are encouraged to plan a program with their advisor and submit it to the appropriate departmental committee for review and approval. The requirements are as follows:
Twenty-four credits selected from the above list of Allied Fields, including at least one laboratory experience in science or engineering. Of these twenty-four credits, at least six must be in courses numbered 2000-level or above, and at least six must be taken in fields 1 to 5. Courses used to satisfy requirement B above may not be used to satisfy this requirement.
D. Humanities and Social Science Courses
(Courses used to satisfy requirement C above may not be used to satisfy this requirement.)
Twenty-four credits of courses selected from categories I, II, and III listed below. These twenty-four credits must be distributed over at least two categories, and at least six credits must be taken in each of the two categories chosen.
Category I: Language and Literature
American Sign Language (ASL); Arabic (ARBC); Chinese (CHIN); Classics (CLAS); English (ENGS); English for Speakers of Other Languages (ESOL); Foreign Language (LANG); French (FREN); German (GERM); Greek (GRK); Hebrew (HEBR); Italian (ITAL); Japanese (JAPN); Latin (LAT); Linguistics (LING); Portuguese (PORT); Russian (RUSS); Spanish (SPAN); World Literature (WLIT).
Category II: Humanities and Fine Arts
Art History (ARTH); Art Studio (ARTS); Dance (DNCE); Film & Television Studies (FTS); Humanities (HUMN); Music (MU); Philosophy (PHIL); Religion (REL); Speech (SPCH); Theatre (THE).
Category III: Social Sciences
Anthropology (ANTH); Communication Sciences & Disorders (CSD); Community Development & Applied Economics (CDAE); Critical Race & Ethnic Studies (CRES); Economics (EC); Environmental Studies (ENVS); Gender, Sexuality & Women's Studies (GSWS); Geography (GEOG); Global & Regional Studies (GRS); History (HST); Holocaust Studies (HS); Human Development & Family Studies (HDFS); Political Science (POLS); Psychological Science (PSYS); Sociology (SOC); Vermont Studies (VS).
Recommendations for Major Courses
Students should discuss an area of specialization with their advisor. This is especially important for students interested in graduate school in mathematics or a related field (including those interested in the Accelerated Masters Program). Below are listed several areas of specialization.
Given the wide variety of paths after graduation pursued by students graduating with a B.S.MSC. in Mathematics, the department does not list specific courses which must be taken in order to satisfy the Professional Development Electives requirement of the CEMS Core Curriculum. However, students should work with their advisor to find appropriate courses which are consistent with their future career goals.
1. 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 2468 | Real Anlys in One Variable | 3 |
MATH 2551 | Groups and Rings | 3 |
MATH 2678 | Basic Combinatorial Theory | 3 |
MATH 3468 | Anyl in Several Real Vars I ^{1} | 3 |
MATH 3472 | Anyl Several Real Vrbes II | 3 |
MATH 3456 | Complex Analysis | 3 |
MATH 3551 | Abstract Algebra I ^{1} | 3 |
MATH 3555 | Abstract Algebra II | 3 |
MATH 4344 | Topology | 3 |
MATH 3517 | Elementary Number Theory | 3 |
MATH 5360 | Foundations of Geometry | 3 |
MATH 5678 | Combinatorial Graph Theory | 3 |
MATH 6441 | Theory of Func of Complex Var | 3 |
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These courses are central to the given area and should be taken as early as is feasible.
2. 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 a problem and allows predictions to be made about an 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 3230 | Ordinary Diffrntl Equation ^{1} | 3 |
MATH 3737 | Intro to Numerical Analysis ^{1} | 3 |
MATH 5678 | Combinatorial Graph Theory | 3 |
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These courses are central to the given area and should be taken as early as is feasible.
3. 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 the solution to the physical problem of interest. Courses in this area include the following:
MATH 2678 | Basic Combinatorial Theory | 3 |
MATH 3230 | Ordinary Diffrntl Equation | 3 |
MATH 3737 | Intro to Numerical Analysis ^{1} | 3 |
MATH 4344 | Topology | 3 |
STAT 3010 | Stat Computing&Data Anlysis | 3 |
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These courses are central to the given area and should be taken as early as is feasible.
