# Mathematics and Statistics Department

http://www.uvm.edu/~cems/mathstat/

## Curricula

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 Mathematical Sciences with a major in either mathematics or statistics.

Accelerated Master’s Programs in mathematics, statistics, and biostatistics are also offered. These programs allow students to earn both a bachelor's and master's degree in as little as five years. Details are given in the following sections for mathematics and statistics.

The Handbook for Majors and Minors, available on the department website or from the department office, provides additional information on the mathematics and statistics programs, honors in mathematics and statistics, mathematics and statistics courses, advising and other support for students, extracurricular activities, career options, and other material of interest to potential majors.

The following outlines the curriculum for the Bachelor of Science in Mathematical Sciences. Candidates for these degrees must meet the Core Curriculum and Requirements A, B, C and D. The requirements for the two available majors (mathematics or statistics) are listed separately where they differ.

## Academic Standards

In order to continue as a major in the Department of Mathematics and Statistics in CEMS, a student must achieve a 2.00 cumulative grade-point average at the end of the semester in which 60 cumulative credits have been attempted. No more than three repeated course enrollments are allowed during this 60-credit period. In the case of transfer students, applicable transfer credits will be included in determining the 60 credits, but grades in these courses will not be included in the grade-point average.

Students who receive a cumulative or semester grade-point average of less than 2.00 will be placed on trial. Students who have failed half their course credits for any semester, or who have had two successive semester averages below 2.00, or three successive semesters in which their cumulative grade-point average falls below 2.00, are eligible for dismissal.

To receive a degree, students must have a minimum cumulative average of 2.00. Students must complete 30 of the last 45 hours of credit in residence at UVM as matriculated students in the College of Engineering and Mathematical Sciences.

No more than three grades of D, D+, or D– at the 200/300 level mathematics and statistics courses used to satisfy the “Core Curriculum” and “Major Courses” requirements will be acceptable.

## Core Curriculum

Mathematics | ||

MATH 021 | Calculus I ^{1} | 4 |

MATH 022 | Calculus II | 4 |

MATH 052 | Fundamentals of Mathematics | 3 |

MATH 121 | Calculus III | 4 |

MATH 122 | Applied Linear Algebra | 3 |

or MATH 124 | Linear Algebra | |

MATH 241 | Anyl in Several Real Vars I | 3 |

MATH 251 | Abstract Algebra I | 3 |

CS 021 | Computer Programming I | 3 |

Statistics | ||

MATH 021 | Calculus I ^{1} | 4 |

MATH 022 | Calculus II | 4 |

MATH 121 | Calculus III | 4 |

MATH 122 | Applied Linear Algebra | 3 |

or MATH 124 | Linear Algebra | |

CS 021 | Computer Programming I | 3 |

STAT 201 | Stat Computing & Data Analysis | 3 |

STAT 221 | Statistical Methods II | 3 |

Choose one of each of the following: | 12 | |

Basic Statistical Methods | ||

or STAT 143 | Statistics for Engineering | |

or STAT 211 | Statistical Methods I | |

Applied Probability | ||

or STAT 251 | Probability Theory | |

Statistical Inference | ||

or STAT 261 | Statistical Theory | |

Statistics Practicum | ||

or STAT 293 | Undergrad Honors Thesis | |

^{1} | A student with a MATH 021 waiver can use it to fulfill the requirement of MATH 021 in the Core Curriculum. However, at least three extra credits of mathematics numbered above MATH 023 must be added to the Major Courses requirement. |

### A. Major Courses

#### Mathematics

A minimum of twenty-one additional credits in mathematics, statistics, or computer science courses numbered 100 or above. At least twelve credits must be in courses numbered 200 or above and no more than twelve credits can be taken in computer science.

#### Statistics

An additional six credits of statistics, so that the total credits earned in statistics is at least twenty-four. A minimum of two additional credits in mathematics, statistics, or computer science courses numbered 100 or above, so that a total of at least forty-five credits in the core and major courses are earned. A total of eighteen credits in the combined core and major courses must be taken at the 200-level and no more than twelve credits can be taken in computer science.

### B. Allied Field Courses

Twenty-four credits selected from the following Allied Fields:

- Physical Sciences
- Biological Sciences
- Medical Sciences
- Engineering
- Computer Science (CS 110 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 100 or above, and at least six 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 to satisfy requirement B above may not be used to satisfy this requirement.)

