Course Descriptions

Lower Division Courses

MATH 100: Basic Math Skills for the Modern World

See Preregistration guide for instructors and times

Description:

Topics in mathematics that every educated person needs to know to process, evaluate, and understand the numerical and graphical information in our society. Applications of mathematics in problem solving, finance, probability, statistics, geometry, population growth. Note: This course does not cover the algebra and pre-calculus skills needed for calculus.

MATH 101: Precalculus, Algebra, Functions and Graphs

See Preregistration guide for instructors and times

Prerequisites:

Prereq: MATH 011 or Placement Exam Part A score above 10. Students needing a less extensive review should register for MATH 104.

Note:

Students cannot receive credit for MATH 101 if they have already received credit for any MATH or STATISTC course numbered 127 or higher.

Description:

First semester of the two-semester sequence MATH 101-102. Detailed, in-depth review of manipulative algebra; introduction to functions and graphs, including linear, quadratic, and rational functions.

MATH 102: Analytic Geometry and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

Math 101

Description:

Second semester of the two-semester sequence MATH 101-102. Detailed treatment of analytic geometry, including conic sections and exponential and logarithmic functions. Same trigonometry as in MATH 104.

MATH 103: Precalculus and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

The equivalent of the algebra and geometry portions of MATH 104. (See also MATH 101, 102, 104.)

Description:

The trigonometry topics of MATH 104.

MATH 104: Algebra, Analytic Geometry and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

MATH 011 or Placement Exam Part A score above 15. Students with a weak background should take the two-semester sequence MATH 101-102.

Description:

One-semester review of manipulative algebra, introduction to functions, some topics in analytic geometry, and that portion of trigonometry needed for calculus.

MATH 113: Math for Elementary Teachers I

See Preregistration guide for instructors and times

Prerequisites:

MATH 011 or satisfaction of R1 requirement.

Description:

Fundamental and relevant mathematics for prospective elementary school teachers, including whole numbers and place value operations with whole numbers, number theory, fractions, ratio and proportion, decimals, and percents. For Pre-Early Childhood and Pre-Elementary Education majors only.

MATH 114: Math for Elementary Teachers II

See Preregistration guide for instructors and times

Prerequisites:

MATH 113

Description:

Various topics that might enrich an elementary school mathematics program, including probability and statistics, the integers, rational and real numbers, clock arithmetic, diophantine equations, geometry and transformations, the metric system, relations and functions. For Pre-Early Childhood and Pre-Elementary Education majors only.

MATH 121: Linear Methods and Probability for Business

See Preregistration guide for instructors and times

Prerequisites:

Working knowledge of high school algebra and plane geometry.

Description:

Linear equations and inequalities, matrices, linear programming with applications to business, probability and discrete random variables.

MATH 127: Calculus for Life and Social Sciences I

See Preregistration guide for instructors and times

Prerequisites:

Proficiency in high school algebra, including word problems.

Description:

Basic calculus with applications to problems in the life and social sciences. Functions and graphs, the derivative, techniques of differentiation, curve sketching, maximum-minimum problems, exponential and logarithmic functions, exponential growth and decay, and introduction to integration.

MATH 127H: Honors Calculus for Life and Social Sciences I

See Preregistration guide for instructors and times

Prerequisites:

Proficiency in high school algebra, including word problems.

Description:

Honors section of Math 127.

MATH 128: Calculus for Life and Social Sciences II

See Preregistration guide for instructors and times

Prerequisites:

Math 127

Description:

Continuation of MATH 127. Elementary techniques of integration, introduction to differential equations, applications to several mathematical models in the life and social sciences, partial derivatives, and some additional topics.

MATH 131: Calculus I

See Preregistration guide for instructors and times

Prerequisites:

High school algebra, plane geometry, trigonometry, and analytic geometry.

Description:

Continuity, limits, and the derivative for algebraic, trigonometric, logarithmic, exponential, and inverse functions. Applications to physics, chemistry, and engineering.

MATH 131H: Honors Calculus I

See Preregistration guide for instructors and times

Prerequisites:

High school algebra, plane geometry, trigonometry, and analytic geometry.

Description:

Honors section of Math 131.

MATH 132: Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

The definite integral, techniques of integration, and applications to physics, chemistry, and engineering. Sequences, series, and power series. Taylor and MacLaurin series. Students expected to have and use a Texas Instruments 86 graphics, programmable calculator.

MATH 132H: Honors Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

Honors section of Math 132.

MATH 233: Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

Techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals. Theorems of Green, Stokes and Gauss. Honors section available. (Gen.Ed. R2)

MATH 233H: Honors Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

Honors section of Math 233.

MATH 235: Introduction to Linear Algebra

See Preregistration guide for instructors and times

Prerequisites:

Math 132 or consent of the instructor.

Description:

Basic concepts of linear algebra. Matrices, determinants, systems of linear equations, vector spaces, linear transformations, and eigenvalues.

MATH 235H: Honors Introduction to Linear Algebra

See Preregistration guide for instructors and times

Prerequisites:

Math 132 or consent of the instructor.

Description:

Honors section of Math 235.

MATH 331: Ordinary Differential Equations for Scientists and Engineers

See Preregistration Guide for instructors and times

Prerequisites:

Math 132; corequisite: Math 233

Text:

TBA

Description:

Introduction to ordinary differential equations. First and second order linear differential equations, systems of linear differential equations, Laplace transform, numerical methods, applications. (This course is considered upper division with respect to the requirements for the major and minor in mathematics.)

STAT 111: Elementary Statistics

See Preregistration guide for instructors and times

Prerequisites:

High school algebra.

Description:

Descriptive statistics, elements of probability theory, and basic ideas of statistical inference. Topics include frequency distributions, measures of central tendency and dispersion, commonly occurring distributions (binomial, normal, etc.), estimation, and testing of hypotheses.

STAT 240: Introduction to Statistics

See Preregistration guide for instructors and times

Description:

Basics of probability, random variables, binomial and normal distributions, central limit theorem, hypothesis testing, and simple linear regression

Upper Division Courses

MATH 300.1: Fundamental Concepts of Mathematics

Eyal Markman TuTh 2:30 -3:45

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

An Introduction to Mathematical Thinking (Algebra and Number Systems),
by Gilbert and Vanstone, Prentice Hall, 2005.

Description:

The goal of this course is to help students learn the language of rigorous mathematics. Students will learn how to read, understand, devise and communicate proofs of mathematical statements. A number of proof techniques (contrapositive, contradiction, and especially induction) will be emphasized. Topics to be discussed include set theory (Cantor's notion of size for sets and gradations of infinity, maps between sets, equivalence relations, partitions of sets), basic logic (truth tables, negation, quantifiers), and number theory (divisibility, Euclidean algorithm, congruences). Other topics will be included as time allows. Math 300 is designed to help students make the transition from calculus courses to the more theoretical junior-senior level mathematics courses.

