## I. INTRODUCTION

We would like to congratulate you on your acceptance to the University of Vermont and on your decision to consider mathematics or statistics as your major. The Department of Mathematics & Statistics is pleased to welcome you to the University and invites you to join the mathematical community of UVM. All of us are aware of the growing importance of the mathematical sciences in our technological society and many of our courses are designed to explore the role of mathematics and statistics in today's world. We are looking forward with excitement and enthusiasm to sharing classroom experiences which reveal the contributions of mathematics and statistics to society. A major in mathematics or statistics represents one of the most flexible and valuable options available at UVM. The degree requirements are encompassing but not restrictive, providing ample opportunity for students to explore other areas of interest. Furthermore, individuals trained in the mathematical sciences have many opportunities to use their knowledge. Mathematics and statistics majors are equally well-prepared for jobs in business, industry, government, or teaching and for advanced study in graduate school. For example, UVM mathematics and statistics graduates are often employed in the computer, information, and communications industries, in engineering, in the insurance business, in government agencies, and in a variety of other occupations. Many attend graduate school in the mathematical sciences, business, the physical sciences, social sciences, medicine, dentistry, or law.

## Orientation

The Department Office and many faculty offices are housed in the Henry Marcus Lord House at 16 Colchester Avenue on the north edge of the main campus, opposite Ira Allen Chapel and the Campus Center Theater. Other departmental buildings are Mansfield House and 12 Colchester Avenue (the Pearl House). Most mathematics and statistics classes are held in Votey Hall, Perkins Building, Waterman Building, Torrey Hall, and Lafayette Hall. Other important buildings are the Billings Student Center, the Bailey-Howe Library and Hills Building, where some Statistics faculty participate in the College of Medicine Biometry Facility and in the College of Agriculture and Life Sciences Statistical Services Unit. The College of Engineering and Mathematical Sciences (CEMS) computing facilities are located in Votey Hall. The Mathematics & Statistics Department offers a major in (1) the College of Engineering and Mathematical Sciences (leading to a B.S. degree in mathematics); and (2) the College of Arts and Sciences (CAS) (leading to a B.A. degree in mathematics). Between 20 and 50 undergraduate degrees are typically awarded each year in mathematics and statistics. There are about 30 full-time faculty members in the Department, several part-time instructors and from 25 to 35 graduate students. A full-time faculty member will be assigned as your advisor to assist you in choosing courses suited to your goals and interests. You are encouraged to see your advisor often – and regard this person as a valuable and essential resource.

## Who Majors or Minors in Mathematics?

Certainly mathematics majors share a common interest in mathematics, but their other academic interests may vary significantly. The applications of mathematics intersect nearly every other discipline on campus, so the "other" interests of mathematics majors and minors vary greatly. This diversity enhances involvement in the university community and offers broad job opportunities upon graduation. More than any other major or minor at UVM, a mathematics major or minor makes you an attractive employee in many fields. If you find mathematics interesting and wish to study it further, regardless of your career plans, you are encouraged to consider majoring or minoring in mathematics. The mathematics curriculum for both Math major and minor is quite flexible. It is designed to provide a sound basic training in the mathematical sciences, which allows you 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. Many majors at UVM are well on their way to having a minor in Mathematics while fulfilling their major requirement. For example, Students who major in Engineering and Computer Science are usually just a couple of 100-level Math courses away from a Math minor at the end of their sophomore year. Mathematics majors a n d m i n o r s gain lasting skills in computational ability and logical reasoning. Statistics majors gain lasting skills in obtaining information and interpreting data for decision making. Those seeking useful and marketable life skills should certainly consider these majors.

## Who Majors or Minors in Statistics?

Students receiving a B. S. in the College of Engineering and Mathematical Sciences may elect statistics as their major. In addition, students receiving a B. A. degree in the College of Arts and Sciences may concentrate in statistics as a part of their mathematics major. Statistics is a mathematical science extensively used in a wide variety of fields. Indeed, every discipline that gathers and interprets data uses statistical concepts and procedures to understand the information implicit in their data base. Statisticians become involved in efforts to solve real world problems by designing surveys and experimental plans, constructing and interpreting descriptive statistics, developing and applying statistical inference procedures, and developing and investigating random models or computer simulations. To investigate new statistical procedures requires knowledge of mathematics and computing as well as statistical theory. To apply concepts and procedures effectively also calls for an understanding of the field of application.

The curriculum is designed for students who plan to enter business, industry, or government as statisticians; to become professional actuaries; or to continue to graduate school in statistics and biostatistics or another field where a quantitative ability can prove valuable (business, operations research, public health, psychology, etc.). The courses and curricula are administered through the Statistics Program Steering Committee, which includes faculty from Statistics, the College of Medicine Biometry Facility, Psychology, Natural Resources, and the Agricultural Experiment Station. Students are encouraged to undertake special projects to gain experience in data analysis, design, and statistical computing. Also, experience can be gained with local industry and other organizations for those interested in such areas as quality control, industrial statistics, survey and market research, or forecasting

## II. GETTING STARTED

As you embark upon a major in mathematics or statistics, you should keep in mind the important principle that there is no substitute for thoughtful planning. As Louis Pasteur once wrote, "fortune favors the prepared mind." In the current context, that adage translates into a long-range schedule of courses, planned by you and your advisor, that takes into account your background, experience, preferences, and expectations in selecting mathematics or statistics as a major. Of course, such a schedule will undoubtedly change as time passes, as you gain experience in the major, and as your exposure to different areas of the mathematical or statistical landscape shapes your vision for the future. Nonetheless, it is important to have a plan and to start out with a focused approach.