ENGS 001 and twenty-one credits of courses selected from categories I, II, and III listed below. These twenty-one credits must be distributed over at least two categories, and at least six credits must be taken in each of the two categories chosen. Statistics majors must take SPCH 011.

I. Language and Literature | II. Fine Arts, Philosophy and Religion | III. Social Sciences |
---|---|---|

Arabic | Art History | ALANA U.S. Ethnic Studies |

Chinese | Dance | Anthropology |

Classics | Film and Television Studies | Communication Sciences and Disorders |

English | Music | Economics |

French | Philosophy | Gender, Sexuality and Women's Studies |

German | Religion | Geography |

Greek | Speech | Global and Regional Studies |

Hebrew | Studio Art | History |

Italian | Theatre | Holocaust Studies |

Japanese | Human Development and Family Studies | |

Latin | Political Science | |

Linguistics | Psychology | |

Portuguese | Sociology | |

Russian | Vermont Studies | |

Spanish | ||

World Literature |

### D. Total Credits

A minimum of 120 credits is required. Students must include two courses that satisfy the University's Diversity requirements (one three-credit course in Diversity Category 1 and a second three-credit course in Diversity Category 1 or 2). Students must also choose one course that meets the University's Sustainability requirement.

## Accelerated Master’s Programs

A master’s degree in Mathematics, Statistics or Biostatistics can be earned in a shortened period of time by careful planning during the junior and senior years. The B.S. and M.S. may be earned in five yeas, as six credits of undergraduate coursework may be counted concurrently toward the M.S. degree requirements.

Students must declare their wish to enter the Accelerated Master’s program in Mathematics in writing to the chair of the Department of Mathematics and Statistics before the end of their sophomore year, and before they have taken MATH 241. Students must apply to the Graduate College for admission, noting their interest in the Accelerated Master’s Program. Once admitted, AMP students receive concurrent undergraduate and graduate credit for one or two courses. Please refer to the Handbook for Graduate Studies in Mathematics for detailed information.

Students should discuss the possibility of an Accelerated Master’s program in statistics or in biostatistics with the director of the Statistics program as soon as they think they may be interested in this program.

Biostatistics AMP

Biostatistics M.S.

Mathematical Sciences Ph.D.

Mathematics AMP

Mathematics M.S.

Mathematics M.S.T.

Statistics AMP

Statistics M.S.

See the online Graduate Catalogue for more information

### Mathematics Courses

**MATH 001. Elementary College Algebra. 3 Credits.**

Fundamental operations and study of high school topics: fractions; exponents; radicals; linear and quadratic equations; proportion; progressions; binomial theorem. No University credit given for this course. Prerequisite: One year of high school algebra.

**MATH 009. College Algebra. 3 Credits.**

Sets, relations, functions with particular attention to properties of algebraic, exponential, logarithmic functions, their graphs and applications in preparation for MATH 019. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered MATH 019 or above. Pre/co-requisites: Two years of secondary school algebra; one year of secondary school geometry.

**MATH 010. Pre-Calculus Mathematics. 3 Credits.**

Skills in working with numerical, algebraic, and trigonometric expressions are developed in preparation for MATH 021. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered MATH 019 or above. Prerequisite: Two years of secondary school algebra; one year of secondary school geometry.

**MATH 015. Elementary School Math. 3 Credits.**

Operations with real numbers: decimals, fractions, percents, integers. Set operations, Venn diagrams, algebra, and problem solving provide background for future instruction in elementary/middle school mathematics. Prerequisite: Three years of secondary school math.

**MATH 016. Fund Concepts Elem School Math. 3 Credits.**

Topics include geometry, measurement, probability, statistics, algebra, number theory, and problem solving to provide background for future instruction in elementary and middle school mathematics. Prerequisite: Three years of secondary school math.

**MATH 017. Applications of Finite Math. 3 Credits.**

Introduction to mathematics of finite systems with applications, such as probability, statistics, graph theory, fair division and apportionment problems, voting systems. Prerequisites: Two years of secondary school algebra or MATH 009 or MATH 010.

**MATH 018. Basic Mathematics. 3 Credits.**

Data, statistics, modeling, algebra, word problems, calculus. Students who do well in the algebra section may continue with MATH 019 or MATH 021. Prerequisite: three years of high school math. No credit for CEMS students.