MATH 300.2: Fundamental Concepts of Mathematics

Eyal Markman TuTh 8:30-9:45

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

An Introduction to Mathematical Thinking (Algebra and Number Systems),
by Gilbert and Vanstone, Prentice Hall, 2005.

Description:

The goal of this course is to help students learn the language of rigorous mathematics. Students will learn how to read, understand, devise and communicate proofs of mathematical statements. A number of proof techniques (contrapositive, contradiction, and especially induction) will be emphasized. Topics to be discussed include set theory (Cantor's notion of size for sets and gradations of infinity, maps between sets, equivalence relations, partitions of sets), basic logic (truth tables, negation, quantifiers), and number theory (divisibility, Euclidean algorithm, congruences). Other topics will be included as time allows. Math 300 is designed to help students make the transition from calculus courses to the more theoretical junior-senior level mathematics courses.

MATH 300.3: Fundamental Concepts of Mathematics

Tom Braden TuTh 1:00-2:15

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

Jay Cummings, Proofs: A Long-Form Mathematics Textbook.

Description:

The goal of this course is to help students learn the language of rigorous mathematics. Students will learn how to read, understand, devise and communicate proofs of mathematical statements. A number of proof techniques (contrapositive, contradiction, and induction) will be emphasized. Topics to be discussed include set theory (Cantor's notion of size for sets and gradations of infinity, maps between sets, equivalence relations, partitions of sets), basic logic (truth tables, negation, quantifiers), and number theory (divisibility, Euclidean algorithm, congruences). Other topics will be included as time allows. Math 300 is designed to help students make the transition from calculus courses to the more theoretical junior-senior level mathematics courses.

MATH 370.1: Writing in Mathematics

Mark Wilson MWF 12:20 -1:10

Prerequisites:

Math 300 or Comp Sci 250 and completion of the College Writing (CW) requirement.

Description:

Essentially all serious mathematics is written using some variant of the LaTeX software, and developing proficiency with this tool is an important part of the course. We will cover a variety of types of writing related to mathematics, such as: critique of seminar presentations and written articles; (auto)biography of mathematicians; expository writing about mathematical topics; aspects of writing a research article; opinion pieces; precise short communications (e.g. abstract, memo, tweet, blog post, newspaper headline); essays about aspects of mathematical culture (e.g. jokes, songs, anecdotes, sociological aspects).

Satisfies Junior Year Writing requirement.

MATH 370.2: Writing in Mathematics

Franz Pedit MW 2:30-3:45

Prerequisites:

MATH 300 or CS 250 and completion of the College Writing (CW) requirement.

Description:

We will study the concept of dimension in geometry and physics beginning from dimension 0 to dimension 3 (and perhaps 4) leading to the Poincare Conjecture, which provides the possible shapes of the spacial 3-dimensional universe. The various ideas and view points humanity had over the past 2000 or so years about those topics will be part of our exploration.There will be lectures on this topic by the instructor and video taped lectures/demonstrations by eminent mathematicians who worked on these problems. We will also explore (in the above context) how mathematics and physics interact, why (whether) mathematics describes the "physical" universe so accurately, how (whether) aesthetics, art, philosophy has an impact on mathematics, and how mathematical ideas could be conveyed to a non-expert audience. The course is structured around writing assignments which will be peer reviewed and/or graded by the instructor and the course TA. During the last third of the semester there will be group project presentations.
All writing has to be done in the word processing system LaTex, which is the only word processing system capable of producing a professional layout. At the beginning of the semester there will be a presentation by the UMass career center director. We will not spend time on resume and job application writing, since there is ample opportunity to receive expert help from the career center.

MATH 370.3: Writing in Mathematics

Mark Wilson MWF 11:15-12:05

Prerequisites:

MATH 300 or CS 250 and completion of the College Writing (CW) requirement.

Description:

Essentially all serious mathematics is written using some variant of the LaTeX software, and developing proficiency with this tool is an important part of the course. We will cover a variety of types of writing related to mathematics, such as: critique of seminar presentations and written articles; (auto)biography of mathematicians; expository writing about mathematical topics; aspects of writing a research article; opinion pieces; precise short communications (e.g. abstract, memo, tweet, blog post, newspaper headline); essays about aspects of mathematical culture (e.g. jokes, songs, anecdotes, sociological aspects).

Satisfies Junior Year Writing requirement.

MATH 370.4: Writing in Mathematics

Franz Pedit MW 4:00-5:15

Prerequisites:

MATH 300 or CS 250 and completion of the College Writing (CW) requirement

Description:

We will study the concept of dimension in geometry and physics beginning from dimension 0 to dimension 3 (and perhaps 4) leading to the Poincare Conjecture, which provides the possible shapes of the spacial 3-dimensional universe. The various ideas and view points humanity had over the past 2000 or so years about those topics will be part of our exploration.There will be lectures on this topic by the instructor and video taped lectures/demonstrations by eminent mathematicians who worked on these problems. We will also explore (in the above context) how mathematics and physics interact, why (whether) mathematics describes the "physical" universe so accurately, how (whether) aesthetics, art, philosophy has an impact on mathematics, and how mathematical ideas could be conveyed to a non-expert audience. The course is structured around writing assignments which will be peer reviewed and/or graded by the instructor and the course TA. During the last third of the semester there will be group project presentations.
All writing has to be done in the word processing system LaTex, which is the only word processing system capable of producing a professional layout. At the beginning of the semester there will be a presentation by the UMass career center director. We will not spend time on resume and job application writing, since there is ample opportunity to receive expert help from the career center.

MATH 397C: ST - Mathematical Computing

Matthew Dobson and Eric Sommers MWF 9:05-9:55

Prerequisites:

COMPSCI 121, MATH 235, and MATH 300

Description:

This course is about how to write and use computer code to explore and solve problems in pure and applied mathematics.  The first part of the course will be an introduction to programming in Python. The remainder of the course (and its goal) is to help students develop the skills to translate mathematical problems and solution techniques into algorithms and code.  Students will work together on group projects with a variety applications throughout the curriculum.

MATH 411.1: Introduction to Abstract Algebra I

Theodosios Douvropoulos MWF 12:20 -1:10

Prerequisites:

Math 235; Math 300 or CS 250.

Description:

Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning.

MATH 411.2: Introduction to Abstract Algebra I

Martina Rovelli TuTh 8:30-9:45

Prerequisites:

MATH 235; MATH 300 or CS 250

Text:

"Abstract Algebra" by Saracino, Dan. 2nd Edition. ISBN: 9781577665366

Description:

Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning.