In the pages that follow we will discuss some of the typical questions that may arise in deciding what courses to take, and we will provide information that may be helpful in making those decisions. Please remember that this written material is informational, and is not a substitute for personalized course planning with your advisor. The section below on advising will discuss in more detail the relationship between you and your advisor. For now, suffice it to say that the goal of advising is to ensure that you have an enriching and beneficial educational experience. Your advisor is a person you can count on for information and guidance at any time.

## Where to Begin: Calculus

The calculus sequence consists of three courses, Math 21, 22, and 121, taken in this order. While Math 21 would be taken by most students in their first semester at UVM, other students, depending upon their secondary school background in mathematics, may choose to bypass this course . If you have not taken calculus in high school, then quite likely you will start calculus with the first course in the sequence, Math 21. However, if you have been exposed to calculus in high school, where to start in the sequence will depend substantially on the quality and quantity of your high school calculus. You and your advisor, together, should review your previous calculus experience in order to make that decision.

There are no blanket recommendations that can be made here, but several considerations that will go into your decision can be discussed. First, you will have the results of the mathematics readiness test to use as a guide. The course placement recommendation is based upon your score on this test, but you may, after consulting with your advisor, begin with a different course if you feel that your test score is not an accurate measure of your mathematical background. However, you should discuss your decision with the instructor in the course to let him or her know of your situation. Finally, note that if you did well in a substantial calculus course in high school that is comparable to our Math 21, we would probably advise you to go directly to Math 22, but this decision should be carefully thought out . On the one hand, we do not want you to be bored sitting through a course in which you already know the material; on the other, we do not want you to have major gaps in your calculus background. The collective judgment of you and your advisor will resolve this issue.

## The First Two Years

In roughly your first two years, you can make a strong start in the major by completing the calculus sequence (Math 21, 22, 121), Computer Programming I (CS 21), Fundamentals of Mathematics (Math 52), and the linear algebra/matrix theory course (Math 124). These courses, which are foundational for the major, introduce fundamental conceptual ideas, methods, and techniques that are important throughout mathematics and statistics, as well as applications. Note that CS 21, Math 52, and Math 124 are normally taken in that order, and CS 21 is only required for the BS Degree.

As just noted, one of the primary curricular goals in the first two years is to give you the mathematical skills, techniques, and methods that form the backbone of mathematical usage and applications. Another goal, less tangible but equally important, is to help you begin to acquire a quality of mind that one refers to as "mathematical maturity. " Thus, for example, we hope that you will learn to reason from the particular to the general and vice versa, to ask yourself why mathematical processes work as they do, to think about when procedures apply in new circumstances or how techniques and definitions can be altered to cover a wider set of problems, and to catalogue problems and cross-reference ideas. These achievements represent your first step in the transition from practice to theory.

## Calculus and Linear Algebra

Your classmates in the calculus sequence, and to a lesser extent linear algebra, will include those majoring in engineering, computer science, and the physical sciences, as well as mathematics and statistics. In view of this diversity, the emphasis in this portion of the core curriculum is more on breadth of coverage than on depth of understanding. In particular, you will be exposed to a variety of topics and be expected to develop various technical and computational skills related to these topics. For example, in calculus you will be evaluated on your ability to compute and use derivatives and definite integrals, and in linear algebra on finding the inverse or determinant or eigenvalues of a matrix. Occasionally you will work at "problem solving", applying the concepts that have been learned to solve a word problem. In these courses, you will also be engaged in conceptual learning that involves definitions, hypotheses, counterexamples, and the like. In the calculus sequence you will be asked primarily to use theorems rather than prove them; while in linear algebra understanding and creating proofs will play a larger role.

## III. REQUIREMENTS AND RECOMMENDATIONS - Areas of Interest in Mathematics and Statistics

There are many options open to you within the mathematics and statistics major. The first decision is whether to select the major within the College of Arts and Sciences or within the College of Engineering and Mathematical Sciences. You may have already made this decision based on your preference for a Bachelor of Arts degree or a Bachelor of Science degree, and the type of education that each connotes. As you would expect, the basic difference between the two options does, in fact, reflect the philosophies of the two colleges. The B.A. degree, granted by the College of Arts and Sciences, embodies a broad liberal arts education and a high degree of flexibility that can lead to a double major, while the B.S. degree, granted by the College of Engineering and Mathematical Sciences, indicates a strong focus on science and technology. In this section of the handbook, you will find the requirements of each degree described in detail. Transferring from one college to another is possible. Talk with your advisor if you feel such a change may be right for you. Many personal goals are compatible with both types of mathematics majors. For example, either major provides excellent preparation for a career in teaching, academics, or medicine. Since these careers interest so many students, special advice is provided here on how to approach them.