**MATH 019. Fundamentals of Calculus I. 3 Credits.**

Introduction to limits and differential calculus with a wide variety of applications. Students interested in intensive use of mathematics should take MATH 021. Credit not given for more than one of the courses MATH 019, MATH 021 unless followed by MATH 022. See MATH 023. Prerequisite: MATH 009 or MATH 010, or sufficiently strong background in secondary school algebra and geometry.

**MATH 020. Fundamentals of Calculus II. 3 Credits.**

Introduction to integral calculus with a wide variety of applications. A student who completes MATH 020 may be admitted to MATH 022; however, MATH 019, MATH 023 is preferable to MATH 019, MATH 021, MATH 022 or MATH 019, MATH 020, MATH 022. Prerequisite: MATH 019.

**MATH 021. Calculus I. 4 Credits.**

Introduction to calculus of functions of one variable including: limits, continuity, techniques and applications of differentiation and integration. Prerequisites: MATH 010, or strong background in secondary school algebra and trigonometry. Credit not given for more than one course in the pair MATH 019, MATH 021 unless followed by MATH 022 or MATH 023.

**MATH 022. Calculus II. 4 Credits.**

Techniques and applications of integration. Polar coordinates, Taylor polynomials, sequences and series, power series. Prerequisite: MATH 021. Credit will not be given for both MATH 022 and MATH 023.

**MATH 023. Transitional Calculus. 5 Credits.**

Intended to make the transition from a B or better in MATH 019 to MATH 121. Topics are similar to MATH 022 but recognizing different backgrounds of students in MATH 019 versus MATH 021. Prerequisite: B or better in MATH 019. Credit will not be given for both MATH 022 and MATH 023.

**MATH 052. Fundamentals of Mathematics. 3 Credits.**

Emphasizing proofs, fundamental mathematical concepts and techniques are investigated within the context of number theory and other topics. Prerequisite: MATH 021 or MATH 023. Credit not given for both MATH 052 and MATH 054.

**MATH 054. Fund of Math of Computation. 3 Credits.**

Introduction to mathematical theory and techniques underlying computer science. Co-requisite: MATH 019 or MATH 021.

**MATH 090. Internship. 1-3 Credits.**

An on-site supervised work experience combined with a structured academic learning plan directed by a faculty member or a faculty-staff team in which a faculty member is the instructor of record, for which academic credit is awarded. Offered at department discretion.

**MATH 095. Special Topics. 1-18 Credits.**

Introductory courses or seminars on topics beyond the scope of existing departmental offerings. See Schedule of Courses for specific titles. Prerequisite: Instructor permission.

**MATH 121. Calculus III. 4 Credits.**

Vectors, vector-valued functions. Calculus of functions of several variables: partial derivatives, gradient, divergence, curl, multiple integrals, line integrals, Stokes' and Green's theorems. Prerequisite: MATH 022 or MATH 023.

**MATH 122. Applied Linear Algebra. 3 Credits.**

Vectors, matrices, linear independence, vector spaces (with focus on real n-space), determinants, linear transformations, eigenvalues and eigenvectors. Applications from engineering and the sciences incorporated through required computer assignments. Credit not given for both MATH 122 and MATH 124. Prerequisite: MATH 022 or MATH 023.

**MATH 124. Linear Algebra. 3 Credits.**

Matrices, linear dependence, vector spaces, linear transformations, characteristic equations and applications. Credit not given for both MATH 122 and MATH 124. Co-requisite: MATH 121.

**MATH 141. Real Analysis in One Variable. 3 Credits.**

Principles of analysis in one variable. Heine-Borel and Bolzano-Weierstrass theorems; rigorous development of differential and integral calculus; infinite sequences and series of functions. May not be taken concurrently with or after MATH 241. Pre/co-requisite: MATH 052.

**MATH 151. Groups and Rings. 3 Credits.**

An introduction to the basic concepts of abstract algebra emphasizing examples, including modular arithmetic, symmetric groups, cyclic groups, polynomial rings, homomorphisms, and isomorphisms. May not be taken concurrently with or after MATH 251. Prerequisite: MATH 052.

**MATH 161. Development of Mathematics. 3 Credits.**

Historical development of mathematical sciences emphasizing interrelations among them. Individual assignments correspond to background and interests of students. Prerequisite: Nine hours of college mathematics.