MATH 411.3: Introduction to Abstract Algebra I

Christopher Elliott MWF 1:25 -2:15

Prerequisites:

MATH 235; MATH 300 or CS 250.

Description:

Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning.

MATH 421: Complex Variables

Paul Hacking TuTh 8:30-9:45

Prerequisites:

Math 233

Text:

Complex Analysis for Mathematics and Engineering, by John H. Mathews and Russell W. Howell. (Any edition may be used.)

Description:

An introduction to functions of a complex variable. Topics include: Complex numbers, functions of a complex variable and their derivatives (Cauchy-Riemann equations). Harmonic functions. Contour integration and Cauchy's integral formula. Liouville's theorem, Maximum modulus theorem, and the Fundamental Theorem of Algebra. Taylor and Laurent series. Classification of isolated singularities. Evaluation of Improper integrals via residues. Conformal mappings.

MATH 437: Actuarial Financial Math

Jinguo Lian MWF 1:25 -2:15

Prerequisites:

Math 131 and 132 or equivalent courses with C or better

Recommended Text:

ASM Study Manual for Exam FM By: Cherry & Shaban Edition: 14th or later Edition
Calculator: BA II Plus Texas Instruments

Description:

This 3 credit hours course serves as a preparation for SOA's second actuarial exam in financial mathematics, known as Exam FM or Exam 2. The course provides an understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. The main topics include time value of money, annuities, loans, bonds, general cash flows and portfolios, immunization, interest rate swaps and determinants of interest rates etc. Many questions from old exam FM will be practiced in the course.

MATH 455: Introduction to Discrete Structures

Tom Braden TuTh 10:00-11:15

Prerequisites:

Calculus (MATH 131, 132, 233), Linear Algebra (MATH 235), and Math 300 or CS 250.

Text:

Combinatorics and Graph Theory, by Harris, Hirst, and Mossinghoff, Second edition, Springer-Verlag.

Note:

A pdf of this book can be downloaded free from the University Library. A print-on-demand softcover is also available for $25.

Description:

This is a rigorous introduction to some topics in mathematics that underlie areas in computer science and computer engineering, including graphs and trees, spanning trees, and matchings; the pigeonhole principle, induction and recursion, generating functions, and discrete probability proofs (time permitting). The course integrates learning mathematical theories with applications to concrete problems from other disciplines using discrete modeling techniques. Student groups will be formed to investigate a concept or an application related to discrete mathematics, and each group will report its findings to the class in a final presentation. This course satisfies the university's Integrative Experience (IE) requirement for math majors.

MATH 456.1: Mathematical Modeling

Alejandro Morales TuTh 1:00-2:15

Prerequisites:

Math 233 and Math 235 (and Differential Equations, Math 331, is recommended). Some familiarity with a programming language is desirable (Mathematica, Matlab or similar)

Description:

We learn how to build, use, and critique mathematical models. In modeling we translate scientific questions into mathematical language, and thereby we aim to explain the scientific phenomena under investigation. Models can be simple or very complex, easy to understand or extremely difficult to analyze. We introduce some classic models from different branches of science that serve as prototypes for all models. Student groups will be formed to investigate a modeling problem themselves and each group will report its findings to the class in a final presentation. The choice of modeling topics will be largely determined by the interests and background of the enrolled students. Satisfies the Integrative Experience requirement for BA-Math and BS-Math majors. Prerequisites: Calculus (Math 131, 132, 233), required; Linear Algebra (Math 235) and Differential Equations (Math 331), or permission of instructor required

MATH 456.2: Mathematical Modeling

Annie Raymond MW 2:30-3:45

Prerequisites:

Math 235 and Math 300/CS 250. Some familiarity with a programming language is very desirable (Python, Java, Matlab, etc.).

Description:

This course is an introduction to mathematical modeling. The main goal of the class is to learn how to translate real-world problems into quantitative terms for interpretation, suggestions of improvement and future predictions. Since this is too broad of a topic for one semester, this class will focus on linear and integer programming to study real world problems that affect real people. The course will culminate in a final modeling project that will involve optimizing different aspects of a community partner. This course satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

MATH 461: Affine and Projective Geometry

Jenia Tevelev TuTh 2:30-3:45

Prerequisites:

Math 235 and Math 300

Description:

We will explore several approaches to geometry: constructions with straight-edge and compass, axiomatic approach of Euclid and Hilbert, analytic geometry via linear algebra, and Klein's approach using symmetries and transformations. This will open the doors to many non-Euclidean flavors of geometry. Projective and spherical geometry will be studied in some detail.

MATH 471: Theory of Numbers

Vefa Goksel MWF 12:20-1:10

Prerequisites:

Math 233 and 235. Math 300 or CS 250 as a co-requisite is not absolutely necessary but highly recommended.

Description:

Basic properties of the positive integers including congruence arithmetic, the theory of prime numbers, quadratic reciprocity, and continued fractions. Some additional topics may be discussed as time permits. To help learn these materials, students will be assigned computational projects using computer algebra software.

MATH 497K: ST - Knot Theory

Prerequisites:

Math 235; Math 300 or CS 250. Math 411 is strongly recommended as a co-requisite.

Text:

The Knot Book by Colin Adams

Recommended Text:

Knot Theory by Charles Livingston

Description:

Introduction to the fascinating theory of knots, links, and surfaces in 3- and 4-dimensional spaces. This course will combine geometric, algebraic, and combinatorial methods, where the students will learn how to utilize visualization and make rigorous arguments.

MATH 523H: Introduction to Modern Analysis

Wei Zhu MW 2:30-3:45

Prerequisites:

Math 300 or CS 250

Text:

Elementary Analysis: The Theory of Calculus, by Kenneth Ross. Springer

Description:

This course is an introduction to mathematical analysis. A rigorous treatment of the topics covered in calculus will be presented with a particular emphasis on proofs. Topics include: properties of real numbers, sequences and series, continuity, Riemann integral, differentiability, sequences of functions and uniform convergence.

MATH 532H: Nonlinear Dynamics

Markos Katsoulakis TuTh 10:00-11:15

Prerequisites:

Math 235 (Linear Algebra), Math 331 (Differential Equations) and the calculus sequence (Math 131, 132, 233), or equivalent background in elementary differential equations, linear algebra, and calculus

Description:

This course provides an introduction to systems of differential equations and dynamical systems, as well as chaotic dynamics, while providing a significant set of connections with phenomena modeled through these approaches in engineering, chemistry, biology, and social sciences. From the mathematical perspective, geometric and analytical methods of describing the behavior of solutions will be developed and illustrated in the context of low-dimensional systems, including behavior near fixed points and periodic orbits, phase portraits, Lyapunov stability, Hamiltonian systems, bifurcation phenomena, and chaotic dynamics. From an applications perspective, numerous specific applications will be touched upon ranging from epidemiological models to chemical reactions and from lasers to the synchronization of fireflies. In addition to the theoretical and modeling aspects of the class, a self-contained Machine Learning component will be introduced and developed that will allow for both forward simulation and statistical learning of dynamical systems from data. However, no prior knowledge of Machine Learning tools will be assumed.