## Teaching of Mathematics

The centrality of mathematics in a technological world requires high quality mathematics teaching in our schools. The Department of Mathematics & Statistics and the College of Education and Social Services (CESS) cooperate closely in the area of mathematics education. A student seeking a career as a mathematics teacher in a middle or secondary school should take a rich array of mathematics courses chosen from Math 141, 161, 173, 230, 237, 255, 260, 273, Stat 151 and Stat 211. Consult the Coordinator of Secondary School Education in the College of Education and Social Services for admission to the Secondary Education Program in CESS and for courses required for certification.

## Pre-Graduate Training

If you intend to pursue an advanced degree in the mathematical sciences, you are urged to obtain a solid foundation in mathematics by including as many of the courses of particular importance as possible (These courses are marked with an asterisk in the Areas of Special Interest later in this section). Furthermore Math 242 and/or Math 252 are highly recommended since many graduate schools require them. You should also consider enrolling in the junior-senior seminar (Math 283) and writing an honors thesis (Math 293 or Stat 293). Most graduate schools require GRE (Graduate Record Examinations) results, so you should plan to take these in your senior year.

## Premedical Training

The mathematics major provides excellent credentials for a student who plans to apply to medical school. It is suggested that the student follow the recommendations for a special interest in Allied Fields (2), (3), or (8) given below. During your first or second year, you should review catalogues of those institutions that interest you. In addition, you should contact the Office of Career Services during your junior year regarding the specifics of the medical school application process. To specialize more exclusively in statistics consider the following Premedical Concentration in Statistics.

## Premedical Training in Statistics

Each student electing the Premedical Concentration in Statistics must fulfill the general requirements for the statistics major. In addition, the premedical concentration should include a minimum of two years of chemistry with laboratory (Chemistry 31, 32 or 35, 36, and 141, 142), at least one year of physics with laboratory (Physics 31 with Math 21 and Physics 42 with Math 22), and at least one year of biology with laboratory (Biology 1, 2). Exposure to medical research problems will be provided through supervised experiences in the College of Medicine Biometry Facility.

## THE COLLEGE OF ENGINEERING AND MATHEMATICAL SCIENCES

The College of Engineering and Mathematical Sciences offers programs in several areas of the mathematical sciences and their applications. The curriculum leads to the Bachelor of Science degree in mathematics. The Statistics Program offers a major in statistics within this degree.

## Basic Requirements

** Mathematics:** Math 21, 22, 121, 52, 124, 241, 251 and CS 21.

With the approval of the student’s advisor(s) and the Math Department Chair, Computer Science majors may count CS 64 instead of Math 52 towards a major in Mathematics.

** Statistics:** Math 21, 22, 121, 124, CS 21; one of Stat 141,143, or 211; Stat 151 or 251; Stat 201; Stat 221 or 227; Stat 241 or 261; and Stat 281 or 293.

## Additional Requirements

In addition to the Basic Requirements, candidates for the degree of Bachelor of Science in mathematics must complete the following requirements A, B, C, and D.

## A: Major Courses

** Mathematics:**A minimum of 21 additional hours in mathematics, statistics, or computer science courses numbered 100 or above. At least 12 hours must be in courses numbered 200 or above and no more than 12 hours may be chosen from computer science.

** Statistics:**An additional six credit hours of statistics, so that the total credits earned in statistics is at least 24 hours. A minimum of two additional hours in mathematics, statistics, or computer science courses numbered 100 or above, so that a total of at least 45 credits in the basic and major courses is earned. A total of 18 credit hours in the combined basic curriculum and major courses must be taken at the 200 level and no more than 12 hours can be taken in computer science.

*Note for Mathematics Majors in the College of Arts and Sciences:*

It is possible for you to major in mathematics and minor in statistics; however you can only double count one 3 credit course in your major and minor (CAS rule). Thus you must earn 12 credits in statistics beyond any statistics courses counted in your major courses.

*Note for Mathematics Majors in the College of Engineering and Mathematical Sciences:*

There is currently no provision for double counting of courses in major and minor programs. Thus you would need to earn 15 credits in statistics beyond any statistics courses counted in meeting your major requirements.

## B: Allied Field Courses

Allied Field Courses include the following:

* Twenty-four hours selected from the following Allied Fields*:

1. Physical Sciences

2. Biological Sciences

3. Medical Sciences

4. Engineering

5. Computer Science (26 or higher)

6. Agricultural Sciences

7. Business Administration

8. Psychology

9. Economics

10.Environmental Sciences & Studies

11. Natural Resources

Each student, in consultation with his or her advisor, must plan a sequence of Allied Field courses consistent with his or her professional and personal goals. A student interested in pursuing intensive studies in an area not specifically listed is encouraged to plan a program with his or her advisor and submit it to the appropriate departmental committee for review and approval.