**MATH 167. Physical Chemistry Preparation. 1 Credit.**

Review of relevant mathematical and physical concepts as applied to physical chemistry. Credit cannot be obtained for both MATH 167 and MATH 121. Not available for credit for E&M students. Prerequisite: MATH 022; CHEM 032 or CHEM 036. Cross-listed with: CHEM 167.

**MATH 168. Mathematics of Biology. 0 or 3 Credits.**

Discrete biological processes: nonlinear difference equations. Continuous processes: ordinary differential equations, phase plane methods, quantitative solutions. Applications: population dynamics, epidemiology, Michaelis-Menten kinetics, autocatalysis, muscle contraction. Includes a lab. May not be taken concurrently with or after MATH 268. Pre/co-requisites: MATH 022 or MATH 023; MATH 122 or MATH 124. Cross-listed with: BIOL 168.

**MATH 173. Basic Combinatorial Theory. 3 Credits.**

Introduction to basic combinatorial principles emphasizing problem-solving techniques. Enumeration, generating functions, Fibonacci numbers, pigeonhole principle, inclusion-exclusion, and graph theory. Prerequisites: MATH 052 or MATH 054 or CS 064.

**MATH 183. Fundamentals of Financial Math. 3 Credits.**

Students will be introduced to the basic ideas and algebraic structures of interest theory, time-value of money, annuities, loans, bonds, cash-flows and portfolios. Prerequisites: MATH 020, MATH 022 or MATH 023.

**MATH 190. Internship. 1-18 Credits.**

An on-site supervised work experience combined with a structured academic learning plan directed by a faculty member or a faculty-staff team in which a faculty member is the instructor of record, for which academic credit is awarded. Offered at department discretion.

**MATH 192. Independent Study. 1-18 Credits.**

A course which is tailored to fit the interests of a specific student, which occurs outside the traditional ?classroom/laboratory setting? under the supervision of a faculty member, for which credit is awarded. Offered at department discretion. Prerequisite: Junior/Senior standing; approval of Department Chair.

**MATH 195. Special Topics. 1-18 Credits.**

See Schedule of Courses for specific titles.

**MATH 197. Teaching Assistantship. 1-3 Credits.**

Undergraduate student service as a teaching assistant, usually in an introductory level course in the discipline, for which credit is awarded. Offered at department discretion.

**MATH 198. Undergraduate Research. 1-18 Credits.**

Undergraduate student work on individual or small team research projects under the supervision of a faculty member, for which credit is awarded. Offered at department discretion.

**MATH 207. Probability Theory. 3 Credits.**

Distributions of random variables and functions of random variables. Expectations, stochastic independence, sampling and limiting distributions (central limit theorems). Concepts of random number generation. Prerequisites: MATH 121; STAT 151 or STAT 153 recommended. Cross-listed with: STAT 251, BIOS 251.

**MATH 221. Deterministic Modls Oper Rsch. 3 Credits.**

The linear programming problem. Simplex algorithm, dual problem, sensitivity analysis, goal programming. Dynamic programming and network problems. Prerequisites: MATH 122 or MATH 124; MATH 121 desirable. Cross-listed with: CSYS 221.

**MATH 222. Stochastic Models in Oper Rsch. 3 Credits.**

Development and solution of some typical stochastic models. Markov chains, queueing problems, inventory models, and dynamic programming under uncertainty. Prerequisite: MATH 207, STAT 151.

**MATH 230. Ordinary Differential Equation. 3 Credits.**

Solutions of linear ordinary differential equations, the Laplace transformation, and series solutions of differential equations. Prerequisite: MATH 121. Corequisite: MATH 122 or MATH 124. Credit not granted for more than one of the courses MATH 230 or MATH 271.

**MATH 235. Mathematical Models & Analysis. 3 Credits.**

Techniques of Undergraduate calculus and linear algebra are applied for mathematical analysis of models of natural and human-created phenomena. Students are coached to give presentations. Prerequisites: MATH 121; MATH 122 or MATH 124 or MATH 230 or MATH 271.

**MATH 236. Calculus of Variations. 3 Credits.**

Necessary conditions of Euler, Legendre, Weierstrass, and Jacobi for minimizing integrals. Sufficiency proofs. Variation and eigenvalue problems. Hamilton-Jacobi equations. Prerequisite: MATH 230.