MATH 537.1: Intro to Mathematics of Finance

Mike Sullivan TuTh 10:00-11:15

Prerequisites:

Single-variable calculus (Math 131, 132), Probability with calculus (Stats 515), multi-variable calculus up to the level of the chain rule for partial derivatives (Math 233).

Description:

This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing financial instruments, or "derivatives." The central topic will be options, culminating in the Black-Scholes formula. The goal is to understand how the models derive from basic principles of economics, and to provide the necessary mathematical tools for their analysis.

MATH 537.2: Intro to Mathematics of Finance

Mike Sullivan TuTh 11:30-12:45

Prerequisites:

Single-variable calculus (Math 131, 132), Probability with calculus (Stats 515), multi-variable calculus up to the level of the chain rule for partial derivatives (Math 233).

Description:

This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing financial instruments, or "derivatives." The central topic will be options, culminating in the Black-Scholes formula. The goal is to understand how the models derive from basic principles of economics, and to provide the necessary mathematical tools for their analysis.

MATH 545.1: Linear Algebra for Applied Mathematics

Rob Kusner MW 2:30-3:45

Prerequisites:

Math 233 and 235 with a grade of C or better, and either Math 300 or CS 250

Description:

Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications.

MATH 545.2: Linear Algebra for Applied Mathematics

Noriyuki Hamada MWF 1:25-2:15

Prerequisites:

Math 233 and 235 with a grade of C or better, and either Math 300 or CS 250

Text:

Gilbert Strang, "Linear Algebra and Its Applications", 4th edition.

Description:

Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications.

MATH 545.3: Linear Algebra for Applied Mathematics

Eric Sarfo Amponsah TuTh 4:00-5:15

Prerequisites:

Math 233 and 235 with a grade of C or better, and either Math 300 or CS 250

Description:

Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications.

MATH 551.1: Intr. Scientific Computing

Hans Johnston MWF 10:10-11:00

Prerequisites:

MATH 233 and 235 and CS 121 or knowledge of a scientific programming language, such as Java, C, Python, or Matlab.

Description:

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis.

MATH 551.2: Intr. Scientific Computing

Prerequisites:

MATH 233 and 235 and CS 121 or knowledge of a scientific programming language, such as Java, C, Python, or MATLAB.

Description:

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis.

MATH 551.3: Intr. Scientific Computing

Navid Mohammad Mirzaei MWF 12:20 -1:10

Prerequisites:

MATH 233 and 235 and CS 121 or knowledge of a scientific programming language, such as Java, C, Python, or MATLAB.

Description:

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis.

STAT 297F.1: ST - Fundamental Concepts/Stats

Anna Liu and Krista J Gile TuTh 2:30-3:45

Prerequisites:

MATH 132

Text:

Statistical Inference via Data Science, Chester Ismay and Albert Y. Kim, 2020. Online edition freely available: https://moderndive.com/

Description:

This course is an introduction to the fundamental principles of statistical science.  It does not rely on detailed derivations of mathematical concepts, but does require mathematical sophistication and reasoning.  It is an introduction to statistical thinking/reasoning, data management, statistical analysis, and statistical computation.  Concepts in this course will be developed in greater mathematical rigor later in the statistical curriculum, including in STAT 515, 516, 525, and 535. It is intended to be the first course in statistics taken by math majors interested in statistics.  Concepts covered include point estimation, interval estimation, prediction, testing, and regression, with focus on sampling distributions and the properties of statistical procedures.  The course will be taught in a hands-on manner, introducing powerful statistical software used in practical settings and including methods for descriptive statistics, visualization, and data management.

STAT 297F.2: ST - Fundamental Concepts/Stats

Haben Michael MW 2:30-3:45

Prerequisites:

MATH 132

Description:

This course is an introduction to the fundamental principles of statistical science.  It does not rely on detailed derivations of mathematical concepts, but does require mathematical sophistication and reasoning.  It is an introduction to statistical thinking/reasoning, data management, statistical analysis, and statistical computation.  Concepts in this course will be developed in greater mathematical rigor later in the statistical curriculum, including in STAT 515, 516, 525, and 535. It is intended to be the first course in statistics taken by math majors interested in statistics.  Concepts covered include point estimation, interval estimation, prediction, testing, and regression, with focus on sampling distributions and the properties of statistical procedures.  The course will be taught in a hands-on manner, introducing powerful statistical software used in practical settings and including methods for descriptive statistics, visualization, and data management.

STAT 501: Methods of Applied Statistics

Joanna Jeneralczuk TuTh 11:30-12:45

Prerequisites:

Knowledge of high school algebra, junior standing or higher.

Text:

Textbook: Introduction to Probability and Statistics,
by Mendenhall, Beaver and Beaver, 14 th edition, Publishers: Brooks/Cole

Description:

For graduate and upper-level undergraduate students, with focus on practical aspects of statistical methods.Topics include: data description and display, probability, random variables, random sampling, estimation and hypothesis testing, one and two sample problems, analysis of variance, simple and multiple linear regression, contingency tables. Includes data analysis using a computer package (R)

STAT 515.1: Introduction to Statistics I

Faith Zhang MW 2:30-3:45

Prerequisites:

Math 131-132 with a grade of “C” or better in Math 132. Knowledge of multivariable calculus is very useful but necessary concepts will be introduced.

Description:

This course provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat516). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, probability inequalities, the central limit theorem, the Poisson approximation and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.

STAT 515.2: Introduction to Statistics I

Instructor TBA MWF 11:15-12:05

Prerequisites:

Math 131-132 with a grade of “C” or better in Math 132. Knowledge of multivariable calculus is very useful but necessary concepts will be introduced.

Description:

This course provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat516). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, probability inequalities, the central limit theorem, the Poisson approximation and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.

STAT 515.3: Introduction to Statistics I

Instructor TBA MWF 10:10-11:00

Prerequisites:

Math 131-132 with a grade of “C” or better in Math 132. Knowledge of multivariable calculus is very useful but necessary concepts will be introduced.

Description:

This course provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat516). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, probability inequalities, the central limit theorem, the Poisson approximation and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.