**Allied Field Course requirements are as follows:**

* Mathematics*: Twenty-four hours selected from the above list of Allied Fields. Of these 24 hours, at least six hours must be in courses numbered 100 or above, and at least six hours must be taken in fields (1) to (5). Courses used to satisfy requirement A above may not be used to satisfy this requirement.

* Statistics*: Twenty-four hours selected from the above list of Allied Fields, including at least one laboratory experience in science or engineering. Of these 24 hours, at least six hours must be in courses numbered 100 or above, and at least six hours must be taken in fields (1) to (5). Courses used to satisfy requirement A above may not be used to satisfy this requirement.

## C: Humanities and Social Science Courses

*(Courses used in B may not be used here.)*

English 1, and 21 hours of courses selected from categories I, II, and III listed below. These 21 hours must be distributed over at least two categories, and at least six hours must be taken in each of the two categories chosen. Statistics majors must include Speech 11.

Chinese | Classics | English | French | German |

General | Russian | Spanish | Hebrew | Greek |

Italian | Linguistics | World Literature |

Art | Film | Music | Philosophy |

Religion | Speech | Theatre |

ALANA U.S. Ethnic Studies | Anthropology | Area & International Studies |

Communication Sciences | Economics | Geography |

History | Political Science | Psychology |

Sociology | Vermont Studies | Women's Studies |

## D: Total Hours

A minimum of 120 semester hours is required. First year students must include two courses approved by the College of Arts and Sciences as meeting the "Race Relations and Ethnic Diversity in the United States" requirement.

* Double Major*: Students may earn a double major in mathematics and statistics by meeting the requirements of the statistics major and earning an additional 15 credits in mathematics, including Math 52 and two of Math 230, 237, 241 or 251.

## E: Grades

*No more than three grades of D, D+ or D- in the 200/300 level Mathematics and Statistics courses used to satisfy the “Core Curriculum” and “Major Courses” requirements will be acceptable.*

## AREAS OF INTEREST WITHIN THE MATHEMATICS AND STATISTICS MAJOR

Because of the enormous range of mathematics, courses are grouped in areas of interest to assist you in planning your Mathematics and Statistics program. Because mathematics also has an inner unity, there is a great deal of overlap among these areas. Selecting courses from different areas helps you achieve breadth in the major, while focusing several courses in the same area assures a depth of concentration in the major. Courses of particular importance in an area are marked with an asterisk. Furthermore, students earning a mathematics major can minor in statistics by earning an additional 15 statistics credits. See “Minor in Statistics” for details.

## Recommendations for Major Courses

In consultation with your advisor, you should choose an area of interest within the mathematics major and plan a coherent program that addresses your interests. This area might be one of those listed below, or it might be one you suggest. If you are interested in one of the areas listed, you would typically take at least three courses in that area, including all of the courses marked with an asterisk. In addition, you should take courses from at least two other areas. Because of its centrality in mathematics, you should make sure that you take at least two courses listed under classical mathematics.

In following these recommendations, a course listed in more than one area is meant to be counted only once.

## 1. Classical Mathematics

Classical mathematics, also called pure mathematics, is the study of the major developments of mathematical thought. Many of these topics are central to any course of mathematical study. Classical mathematics includes analysis, abstract algebra, number theory, combinatorics, graph theory, geometry, topology, measure theory, and the theory of complex variables. Current research interests of the faculty include graph theory, combinatorial design theory, algebraic number theory, group theory, and harmonic analysis. Courses in this area include: Math 141, 151, 173, 236, 240, 241*, 242, 251*, 252, 255, 257, 260, 264, 273, 331, 353.

## 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 the problem and allows predictions to be made about the actual physical situation. Current research interests of the faculty include biomedical mathematics, nonlinear dynamics, complex networks, complex systems, fluid mechanics and hydrodynamic stability, asymptotics, singular perturbation theory, and weather prediction. Courses in this area include: Math 230*, 235, 236, 237*, 240, 266, 268, 272, 273, 274, 300, 303, 330, 337.

## 3. Computational Mathematics

Computational mathematics involves the development of new computational techniques and the innovative modification and application of existing computational strategies to new contexts. 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. In these areas, mathematics provides a formulation for the rules governing the systems under study. Computational mathematics provides useful methods for making comprehensive predictions about these systems.

Many physical problems can be simulated on computers, with computational experiments complementing physical experiments so that expensive and dangerous procedures are minimized. Computational mathematics provides the methods and, in some cases, a valuable conceptual framework for these simulations.

Computational mathematics is often interdisciplinary in nature since the source of the problems under study is often outside mathematics. Algorithm development and implementation form a bridge between underlying mathematical results and the solutions of related physical problem. In the process of forming this bridge, ideas and insight are produced in addition to the numerical results. In recent decades, "pure" mathematics has also become a large user of computation, with the computation being used to test cases and suggest patterns in the pursuit of mathematical results. Courses in this area include: Math 173, 230, 237*, 274, 337, and Stat 201.

## 4. Theory of Computing

The mathematical theory of computing deals with the mathematical underpinnings which allow 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: Math 173, 223, 224*, 243, 273, 325, Computer Science 346, 353.

## 5. Mathematics of Management

Mathematics of management involves the use of mathematics in making the kinds of decisions that occur in such area as business, government, medicine and the military.