**MATH 237. Intro to Numerical Analysis. 3 Credits.**

Error analysis, root-finding, interpolation, least squares, quadrature, linear equations, numerical solution of ordinary differential equations. Prerequisites: MATH 121; MATH 122, MATH 124 or MATH 271; knowledge of computer programming.

**MATH 238. Applied Computational Methods. 3 Credits.**

Direct and iterative methods for solving linear systems; numerical solution of ordinary and partial differential equations. Focus will be on application of numerical methods. Prerequisites: MATH 121; MATH 122 or MATH 124 or MATH 271.

**MATH 240. Fourier Series&Integral Trans. 3 Credits.**

Fourier series, orthogonal functions, integral transforms and boundary value problems. Prerequisite: MATH 230 or MATH 271.

**MATH 241. Anyl in Several Real Vars I. 3 Credits.**

Properties of the real numbers, basic topology of metric spaces, infinite sequences and series, continuity. Prerequisites: MATH 052; MATH 121; MATH 122 or MATH 124.

**MATH 242. Anyl Several Real Variables II. 3 Credits.**

Differentiation and integration in n-space, uniform convergence of functions, fundamental theorem of calculus, inverse and implicit function theorems. Prerequisite: MATH 241.

**MATH 251. Abstract Algebra I. 3 Credits.**

Basic theory of groups, rings, fields, homomorphisms, and isomorphisms. Prerequisite: MATH 052; MATH 122 or MATH 124.

**MATH 252. Abstract Algebra II. 3 Credits.**

Modules, vector spaces, linear transformations, rational and Jordan canonical forms. Finite fields, field extensions, and Galois theory leading to the insolvability of quintic equations. Prerequisite: MATH 251.

**MATH 255. Elementary Number Theory. 3 Credits.**

Divisibility, prime numbers, Diophantine equations, congruence of numbers, and methods of solving congruences. Prerequisite: MATH 052 or MATH 054.

**MATH 257. Topics in Group Theory. 3 Credits.**

Topics may include abstract group theory, representation theory, classical groups, Lie groups. Prerequisite: MATH 251.

**MATH 260. Foundations of Geometry. 3 Credits.**

Geometry as an axiomatic science; various non-Euclidean geometries; relationships existing between Euclidean plane geometry and other geometries; invariant properties. Prerequisite: MATH 022 and either MATH 052 or MATH 054.

**MATH 264. Vector Analysis. 3 Credits.**

Gradient, curl and divergence, Green, Gauss, and Stokes Theorems, applications to physics, tensor analysis. PrerequisiteS: MATH 121; MATH 122 or MATH 124 or MATH 271.

**MATH 266. Chaos,Fractals&Dynamical Syst. 3 Credits.**

Discrete and continuous dynamical systems, Julia sets, the Mandelbrot set, period doubling, renormalization, Henon map, phase plane analysis and Lorenz equations. Co-requisite: MATH 271 or MATH 230. Cross-listed with: CSYS 266.

**MATH 268. Mathematical Biology&Ecology. 3 Credits.**

Mathematical modeling in the life sciences. Topics include population modeling, dynamics of infectious diseases, reaction kinetics, wave phenomena in biology, and biological pattern formation. Prerequisite: MATH 122 or MATH 124; MATH 230; or Instructor permission. Cross-listed with: CSYS 268.

**MATH 271. Adv Engineering Mathematics. 3 Credits.**

Differential equations and linear algebra, including linear ordinary differential equations, Laplace transforms, matrix theory, and systems of differential equations. Examples from engineering and physical sciences. Prerequisite: MATH 121. Credit not granted for both MATH 230 and MATH 271. No credit for Mathematics majors.

**MATH 272. Applied Analysis. 3 Credits.**

Basics of Fourier series, partial differential equations of mathematical physics, functions of a complex variable, Cauchy's theorem, integral formula. Prerequisites: MATH 230 or MATH 271.

**MATH 273. Combinatorial Graph Theory. 3 Credits.**

Paths and trees, connectivity, Eulerian and Hamiltonian cycles, matchings, edge and vertex colorings, planar graphs, Euler's formula and the Four Color Theorem, networks. Prerequisite: MATH 052 or MATH 054.

**MATH 274. Numerical Linear Algebra. 3 Credits.**

Direct and iterative methods for solving linear equations, least square factorization methods, eigenvalue computations, ill-conditioning and stability. Prerequisite: MATH 237.