STAT 515.4: Introduction to Statistics I

Luc Rey-Bellet TuTh 10:00-11:15

Prerequisites:

Math 131-132 with a grade of “C” or better in Math 132. Knowledge of multivariable calculus is very useful but necessary concepts will be introduced.

Description:

This course provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat516). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, probability inequalities, the central limit theorem, the Poisson approximation and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.

STAT 515.5: Introduction to Statistics I

Brian Van Koten TuTh 2:30-3:45

Prerequisites:

Math 131-132 with a grade of “C” or better in Math 132. Knowledge of multivariable calculus is very useful but necessary concepts will be introduced.

Text:

Mathematical Statistics with Applications, Authors: Wackerly, Mendenhall, Schaeffer (ISBN-13: 978-0495110811), Edition: 7th

Description:

This course provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat516). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, probability inequalities, the central limit theorem, the Poisson approximation and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.

STAT 515.6: Introduction to Statistics I

Jiayu Zhai MW 4:00 -5:15

Prerequisites:

Math 131-132 with a grade of “C” or better in Math 132. Knowledge of multivariable calculus is very useful but necessary concepts will be introduced.

Description:

This course provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat516). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, probability inequalities, the central limit theorem, the Poisson approximation and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.

STAT 516.1: Statistics II

Budhinath Padhy TuTh 4:00-5:15

Prerequisites:

Stat 515 or 515H with a grade of “C" or better

Description:

Continuation of Stat 515. The overall objective of the course is the development of basic theory and methods for statistical inference from a mathematical and probabilistic perspective. Topics include: sampling distributions; point estimators and their properties; method of moments; maximum likelihood estimation; Rao-Blackwell Theorem; confidence intervals, hypothesis testing; contingency tables; and non-parametric methods (time permitting).

STAT 516.2: Statistics II

Haben Michael MW 4:00 -5:15

Prerequisites:

Stat 515 or 515H with a grade of “C" or better

Description:

Continuation of Stat 515. The overall objective of the course is the development of basic theory and methods for statistical inference from a mathematical and probabilistic perspective. Topics include: sampling distributions; point estimators and their properties; method of moments; maximum likelihood estimation; Rao-Blackwell Theorem; confidence intervals, hypothesis testing; contingency tables; and non-parametric methods (time permitting).

STAT 516.3: Statistics II

Instructor TBA TuTh 8:30-9:45

Prerequisites:

Stat 515 or 515H with a grade of “C" or better

Description:

Continuation of Stat 515. The overall objective of the course is the development of basic theory and methods for statistical inference from a mathematical and probabilistic perspective. Topics include: sampling distributions; point estimators and their properties; method of moments; maximum likelihood estimation; Rao-Blackwell Theorem; confidence intervals, hypothesis testing; contingency tables; and non-parametric methods (time permitting).

STAT 516.4: Statistics II

Instructor TBA TuTh 2:30-3:45

Prerequisites:

Stat 515 or 515H with a grade of “C" or better

Description:

Continuation of Stat 515. The overall objective of the course is the development of basic theory and methods for statistical inference from a mathematical and probabilistic perspective. Topics include: sampling distributions; point estimators and their properties; method of moments; maximum likelihood estimation; Rao-Blackwell Theorem; confidence intervals, hypothesis testing; contingency tables; and non-parametric methods (time permitting).

STAT 525.1: Regression Analysis

Maryclare Griffin TuTh 8:30-9:45

Prerequisites:

Stat 516 or equivalent: Previous coursework in Probability and Statistics, including knowledge of estimation, confidence intervals, and hypothesis testing and its use in at least one and two sample problems. Stat 515 is NOT sufficient background for this course. Familiarity with basic matrix notation and operations is helpful.

Text:

Applied Linear Regression Models by Kutner, Nachsteim and Neter (4th edition) or, Applied Linear Statistical Models by Kutner, Nachtsteim, Neter and Li (5th edition). Both published by McGraw-Hill/Irwin.

Note:

The first 14 chapters of Applied Linear Statistical Models (ALSM) are EXACTLY equiva- lent to the 14 chapters that make up Applied Linear Regression Models, 4th ed., with the same pagination. The second half of ALSM covers experimental design and the analysis of variance, and is used in our STAT 526. If you are going to take STAT 526, you should buy the Applied Linear Statistical Models (but it is a large book).

Description:

Regression analysis is the most popularly used statistical technique with application in almost every imaginable field. The focus of this course is on a careful understanding and of regression models and associated methods of statistical inference, data analysis, interpretation of results, statistical computation and model building. Topics covered include simple and multiple linear regression; correlation; the use of dummy variables; residuals and diagnostics; model building/variable selection; expressing regression models and methods in matrix form; an introduction to weighted least squares, regression with correlated errors and nonlinear regression. Extensive data analysis using R or SAS (no previous computer experience assumed). Requires prior coursework in Statistics, preferably ST516, and basic matrix algebra. Satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

STAT 525.2: Regression Analysis

Zheni Utic TuTh 1:00-2:15

Prerequisites:

Stat 516 or equivalent: Previous coursework in Probability and Statistics, including knowledge of estimation, confidence intervals, and hypothesis testing and its use in at least one and two sample problems. Stat 515 is NOT sufficient background for this course. Familiarity with basic matrix notation and operations is helpful.

Description:

Regression analysis is the most popularly used statistical technique with application in almost every imaginable field. The focus of this course is on a careful understanding and of regression models and associated methods of statistical inference, data analysis, interpretation of results, statistical computation and model building. Topics covered include simple and multiple linear regression; correlation; the use of dummy variables; residuals and diagnostics; model building/variable selection; expressing regression models and methods in matrix form; an introduction to weighted least squares, regression with correlated errors and nonlinear regression. Extensive data analysis using R or SAS (no previous computer experience assumed). Requires prior coursework in Statistics, preferably ST516, and basic matrix algebra. Satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

STAT 535.1: Statistical Computing

Patrick Flaherty TuTh 2:30-3:45

Prerequisites:

Stat 516 and CS 121

Description:

This course provides an introduction to fundamental computer science concepts relevant to the statistical analysis of large-scale data sets. Students will collaborate in a team to design and implement analyses of real-world data sets, and communicate their results using mathematical, verbal and visual means. Students will learn how to analyze computational complexity and how to choose an appropriate data structure for an analysis procedure. Students will learn and use the python language to implement and study data structure and statistical algorithms.

STAT 535.2: Statistical Computing

Shai Gorsky W 6:00-8:30

Prerequisites:

Stat 516 and CS 121

Note:

This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

This class meets on the Newton Campus of UMass-Amherst.

Description:

This course will introduce computing tools needed for statistical analysis including data acquisition from database, data exploration and analysis, numerical analysis and result presentation. Advanced topics include parallel computing, simulation and optimization, and package creation. The class will be taught in a modern statistical computing language.