The following examples illustrate some typical problems that occur.

• a bank manager must determine the number of tellers that should be utilized during the noon hour;

• a manager of a trucking firm must decide on a transportation schedule that minimizes cost and meets demand requirements;

• a city manager must determine the set of one-way streets which allows the maximum traffic flow.

When such a situation requiring a decision arises, pertinent information is investigated, quantified if possible, and formulated into a mathematical structure, commonly known as a mathematical model. This model might take the form of a differential equation, a system of linear equations, or a set of logical statements. After the problem is translated into a mathematical framework, an attempt is made to find a solution. If successful, the information from the mathematical solution is utilized in choosing the appropriate course of action. The mathematics used in these types of problems is drawn from several areas including: calculus, linear algebra, probability, statistics, differential equations, combinatorics, and graph theory. Furthermore, mathematical models can frequently be generalized so that the same model can be used in many seemingly different situations. On the other hand, new models are developed daily as new and unique problems arise.

Courses in this area include: Math 173, 221*, 222, 230, 236, 273 Stat 141 or 211, Stat 151 or Math 207, Stat 224, 241, 253.

## 6. Actuarial Mathematics

Actuaries use quantitative skills to address a variety of problems within business environments, such as managing risks that have financial consequences. Some responsibilities may include, but are not limited to: designing retirement programs for large organizations, assessing the impact of various causes on the mortality experience of insured populations, estimating benefit costs associated with labor contracts, determining fair premiums, and assisting companies with investment decisions. Actuaries are proficient in statistics and mathematics, and additionally are interested in business, legal, and political issues. The majority of actuaries work for life, health, and casualty insurance companies. Opportunities also exist with consulting firms, universities, and government agencies such as the Social Security Administration. Actuaries enjoy a high degree of responsibility and visibility and are compensated accordingly.

Two professional organizations, The Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS), sponsor qualifying examinations and certify actuaries in the United States and Canada. A unique feature of the actuarial profession is that formal training is typically completed "on-the-job" after graduation. Most employers of actuaries support and encourage advancement to Associateship and Fellowship in one of the Societies. Many of these organizations will sustain trainees by providing examination support, materials, study time, review classes, and examination raises or bonuses.

If you are planning an actuarial career, you can prepare for and complete some associateship level examinations prior to graduation. Several departmental course offerings serve as preparation for the examinations:

General Preparation:

Math 21, 22, 121, 124, 173 Stat (141 or 211) 151, 221, 183 (Stat for Business), 295 (Time Series Analysis)

Exam P –

Probability: Stat 151, 251, (241 or 261)

Exam FM –

Financial Mathematics: Math 183 (Fundamentals of Financial Mathematics)

Exam M –

Actuarial Models: Stat 229, 251, Math 222

Exam C –

Construction and Evaluation of Actuarial Models: Stat 237, 251, 261, 295 (Bayesian Statistics)

In order to enhance career opportunities, courses in accounting, business management, finance, economics, computer science, speech and writing are also recommended.

All entry level positions require a B.S. degree in mathematics or statistics or B.A. degree with substantial coursework in mathematics and statistics. Many also require a minimum GPA of 3.0 and successful completion of one or two of the actuarial examinations. Summer intern programs are sometimes available for qualified junior level students.

## 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 include models with random components. 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. It opens the door to the theory of statistical methods for the interpretation of scientific and technological data. Courses in this area include: Math 222, 241, 242, (Stat 151 or Math 207)*, Stat 241*, 252a, 252b, 261, 262, 270.

## Recommendations for Allied Field Courses

If you select the * Mathematics* option you should also discuss Allied Field courses with your advisor and then choose those courses that complement your mathematical interests. For the mathematical interests listed below, you should take at least six hours in courses numbered 100 or above in one of the designated fields.

*Applied Mathematics:* Allied Field (1), (2), (3), (4), (6), (9), (10) or (11).

*Computational Mathematics*: Allied Field (4) or (5).

*Mathematics of Management*: Allied Field (7).

Students interested in Mathematics of Management are advised to include Econ 11 and 12 in their choice of Humanities and Social Sciences courses, and to include BSAD 60 and 61 in their choice of Allied Field courses. Those wishing to minor in Business Administration should contact the School of Business Administration and also take BSAD 173 and two other courses chosen from BSAD 168, 170, 174, 177, 178 and 272.

## THE COLLEGE OF ARTS AND SCIENCES

The mathematics or statistics major within the College of Arts and Sciences allows you to concentrate in mathematics while at the same time pursuing a broad foundation in the liberal arts which includes a minor in another discipline as well. The curriculum leads to the Bachelor of Arts degree in mathematics. The UVM catalogue provides full details of major, minor, distribution, grade point average and other college requirements in the beginning of the section on the Arts and Sciences College. A brief summary of requirements is given below. Checklists for the fulfillment of requirements, including lists of approved courses for various categories, are provided on pages 50-52.

Mathematics majors may choose from the two concentrations listed below. Students interested in any of these should consult an advisor in the Mathematics and Statistics Department.