**MATH 283. Junior-Senior Seminar. 1 Credit.**

Students required to give presentations on selected topics.

**MATH 290. Internship. 1-18 Credits.**

An on-site supervised work experience combined with a structured academic learning plan directed by a faculty member or a faculty-staff team in which a faculty member is the instructor of record, for which academic credit is awarded. Offered at department discretion.

**MATH 292. Independent Study. 1-18 Credits.**

A course which is tailored to fit the interests of a specific student, which occurs outside the traditional ?classroom/laboratory setting? under the supervision of a faculty member, for which credit is awarded. Offered at department discretion.

**MATH 293. Undergraduate Honors Thesis. 3-4 Credits.**

Program of reading and research culminating in written thesis and oral presentation. Honors notation appears on transcript and Commencement Program. Contact department chairperson for procedures.

**MATH 294. Undergraduate Honors Thesis. 3-4 Credits.**

Program of reading and research culminating in written thesis and oral presentation. Honors notation appears on transcript and Commencement Program. Contact department chairperson for procedures.

**MATH 295. Special Topics. 1-18 Credits.**

For advanced students in the indicated fields. Lectures, reports, and directed readings on advanced topics. Credit as arranged. Offered as occasion warrants.

**MATH 297. Teaching Assistantship. 1-3 Credits.**

Undergraduate student service as a teaching assistant, usually in an introductory level course in the discipline, for which credit is awarded. Offered at department discretion.

**MATH 298. Undergraduate Research. 1-18 Credits.**

Undergraduate student work on individual or small team research projects under the supervision of a faculty member, for which credit is awarded. Offered at department discretion.

### Statistics Courses

**STAT 051. Probability With Statistics. 3 Credits.**

Introduction to probabilistic and statistical reasoning, including probability distribution models and applications to current scientific/social issues. Roles of probability, study design, and exploratory/confirmatory data analysis. Prerequisite: Two years H.S. algebra. No credit for Sophomores, Juniors, or Seniors in the mathematical and engineering sciences.

**STAT 087. Introduction to Data Science. 3 Credits.**

Basic techniques of data harvesting and cleaning; association rules, classification and clustering; analyze, manipulate, and visualize data using programming languages. Basic principles of probability and statistical modeling/inference to make meaning out of large datasets.

**STAT 090. Internship. 1-3 Credits.**

**STAT 095. Special Topics. 1-18 Credits.**

Lectures, reports, and directed readings at an introductory level. Prerequisite: As listed in schedule of courses.

**STAT 111. Elements of Statistics. 3 Credits.**

Basic statistical concepts, methods, and applications, including correlation, regression, confidence intervals, and hypothesis tests. Prerequisites: Two years of high school algebra; Sophomore standing.

**STAT 141. Basic Statistical Methods. 3 Credits.**

Foundational course for students taking further quantitative courses. Exploratory data analysis, probability distributions, estimation, hypothesis testing. Introductory regression, experimentation, contingency tables, and nonparametrics. Computer software used. Prerequisites: Minimum Sophomore standing.

**STAT 143. Statistics for Engineering. 3 Credits.**

Data analysis, probability models, parameter estimation, hypothesis testing. Multi- factor experimental design and regression analysis. Quality control, SPC, reliability. Engineering cases and project. Statistical analysis software. Prerequisites: MATH 020 or MATH 022; Sophomore standing.

**STAT 151. Applied Probability. 3 Credits.**

Foundations of probability, conditioning, and independence. Business, computing, biological, engineering reliability, and quality control applications. Classical discrete and continuous models. Pseudo-random number generation. Prerequisites: MATH 020 or MATH 022.

**STAT 153. Prob & Stat for Cmptr Sci. 3 Credits.**

Foundations of probability, conditioning, independence, expectation and variance. Discrete and continuous probability distributions. Computer simulation examples. Introductory descriptive and inferential statistics. Simple regression analysis. Pre/co-requisite: MATH 020 or MATH 022.

**STAT 183. Statistics for Business. 3 Credits.**

Advanced quantitative methodologies for contemporary business scenarios. Analysis of variance, multiple regression, time series analysis, non-parametric methods, Bayesian statistics and decision analysis. Prerequisite: STAT 141 or EC 170.