STAT 598C: Statistical Consulting Practicum (1 cr)

Anna Liu and Krista J Gile TuTh 1:00-2:15

Prerequisites:

Graduate standing, STAT 515, 516, 525 or equivalent, and consent of instructor.

Description:

This course provides a forum for training in statistical consulting. Application of statistical methods to real problems, as well as interpersonal and communication aspects of consulting are explored in the consulting environment. Students enrolled in this class will become eligible to conduct consulting projects as consultants in the Statistical Consulting and Collaboration Services group in the Department of Mathematics and Statistics. Consulting projects arising during the semester will be matched to students enrolled in the course according to student background, interests, and availability. Taking on consulting projects is not required, although enrolled students are expected to have interest in consulting at some point. The class will include some presented classroom material; most of the class will be devoted to discussing the status of and issues encountered in students' ongoing consulting projects.

Graduate Courses

MATH 605: Probability Theory I

HongKun Zhang TuTh 1:00-2:15

Prerequisites:

Stat 515 or equivalent, Math 523 or equivalent is extremely useful. A good working knowledge of undergraduate probability and analysis, contact the instructor if in doubt.

Note:

Previously Stat 605

Description:

This class introduces the fundamental concepts in probability. Prerequisite are a solid working knowledge of undergraduate probability and analysis. Measure theory is not a prerequisite.
Among the topics covered are

1)Axioms of probability and the construction of probability spaces.
2) Random variables, integration, convergence of sequences of random variables, and the law of large numbers.
3) Gaussian random variables, characteristic and moment generating functions, and the central limit theorem.
4) Conditional expectation, the Radon--Nikodym theorem, and martingales.

MATH 611: Algebra I

Siman Wong MWF 10:10-11:00

Prerequisites:

Undergraduate algebra (equivalent of our Math 411-412).

Text:

(required) Abstract Algebra, 3rd edition by Dummit and Foote

Description:

This fast-paced course (and its continuation - Math 612) will introduce modern algebra concepts with an emphasis on topics required for the qualifying exam in algebra. Syllabus of Math 611 - Math 612:

I. Group Theory and Representation Theory.

Group actions. Counting with groups. P-groups and Sylow theorems. Composition series. Jordan-Holder theorem. Solvable groups. Automorphisms. Semi-direct products. Finitely generated Abelian groups. Complex representations of finite groups. Schur's Lemma. Maschke's Theorem. Representations of Abelian groups. Characters. Schur's orthogonality relations. The number of irreducible representations is equal to the number of conjugacy classes. The sum of squares of dimensions of irreducible representation is equal to the size of the group. The dimension of any irreducible representation divides the size of the group.

II. Linear Algebra and Commutative Algebra.

Euclidean domain is a PID. PID is a UFD. Gauss Lemma. Eisenstein's Criterion. Exact sequences. First and second isomorphism theorems for R-modules. Free R-modules. Hom. Tensor product of vector spaces, Abelian groups, and R-modules. Right-exactness of the tensor product. Restriction and extension of scalars. Complexification. Bilinear forms. Symmetric and alternating forms. Symmetric and exterior algebras. Structure Theorem for finitely generated modules of a PID. Rational canonical form. Jordan canonical form. Chain conditions. Noetherian rings. Hilbert's Basis Theorem. Prime and maximal ideals. Field of fractions. Localization of rings and modules. Exactness of localization. Local rings. Nakayama's Lemma. Integral extensions. Noether's Normalization Lemma. Integral closure. Nullstellensatz. Closed affine algebraic sets.

III. Field Theory and Galois Theory

Algebraic extensions. Finite extensions. Degree. Minimal polynomial. Adjoining roots of polynomials. Splitting field. Algebraic closure. Separable extensions. Theorem of the primitive element. Galois extensions. Fundamental Theorem of Galois Theory. Finite fields and their Galois groups. Frobenius endomorphism. Cyclotomic polynomial. Cyclotomic fields and their Galois groups. Cyclic extensions. Lagrange resolvents. Solvable extensions. Solving polynomial equations in radicals. Norm and trace. Transcendence degree.

MATH 623: Real Analysis I

Sohrab Shahshahani MW 8:40-9:55

Prerequisites:

Math 523 or equivalent
(Undergraduate Analysis (calculus with proofs), also basics of metric spaces and linear algebra)

Description:

General theory of measure and integration and its specialization to Euclidean spaces and Lebesgue measure; modes of convergence, Lp spaces, product spaces, differentiation of measures and functions, signed measures, Radon-Nikodym theorem.

MATH 645: ODE and Dynamical Systems

Jiayu Zhai MW 2:30-3:45

Prerequisites:

Advanced Calculus, Linear Algebra, Elementary Differential Equations (one semester at the undergraduate level)

Description:

Classical theory of ordinary differential equations and some of its modern developments in dynamical systems theory. Topics to be chosen from: Linear systems and exponential matrix solutions; Well-posedness for nonlinear systems; Floquet theory for linear periodic systems. Qualitative theory: limit sets, invariant sets and manifolds. Stability theory: linearization about equilibria and periodic orbits, Lyapunov functions. Numerical simulations will be used to illustrate the behavior of solutions and to motivate the theoretical discussion.

MATH 651: Numerical Analysis I

Qian-Yong Chen TuTh 10:00-11:15

Prerequisites:

Knowledge of Math 523 and 235 (or 545) or permission of the instructor

Description:

This course covers a broad range of fundamental numerical methods, including: machine zeros nonlinear equations and systems, interpolation and least square method, numerical integration, and the methods solving initial value problems of ODEs, linear algebra, direct and iterative methods for solving large linear systems. There will be regular homework assignments and programming assignments (in MATLAB). The grade will be based on homework assignments, class participation, and exams.

MATH 671: Topology I

Paul Gunnells TuTh 8:30-9:45

Prerequisites:

Strong performance in Math 300, 411, 523, or equivalent.

Description:

Mostly point set topology including product and quotient topologies, continuity, compactness, connectedness, and complete metric spaces. Introduction to algebraic topology, specifically the fundamental group. Grade will be based on homework problems and exams.

MATH 691T: S-Teachng In Univ C

TBD M 4:00-5:15

Prerequisites:

Open to Graduate Teaching Assistants in Math and Statistics

Description:

The purpose of the teaching seminar is to support graduate students as they teach their first discussion section at UMass. The seminar will focus on four components of teaching: Who the students are, teaching calculus concepts, instruction techniques, and assessment.