* Mathematics*: Math 21, Math 22, Math 121, Math 52, and Math 124, plus 18 additional credits in mathematics or statistics courses at 100 level or above, with at least 12 hours numbered 200 or higher.

** Statistics**: CS 21. Thirty-three hours of mathematics or statistics courses numbered 21 or higher, including Math 21, 22 and 121 and 124; Stat. 141, 143, or 211; Stat 151 or 251; Stat 201; Stat 221 or 227; Stat 241 or 261; and Stat 281 or 293. At least 12 hours must be in mathematics and statistics courses numbered 200 or above.

**General College Requirements:**

A. *Race Relations & Ethnicity* One course from approved list.

B. *Non-European Cultures* One course from the list of approved courses (may overlap with one distributive course.)

**College Distribution Requirements**: (All 7 categories must be completed.)

1. *Foreign Language*: Two courses in the same foreign language at the appropriate level, as determined by the offering department.

2.* Mathematical Sciences*: One mathematics course numbered 17 or higher, or statistics 51 or higher or computer science 11 or above or Philosophy 13.

3. *Fine Arts*: One course in art history, dance, film and television studies, studio art, music, or theater (except speech).

4. *Literature*: One course from the list of approved courses.

5. *Humanities*: Two courses from the list of approved courses.

6. *Social Sciences*: Two courses from the list of approved courses.

7. *Natural Sciences*: Two courses, one of which must include a laboratory experience, from the list of approved courses.

**Minor Subject Requirements: **

Candidates must declare and complete a minor subject as described in the catalogue under Arts and Sciences. Note that mathematics majors may minor in statistics. (See information on pages 53 and 54.) A second major is also an option.

**Total Hours: **

A total of 120 hours, see the catalogue for the details of where these 120 hours may be taken.

## MATHEMATICS HONORS THESIS PROGRAM

If you would enjoy the freedom to explore a particular topic in depth, and if you would appreciate the challenge, satisfaction and recognition that come from working closely with a faculty member to produce a mathematical exposition which is uniquely your own, then you should consider writing a Senior Honors Thesis. Students with a GPA of 3.0 or higher in all courses for their sophomore and junior work are welcome; those with a GPA of 3.2 or higher in the mathematics major are especially encouraged to participate. This program leads to College Honors for majors in the College of Engineering and Mathematical Sciences and to Departmental Honors for majors in the College of Arts and Sciences, and provides excellent preparation for research-oriented careers and for graduate study in mathematics. Preparation for the thesis begins during the junior year, when you must identify a willing advisor and either a topic of study or a project to carry out. A written non- technical proposal must be submitted and approved in time to file an Honors Application Form. Detailed information on this procedure is available from faculty, your advisor, or the Department Office. In the fall of your senior year, you should enroll in Math 293 for 1-3 credits. Then in the spring, you will enroll in Math 294 for 1-2 credits and Math 283 for 1 credit. Math 283 is the junior- senior seminar in which each participant gives one fifty- minute presentation. Your presentation will be a report on your thesis topic. Your chosen thesis advisor can help you with the selection of a thesis topic or project, if you like, and will act as a resource person throughout the year. Different faculty members have different styles and areas of expertise, so you will want to choose carefully and clarify expectations at the outset. See the faculty profiles in the appendix to this handbook for some guidance, and discuss your options with your academic advisor and other professors. The thesis should represent substantial investigation of a mathematical topic or project which goes beyond course work, and a clear and original exposition of that topic or project. Originality of results is not required. After making a presentation in Math 283 and earning a grade of B- or better on your thesis, you will be awarded honors and recognized on Honors Day. The title of your thesis will be listed in the program at Commencement, and the designation ``Honors Thesis'' will appear on your transcript. In the case of a grade below B-, your transcript will list the independent study project as Math 295 (Special Topics), rather than Math 294 (Senior Honors Thesis).

## STATISTICS HONORS THESIS PROGRAM

All statistics majors receive research and analysis experience through Statistics Practicum (Stat 281), which is normally taken in the senior year for three credits. However, if you want to try something special, and are interested in getting more deeply involved in a particular research project, consider doing an Honors Thesis. Typically, you would register for Stat 293 in the Fall of your senior year (3 credits) and Stat 294 in the Spring of your senior year (3 credits), but the credits can be split other ways at your convenience to total 6 credits. Also you may begin your research in the summer preceding your senior year. Satisfactory completion of 293 would fulfill your practicum requirement of the major. Potential topics are numerous, and are not just restricted to "pure" statistical research. Some past theses have been done in collaboration with professors in other departments (e.g. business and clinical medicine). If you think you may be interested, please contact the Director of the Statistics Program. You must choose a statistics advisor for your thesis. Your thesis committee will contain at least two statisticians, but can contain other faculty of the university as well. The best time to consider the thesis is at pre-registration time in the spring semester of your junior year. You prepare a proposal for approval during the first few weeks of your senior year. To be eligible for the thesis program, the College of Engineering and Mathematical Sciences requires that you have at least a 3.0 cumulative GPA for your sophomore and junior years, while the College of Arts and Sciences requires a 3.2 cumulative GPA and at least three semesters on the Dean's list. Your thesis, upon completion, will be presented orally to the thesis committee and other interested students or faculty. At graduation, your transcript and the graduation program will list your thesis title and the honors designation. See the description of this program in the Division of CEMS part of the catalogue. Go for it!