4. 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 2678 | Basic Combinatorial Theory | 3 |
MATH 5678 | Combinatorial Graph Theory | 3 |
CS 3240 | Algorithm Design & Analysis ^{1} | 3 |
CS 3430 | Theory of Computation | 3 |
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These courses are central to the given area and should be taken as early as is feasible.
5. 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 2678 | Basic Combinatorial Theory | 3 |
MATH 3230 | Ordinary Diffrntl Equation | 3 |
MATH 5678 | Combinatorial Graph Theory | 3 |
STAT 1410 | Basic Statistical Methods 1 | 3 |
or STAT 2430 | Statistics for Engineering | |
STAT 2510 | Applied Probability | 3 |
STAT 3240 | Stats for Qualty&Productvty | 3 |
STAT 3410 | Statistical Inference | 3 |
6. 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:
- Preliminary Education Requirements, PE;
- the Fundamentals of Actuarial Practice Course, FAP; and
- 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.
The Preliminary Education Requirements consist of
- prerequisites
- subjects to be validated by educational experience (VEE), and
- 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 1234 | Calculus I | 4 |
MATH 1248 | Calculus II | 4 |
MATH 2248 | Calculus III | 4 |
LINEAR ALGEBRA | ||
MATH 2544 | Linear Algebra | 3 |
INTRODUCTORY ACCOUNTING | ||
BUS 1610 | Financial Accounting | 3 |
BUS 2620 | Managerial Accounting | 3 |
MATHEMATICAL STATISTICS | ||
STAT 5610 | Statistical Theory | 3 |
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 | ||
ECON 1400 | Principles of Macroeconomics | 3 |
ECON 1450 | Principles of Microeconomics | 3 |
CORPORATE FINANCE | ||
BUS 2800 | Managerial Finance | 3 |
BUS 2810 | Intermediate Financial Mgmt | 3 |
APPLIED STATISTICAL METHODS | ||
STAT 3210 | Advanced Statistical Methods | 3 |
Candidates will demonstrate proficiency in these subjects by submitting transcripts.
Preliminary Examinations
EXAM P - PROBABILITY | ||
STAT 2510 | Applied Probability | 3 |
STAT 5510 | Probability Theory | 3 |
EXAM FM - MATHEMATICS OF FINANCE | ||
BUS 2800 | Managerial Finance | 3 |
BUS 2810 | Intermediate Financial Mgmt | 3 |
Other applicable departmental courses include:
STAT 2990 | Special Topics | 1-18 |
STAT 3010 | Stat Computing&Data Anlysis | 3 |
STAT 5290 | Survivl/Logistic Regression | 3 |
STAT 5350 | Categorical Data Analysis | 3 |
MATH 2678 | Basic Combinatorial Theory | 3 |
7. 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 inferences can be drawn from real data in any of the social or physical sciences. Courses in this area include the following:
MATH 3468 | Anyl in Several Real Vars I | 3 |
MATH 3472 | Anyl Several Real Vrbes II | 3 |
STAT 2510 | Applied Probability | 3 |
STAT 3410 | Statistical Inference ^{1} | 3 |
STAT 5610 | Statistical Theory | 3 |
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These courses are central to the given area and should be taken as early as is feasible.
Recommendations for Allied Field Courses
Students should discuss Allied Field courses with their advisor and choose ones that 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 2000-level 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 (ECON 1400 and ECON 1450) in their choice of Humanities and Social Sciences courses, and to include business administration (BUS 1610 and BUS 2620) in their choice of Allied Field courses. Those wishing to minor in business administration should contact the School of Business Administration and also take BUS 2700 and two other courses chosen from business administration Allied Field courses.
Double Major in Mathematics and Statistics
Students may earn a double major in mathematics and statistics by meeting the requirements of the statistics major and earning an additional fifteen credits in mathematics, to include:
MATH 2055 | Fundamentals of Mathematics | 3 |
Choose two of the following: | 6 | |
MATH 3230 | Ordinary Diffrntl Equation | 3 |
MATH 3737 | Intro to Numerical Analysis | 3 |
MATH 3468 | Anyl in Several Real Vars I | 3 |
MATH 3551 | Abstract Algebra I | 3 |
Note: Students pursuing the double major in mathematics and statistics must earn a total of 120 credits. The above outlined courses must be additional to the courses defined for the stat major (core, major, allied field and HSS).