**STAT 190. Internship. 1-18 Credits.**

**STAT 191. Independent Study. 1-18 Credits.**

A course which is tailored to fit the interests of a specific student, which occurs outside the traditional ?classroom/laboratory setting? under the supervision of a faculty member, for which credit is awarded. Offered at department discretion. Prerequisites: Junior standing; permission of Program Director.

**STAT 195. Intermediate Special Topics. 1-18 Credits.**

Lectures, reports, and directed readings. Prerequisite: As listed in schedule of courses.

**STAT 197. Teaching Assistantship. 1-3 Credits.**

Undergraduate student service as a teaching assistant, usually in an introductory level course in the discipline, for which credit is awarded. Offered at department discretion.

**STAT 198. Undergraduate Research. 1-18 Credits.**

Undergraduate student work on individual or small team research projects under the supervision of a faculty member, for which credit is awarded. Offered at department discretion.

**STAT 200. Med Biostatistics&Epidemiology. 3 Credits.**

Introductory design and analysis of medical studies. Epidemiological concepts, case-control and cohort studies. Clinical trials. Students evaluate statistical aspects of published health science studies. Prerequisite: STAT 111, STAT 141, STAT 143, or STAT 211. Cross-listed with: BIOS 200.

**STAT 201. Stat Computing & Data Analysis. 3 Credits.**

Fundamental data processing, code development, graphing and analysis using statistical software packages, including SAS and R. Analysis of data and interpretation of results. Prerequisite: STAT 111 with Instructor permission, or STAT 141 or STAT 211.

**STAT 211. Statistical Methods I. 3 Credits.**

Fundamental concepts for data analysis and experimental design. Descriptive and inferential statistics, including classical and nonparametric methods, regression, correlation, and analysis of variance. Statistical software. Prerequisite: Junior standing. Cross-listed with: BIOS 211.

**STAT 221. Statistical Methods II. 3 Credits.**

Cross-listed with: BIOS 221. Multiple regression and correlation. Basic experimental design. Analysis of variance (fixed, random, and mixed models). Analysis of covariance. Computer software usage. Prerequisite: STAT 141, STAT 143, or STAT 211.

**STAT 223. Applied Multivariate Analysis. 3 Credits.**

Multivariate normal distribution. Inference for mean vectors and covariance matrices. Multivariate analysis of variance (MANOVA), discrimination and classification, principal components, factor and cluster analysis. Prerequisite: Any 200-level Statistics course, STAT 221 or STAT 225 recommended, matrix algebra recommended. Cross-listed with: BIOS 223.

**STAT 224. Stats for Quality&Productivity. 3 Credits.**

Statistical process control; Shewhart, cusum and other control charts; process capability studies. Total Quality Management. Acceptance, continuous, sequential sampling. Process design and improvement. Case studies. Prerequisite: STAT 141, STAT 143, or STAT 211.

**STAT 225. Applied Regression Analysis. 3 Credits.**

Simple linear and multiple regression models; least squares estimates, correlation, prediction, forecasting. Problems of multicollinearity and influential data (outliers).

**STAT 229. Survival/Logistic Regression. 3 Credits.**

Models and inference for time-to-event and binary data. Censored data, life tables, Kaplan-Meier estimation, logrank tests, proportional hazards models. Logistic regression-interpretation, assessment, model building, special topics. Prerequisite: STAT 221 or above. Cross-listed with: BIOS 229.

**STAT 231. Experimental Design. 3 Credits.**

Randomization, complete and incomplete blocks, cross-overs, Latin squares, covariance analysis, factorial experiments, confounding, fractional factorials, nesting, split plots, repeated measures, mixed models, response surface optimization. Prerequisite: STAT 211; STAT 221 recommended.

**STAT 233. Survey Sampling. 3 Credits.**

Design and data analysis for sample surveys. Simple random, stratified, systematic, cluster, multistage sampling. Practical issues in planning and conducting surveys. Prerequisite: STAT 211; or STAT 141 or STAT 143 with Instructor permission.

**STAT 235. Categorical Data Analysis. 3 Credits.**

Measures of association and inference for categorical and ordinal data in multiway contingency tables. Log linear and logistic regression models. Prerequisite: STAT 211. Cross-listed with: BIOS 235.

**STAT 237. Nonparametric Statistical Mthd. 3 Credits.**

Nonparametric and distribution free methods; categorical, ordinal, and quantitative data; confidence intervals; rank and chi-square hypothesis tests; computer-intensive procedures (bootstrap, exact tests). Prerequisite: STAT 211; or STAT 141 or STAT 143 with Instructor permission.