## MINOR IN MATHEMATICS

The Department of Mathematics Statistics offers a minor in mathematics which is available to students in all UVM undergraduate major programs. Please contact the Chair of the Department at Jeff.Buzas@uvm.edu or 656-2940 as soon as you think you may be interested in pursuing the mathematics minor.

**Requirements**: Math 21, 22 or 19, 23; Math 52 or 121, and nine additional credits in mathematics courses numbered 100 or above. If both Math 52 and 121 are taken, Math 121 counts as one of the three 100- or 200-level courses needed. The course plan for a mathematics minor must be approved by a mathematics faculty advisor.

## MINOR IN STATISTICS

The Statistics Program offers a minor in statistics which is available to students in any UVM undergraduate major program. Please contact the Director of the Statistics Program at 656-2940 as soon as you think you may be interested in pursuing the statistics minor, so that any questions you have can be answered.

**Admissions**: You will be asked to complete a background form and will be assigned a Minor Advisor, who will ultimately approve your program completion. You are also invited to take part in the social and professional activities of the Statistics Student Association.

**Requirements:**

1) Each student will have a minor advisor from the Statistics Program, appointed by the Program Director, in consultation with the student and faculty.

2) One course in Calculus (3-4 credits). This could include Math 19, 20, 21, or 22 for example, or one year of calculus at the high school level.

3) Fifteen (15) credits of statistics courses selected in consultation with their advisor in order to represent a cohesive package related to their educational and career goals and to their mathematical background

a) Three (3) credits of introductory methods are required. Stat 141: Basic Statistical Methods or Stat 211: Statistical Methods I is recommended. No more than 6 credits of Stat 11/111/141/211 may be counted towards the minor

b) Three (3) credits of probability are recommended. Stat 51: Discrete Probability Models; Stat 151: Applied Probability; or Stat 251: Probability Theory is recommended.

c) Experience in computing through relevant course work is required. Stat 201: Statistical Analysis via Computers is recommended, but students could meet this requirement by taking an appropriate CS or Math course. (CS 16 or above, Math 52)

d) For students who have taken Stat 151 or 251, a semester course in statistical inference is recommended (i.e., Stat 241: Statistical Inference or Stat 261: Statistical Theory I).

e) The elective credits may include independent project or practicum work, such as Stat 191: Special Projects or Stat 281: Statistics Practicum, or even Stat 293-294: Undergraduate Honors Thesis.

f) Elective methods courses would include:

Stat 200: Medical Biostatistics

Stat 221: Statistical Methods II

Stat 223: Applied Multivariate Analysis

Stat 224: Statistics for Quality and Productivity

Stat 225: Applied Regression Analysis

Stat 227: Statistical Methods for the Behavioral Sciences

Stat 229: Reliability and Survival Analysis

Stat 231: Experimental Design

Stat 233: Design of Sample Surveys

Stat 237: Nonparametric Statistical Methods

Stat 253: Applied Time Series and Forecasting

Stat 295: Special Topics in Statistics

## IV. ADVISING

There is no substitute for careful planning, and in that regard your advisor is an indispensable resource. Rapport between you and your advisor adds an experienced and knowledgeable dimension to your long-range academic planning. Career options, course selection for the upcoming semester, and other educational or personal decisions are matters you can discuss with your advisor. Frequently, a relationship that began as student/advisor blossoms into a friendship that lasts beyond college graduation. Be sure to find an advisor with whom you are compatible, and cultivate that relationship. In what follows we list some of the technical aspects and details of the advising process.

## How to get an Advisor

You are assigned an advisor when you enter UVM. However, in some cases (e.g., if you enter with major "undeclared") the faculty member assigned to you may not be in a discipline of interest to you. Students considering a major in mathematics or statistics should have an advisor who is a faculty member of the Department of Mathematics & Statistics. To obtain an advisor in the department or to find out who your advisor is, stop by the department office and ask.

## Changing Your Advisor

It is easy to change your advisor. If you decide to change and want a specific faculty member as your advisor, you must discuss this with the faculty member involved. If you do not have a specific advisor in mind, but desire to have an advisor from Mathematics and Statistics, come to the department office and make your wishes known to the department's administrative assistant, the department Chair, or other faculty member. By the way, it is not your job to make sure that your records are transferred to your new advisor; however, it is a good idea to check before the next advising period to make sure that your new advisor has your records.

If you are changing advisors at the same time you change majors, the two processes can be combined. When you inform the Dean's Office that you are changing your major, that office will inform the Department of Mathematics & Statistics. At that time you will be assigned a new advisor. If you have a specific choice of advisor, be sure to make your preference known at this time. If you are not changing majors but still wish to change advisors, the department office will handle this for you.