MATH 691Y: Applied Math Project Seminar

Qian-Yong Chen F 1:25-2:40

Prerequisites:

Graduate Student in Applied Math MS Program

Description:

This course is the group project that is required for the MS program in Applied Mathematics. Each academic year we undertake an in-depth study of select applied science problems, combining modeling, theory, and computation to understand it. The main goal of the course is to emulate the process of teamwork in problem solving, such as is the norm in industrial applied mathematics.

MATH 703: Topics in Geometry I

Weimin Chen TuTh 10:00-11:15

Prerequisites:

Solid understanding of abstract linear algebra, topology (e.g., as in Math 671) and calculus in n dimensions.

Description:

Topics to be covered: smooth manifolds, smooth maps, tangent vectors, vector fields, vector bundles (in particular, tangent and cotangent bundles), submersions,immersions and embeddings, sub-manifolds, Lie groups and Lie group actions, Whitney's theorems and transversality, tensors and tensor fields, differential forms, orientations and integration on manifolds, The De Rham Cohomology, integral curves and flows, Lie derivatives, The Frobenius Theorem.

MATH 713: Intr-Algbrc Nmbr Th

Tom Weston TuTh 11:30-12:45

Prerequisites:

Math 611, 612 or equivalent.

Description:

Valuations, rings of integral elements, ideal theory in algebraic number fields of algebraic functions of one variable, Dirichlet unit theorem and Riemann-Roch theorem for curves.

MATH 718: Lie Algebras

Alexei Oblomkov TuTh 8:30-9:45

Prerequisites:

MATH 611 and 612

Description:

Lie algebras are linear algebra devices of great usefulness in mathematics and physics as an efficient tool for the study of symmetries of objects. This course will cover the fundamentals of the subject, including nilpotent and solvable Lie algebras, as well as semisimple Lie algebras and their representations.

MATH 731: Partial Differential Equations I

Robin Young TuTh 2:30-3:45

Prerequisites:

The course assumes that the student has familiarity with the elementary methods of solution of linear ODEs and PDEs.
Modern Real Analysis (Measure Theory, Hilbert Spaces, L^p-theory, etc) at the first-year graduate level is assumed.
Math 623 and Math 624 (or equivalents) are a prerequisite for this class.

Text:

Partial Differential Equations: Methods and Applications, 2nd ed., by Robert C. McOwen

Recommended Text:

Evans, Partial Differential Equations

Rauch, Partial Differential Equations

Description:

This course is a one semester introduction to the theory and methods of linear partial differential equations at the beginning graduate level. The most basic and important linear PDEs that arise in mathematical physics--namely, the wave equation, heat/diffusion equation and Laplace/Poisson equation--will be derived from first principles and their key properties will be exhibited. This approach will make the course accessible to students with a strong mathematics background who have not already studied PDEs. The second half of the course will develop the essential features of the modern theory of PDEs for elliptic, parabolic and hyperbolic equations. Analysis topics will be introduced as needed, including distributions and generalized functions, Fourier analysis, Sobolev spaces and analytic semigroups.

MATH 797E: ST - Homological Algebra

Owen Gwilliam MWF 11:15-12:05

Prerequisites:

Comfort with basic module theory, and an acquaintance with basic terminology from category theory (e.g., category, functor, natural transformation).

Text:

None.

Recommended Text:

We will draw on classic texts, such as Weibel and Gelfand-Manin, but we will not follow any textbook.

Description:

Homological algebra can be seen as a generalization and extension of linear algebra, and so it plays an essential role in many areas of contemporary mathematics. Like linear algebra, it is important to understand both algorithms but also powerful structural results, and we will give due attention to both aspects. This course will lay foundations in a way guided by modern views (e.g., we will introduce model categories) but will also explore classic applications, like group cohomology and Lie algebra cohomology, so that computational facility is developed. By the end of the course, you will know what a derived category is and how to run a spectral sequence.

MATH 797NS: ST - Networks and Spectral Graph Thry

HongKun Zhang TuTh 11:30-12:45

Description:

This course provides an introduction to complex networks, their structure, and function, with examples from applied mathematics and social sciences. Topics include spectral graph theory, notions of centrality, random graph models, Markov chains and random walks, cascades and diffusion.  We will also introduce wavelet transformation on signals, as well as spectral graph wavelet transform that captures abrupt changes of signals on a network. Students will be able to learn fundamental tools to study networks, mathematical models of network structure and for network data analysis, as well as the theories of processes taking place on networks.

STAT 607.1: Mathematical Statistics I

Daeyoung Kim TuTh 11:30-12:45

Prerequisites:

For graduates students: Multivariable calculus and linear algebra; For undergraduate students: permission of instructor

Text:

Statistical Inference (second edition), by George Casella and Roger L. Berger

Recommended Text:

All of Statistics: A Concise Course in Statistical Inference, by Larry Wasserman

Description:

The first part of a two-semester graduate level sequence in probability and statistics, this course develops probability theory at an intermediate level (i.e., non measure-theoretic - Stat 605 is a course in measure-theoretic probability) and introduces the basic concepts of statistics.
Topics include: general probability concepts; discrete probability; random variables (including special discrete and continuous distributions) and random vectors; independence; laws of large numbers; central limit theorem; statistical models and sampling distributions; and a brief introduction to statistical inference. Statistical inference will be developed more fully in Stat 608.
This course is also suitable for graduate students in a wide variety of disciplines and will give strong preparation for further courses in statistics, econometrics, and stochastic processes, time series, decision theory, operations research, etc.
You will be expected to read sections of the text book in parallel with topics covered in lectures, since important part of graduate study is to learn how to study independently.

STAT 607.2: Mathematical Statistics I

Hyunsun Lee M 6:00-8:30

Prerequisites:

For graduates students: Multivariable calculus and linear algebra; For undergraduate students: permission of instructor

Note:

This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

This class meets on the Newton Campus of UMass-Amherst.

Description:

Probability theory, including random variables, independence, laws of large numbers, central limit theorem; statistical models; introduction to point estimation, confidence intervals, and hypothesis testing.

STAT 610: Bayesian Statistics

John Staudenmayer MWF 11:15-12:05

Prerequisites:

STAT 607 and 608 or permission of the instructor.

Description:

This course will introduce students to Bayesian data analysis, including modeling and computation. We will begin with a description of the components of a Bayesian model and analysis (including the likelihood, prior, posterior, conjugacy and credible intervals). We will then develop Bayesian approaches to models such as regression models, hierarchical models and ANOVA. Computing topics include Markov chain Monte Carlo methods. The course will have students carry out analyses using statistical programming languages and software packages.

STAT 625.1: Regression Modeling

Krista J Gile TuTh 10:00-11:15

Prerequisites:

Previous coursework in Probability and Statistics, including knowledge of estimation, confidence intervals, and hypothesis testing and its use in at least one and two sample problems; e.g., ST516 or equivalent. You must be familiar with these statistical concepts beforehand. ST515 by itself is NOT a sufficient background for this course! Familiarity with basic matrix notation and operations is helpful.