**STAT 241. Statistical Inference. 3 Credits.**

Introduction to statistical theory: related probability fundamentals, derivation of statistical principles, and methodology for parameter estimation and hypothesis testing. Prerequisites: STAT 151, STAT 153, or STAT 251, and STAT 141 or equivalent, and MATH 121. Cross-listed with: BIOS 241.

**STAT 251. Probability Theory. 3 Credits.**

Distributions of random variables and functions of random variables. Expectations, stochastic independence, sampling and limiting distributions (central limit theorems). Concepts of random number generation. Prerequisite: MATH 121; STAT 151 or STAT 153 recommended. Cross-listed with: MATH 207, BIOS 251.

**STAT 252. Appl Discr Stochas Proc Models. 1 Credit.**

Markov chain models for biological, social, and behavioral systems models. Random walks, transition and steady-state probabilities, passage and recurrence times. Prerequisite: STAT 151, STAT 153, or STAT 251.

**STAT 253. Appl Time Series & Forecasting. 3 Credits.**

Autoregressive moving average (Box-Jenkins) models, autocorrelation, partial correlation, differencing for nonstationarity, computer modeling. Forecasting, seasonal or cyclic variation, transfer function and intervention analysis, spectral analysis. Prerequisite: STAT 211 or STAT 225; or STAT 141 or STAT 143 with Instructor permission. Cross-listed with: CSYS 253.

**STAT 256. Neural Computation. 3 Credits.**

Introduction to artificial neural networks, their computational capabilities and limitations, and the algorithms used to train them. Statistical capacity, convergence theorems, backpropagation, reinforcement learning, generalization. Prerequisites: MATH 122 or MATH 124 or MATH 271; STAT 143 or STAT 153 or equivalent; CS 110. Cross-listed with: CS 256, CSYS 256.

**STAT 261. Statistical Theory. 3 Credits.**

Point and interval estimation, hypothesis testing, and decision theory. Application of general statistical principles to areas such as nonparametric tests, sequential analysis, and linear models. Prerequisite: STAT 251; or STAT 151 or STAT 153 with Instructor permission. Cross-listed with: BIOS 261.

**STAT 265. Integrated Product Development. 3 Credits.**

Project-based course focusing on the entire product life cycle. Team dynamics, process and product design, quality, materials, management, and environmentally-conscious manufacturing. Prerequisite: Senior standing. Cross-listed with: BSAD 293.

**STAT 281. Statistics Practicum. 1-3 Credits.**

Intensive experience in carrying out a complete statistical analysis for a research project in substantive area with close consultation with a project investigator. Prerequisite: STAT 200 or STAT 201 or STAT 221 through STAT 237 or STAT 253; some statistical software experience; Instructor permission.

**STAT 287. Data Science I. 3 Credits.**

Data harvesting, cleaning, and summarizing. Working with non-traditional, non-numeric data (social network, natural language textual data, etc.). Scientific visualization using static and interactive "infographics". A practical focus on real datasets, and developing good habits for rigorous and reproducible computational science. Prerequisites: CS 020 or CS 021; STAT 141 or STAT 143 or STAT 211; CS 110 and MATH 124 recommended.

**STAT 290. Internship. 1-18 Credits.**

**STAT 291. Independent Study. 1-18 Credits.**

A course which is tailored to fit the interests of a specific student, which occurs outside the traditional ?classroom/laboratory setting? under the supervision of a faculty member, for which credit is awarded. Offered at department discretion.

**STAT 293. Undergrad Honors Thesis. 1-18 Credits.**

A program of reading, research, design, and analysis culminating in a written thesis and oral defense. Honors notation appears on transcript and Commencement Program. Contact Statistics Program Director for procedures.

**STAT 294. Undergrad Honors Thesis. 1-8 Credits.**

A program of reading, research, design, and analysis culminating in a written thesis and oral defense. Honors notation appears on transcript and Commencement Program. Contact Statistics Program Director for procedures.

**STAT 295. Advanced Special Topics. 1-18 Credits.**

For advanced students. Lectures, reports, and directed readings on advanced topics. Prerequisite: As listed in schedule of courses.

**STAT 297. Teaching Assistantship. 1-3 Credits.**

**STAT 298. Undergraduate Research. 1-18 Credits.**