## Meeting With Your Advisor

Your advisor can be an invaluable source of information. Your experience at UVM can only be enhanced by getting to know your advisor, and other faculty. The best way to meet with your advisor is to see him/her during office hours or call for an appointment. The Department Office has a list of office hours, email addresses and telephone numbers. If your advisor's office hours conflict with your schedule, you will need to make an appointment. Make appointments directly with your advisor. If you cannot reach your advisor for an appointment, leave a message requesting a return call.

## Deciding if Graduation Requirements Are Met

In the College of Arts and Sciences, the Dean's Office determines if you have met the requirements for graduation. They will send you a letter before your fourth year listing which requirements still need to be met. It is extremely important that you review this letter carefully. If you have any questions about it, you should consult your advisor and/or the Dean's Office.

In the College of Engineering and Mathematical Sciences, it is the advisor who decides if you have met the requirements for graduation. You need to work carefully with your advisor to be sure that you are meeting all of the necessary requirements.

It is ultimately your responsibility to make sure that all requirements are met. You need to read and follow the catalogue carefully so that there are no problems. However, if you encounter any difficulties, be sure to ask for help.

Ordinarily, you will follow the requirements listed in the catalogue for the year you first enrolled at UVM. However, if you leave and then return, you will be expected to fulfill the requirements in the catalogue for the year that you return. If this happens and your requirements change, you need to discuss this with your advisor.

You may discuss with your advisor alternative ways of fulfilling your requirements. If you both agree that your request makes sense, you may petition the appropriate college for the change. The request must be approved by your advisor, the Department Chair, and then the college.

## Taking a Course - PASS/NO PASS

The rules for taking a course under the PASS/NO PASS option are as follows.

- You must be a degree student.
- You must be at least a sophomore.
- You cannot be on academic trial.
- You cannot take more than six courses using this option.
- The course must be a free elective. This means that it is not being used to fulfill any requirement except attaining the necessary hours to graduate.
- You are expected to complete all of the required course work.
- Any grade of D- or higher will be recorded as a PASS. A grade of F will be recorded as NO PASS. Neither grade will affect your grade point average.
- Physical education activity courses, even the required ones, may be taken on a PASS/NO PASS option. These do not count toward the six courses that you are allowed under this option.

If you decide to take a course under this option, you may obtain the necessary form from the Registrar's Office. You then need to consult your advisor for approval. Note that the deadline for choosing the PASS/NO PASS option is within two weeks of the beginning of the semester.

## What to do if you started with MATH 19 or 20

You may have decided that you want to major in mathematics or statistics after completing Math 19 and/or Math 20. In this case, you must decide where to enter the Math 21, 22, 121 sequence; it is crucial to obtain expert advice from your advisor.

If you have completed Math 19 and wish to change to the 21, 22, 121 sequence, there are two options. You can take Math 21 next or you can take Math 23. If you choose to take Math 21 you would follow that with Math 22 and Math 121. In this case you will receive credit toward graduation for both Math 19 and Math 21 upon completion of Math 22. If you do well in Math 19, then the second option is to take Math 23. This is a transition course designed to fill in the gaps between Math 19 and Math 21 as well as cover all the material in Math 22. Following your successful completion of Math 23 you would enter Math 121. Only in unusual cases should you consider going from Math 19 directly to Math 22.

If you have completed Math 19 and 20, and then decide to major in mathematics or statistics, you should enter the Math 21, 22, 121 sequence with Math 22. If you decide to enter the sequence with Math 21, you will receive credit toward graduation for only Math 19, 21 and 22. That is, if you take all four of Math 19, 20, 21 and 22, then 11 of these 14 hours will count toward graduation.

Even though the requirements for either a major or minor in mathematics or statistics explicitly state that you must take Math 21, you should not take Math 21 after Math 22.

## Transfer Credit for Courses Taken at Another Institution

The Office of Transfer Affairs (367 Waterman, Ext. 60867) coordinates transfer activities, but, ultimately, each department determines if a transfer course is equivalent to one in its department.

If you transfer to UVM from another school, the Office of Transfer Affairs will coordinate which courses transfer. If you have questions about their decisions, discuss them with your advisor. It is sometimes possible to get changes made if you provide additional information.

If you plan to take courses at another institution after you have entered UVM (e.g., summer courses), get approval for these courses before you take them. The Dean's Office has a form which, upon completion, guarantees transfer credit if you finish the course satisfactorily. Getting prior approval will eliminate many problems which might occur about the transfer of credit. If you take a course without prior authorization, saving the course syllabus, notes and exams will be helpful in gaining transfer approval.

## Repeating a Course

You may repeat a course at any time for any reason. The most common reasons for repeating a course are to improve your grade in the course or to improve your understanding of the material in the course. If you repeat a course, it will appear on your transcript both times and both grades will count toward your cumulative grade point average. However, the course will not count twice toward credits needed for graduation. If you do repeat a course, you need to be careful not to count the course twice when you figure your total credits.

## The Most Important Thing to Remember!

Your advisor is a great resource in all aspects of planning your schedule of courses, and ensuring that your course selections meet graduation requirements. However, you are ultimately responsible for deciding which courses to take and whether they meet the degree requirements. Read the requirements carefully!