Text:

Applied Linear Regression Models by Kutner, Nachsteim and Neter (4th edition) or, Applied Linear Statistical Models by
Kutner, Nachtsteim, Neter and Li (5th edition). Both published by McGraw-Hill/Irwin. NOTE on the book(s). The rst 14
chapters of Applied Linear Statistical Models (ALSM) are EXACTLY equivalent to the 14 chapters that make up Applied
Linear Regression Models, 4th ed., with the same pagination. The second half of ALSM covers experimental design and the
analysis of variance, and is used in our STAT 526. If you are going to take STAT 526, you should buy the Applied Linear
Statistical Models (but it is a large book).

Description:

Regression is the most widely used statistical technique. In addition to learning about regression methods this course will also reinforce basic statistical concepts and introduce students to "statistical thinking" in a broader context. This is primarily an applied statistics course. While models and methods are written out carefully with some basic derivations, the primary focus of the course is on the understanding and presentation of regression models and associated methods, data analysis, interpretation of results, statistical computation and model building. Topics covered include simple and multiple linear regression; correlation; the use of dummy variables; residuals and diagnostics; model building/variable selection, regression models and methods in matrix form. With time permitting, further topics include an introduction to weighted least squares, regression with correlated errors and nonlinear (including binary) regression.

STAT 625.2: Regression Modeling

Shai Gorsky Tu 6:00-8:30

Prerequisites:

Previous coursework in Probability and Statistics, including knowledge of estimation, confidence intervals, and hypothesis testing and its use in at least one and two sample problems; e.g., ST516 or equivalent. You must be familiar with these statistical concepts beforehand. ST515 by itself is NOT a sufficient background for this course! Familiarity with basic matrix notation and operations is helpful.

Note:

This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

This class meets on the Newton Campus of UMass-Amherst.

Description:

Regression is the most widely used statistical technique. In addition to learning about regression methods this course will also reinforce basic statistical concepts and expose students (for many for the first time) to "statistical thinking" in a broader context. This is primarily an applied statistics course. While models and methods are written out carefully with some basic derivations, the primary focus of the course is on the understanding and presentation of regression models and associated methods, data analysis, interpretation of results, statistical computation and model building. Topics covered include simple and multiple linear regression; correlation; the use of dummy variables; residuals and diagnostics; model building/variable selection, regression models and methods in matrix form; an introduction to weighted least squares, regression with correlated errors and nonlinear including binary) regression.

STAT 691P: S - Project Seminar

Erin Conlon Saturday 1:00-3:30

Prerequisites:

Permission of instructor.

Note:

This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

This class meets on the Newton Campus of UMass-Amherst.

Description:

This course is designed for students to complete the master's project requirement in statistics, with guidance from faculty. The course will begin with determining student topics and groups. Each student will complete a group project. Each group will work together for one semester and be responsible for its own schedule, work plan, and final report. Regular class meetings will involve student presentations on progress of projects, with input from the instructor. Students will learn about the statistical methods employed by each group. Students in the course will learn new statistical methods, how to work collaboratively, how to use R and other software packages, and how to present oral and written reports.

STAT 697L: ST - Categorical Data Analysis

Zijing Zhang Th 6:00-8:30

Prerequisites:

Previous course work in probability and mathematical statistics including knowledge of distribution theory, estimation, confidence intervals, hypothesis testing and multiple linear regression; e.g. Stat 516 and Stat 525 (or equivalent). Prior programming experience.

Note:

This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

This class meets on the Newton Campus of UMass-Amherst.

Description:

Distribution and inference for binomial and multinomial variables with contingency tables, generalized linear models, logistic regression for binary responses, logit models for multiple response categories, loglinear models, inference for matched-pairs and correlated clustered data.

STAT 697ML: ST - Stat Machine Learning

Patrick Flaherty TuTh 1:00-2:15

Prerequisites:

Students should have taken Stat 515 as a prerequisite or Stat 607 as a co-requisite. Students must have an understanding of linear algebra at the level of Math 235. Students must be comfortable with a high-level programming language such as MATLAB, R or python.

Description:

This course is intended as an introductory course in statistical machine learning with emphasis on statistical methodology as it applies to large-scale data applications. At the end of this course, students will be able to build and test a latent variable statistical model with companion inference algorithm to solve real problems in a domain of their interest. Course topics include: introduction to exponential families, sufficiency and conjugacy, graphical model framework and approximate inference methods such as expectation-maximization, variational inference, and sampling-based methods. Additional topics may include: cross-validation, bootstrap, empirical Bayes, and deep learning networks. Graphical model examples will include: naive Bayes, regression, hidden Markov models, principal component, factor analysis, and latent variable/topic models.

STAT 697TS: ST - Time Series Analysis and Appl

Hyunsun Lee W 6:00-8:30

Prerequisites:

STAT 607/608 for familiarity with maximum likelihood estimation. STAT 625 or 705 for familiarity with linear algebra, specifically in the context of regression, recommended but not required.

Note:

This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

This class meets on the Newton Campus of UMass-Amherst.

Description:

This course will cover several workhorse models for analysis of time series data. The course will begin with a thorough and careful review of linear and general linear regression models, with a focus on model selection and uncertainty quantification. Basic time series concepts will then be introduced. Having built a strong foundation to work from, we will delve into several foundational time series models: autoregressive and vector autoregressive models. We will then introduce the state-space modeling framework, which generalizes the foundational time series models and offers greater flexibility. Time series models are especially computationally challenging to work with - throughout the course we will explore and implement the specialized algorithms that make computation feasible in R and/or STAN. Weekly problem sets, two-to-three short exams, and a final project will be required.

STAT 705: Linear Models I

John Staudenmayer MWF 10:10-11:00

Prerequisites:

Calculus based Probablity and Mathematical Statistics (preferably Stat 607-608 or rough equivalent), matrix theory and linear algebra.

Description:

Linear models are at the heart of many statistics techniques (linear regression and design of experiments), are closely related to many other important areas (multivariate analysis, time series, econometrics, etc.) and form the basis for many more modern techniques dealing with mixed and hierarchical models, both linear and nonlinear. Stat 705 is the first of two semester sequence covering the theory of linear models and related topics, but can also be taken as a stand-alone course. Coverage includes i) a brief review of important definitions and results from linear and matrix algebra and then what is assumed to be some new topics (idempotency, generalized inverses, etc.) in linear algebra; ii) Random vectors, multivariate distribution, the multivariate normal, linear and quadratic forms including an introduction to non-central t, chi-square and F distributions; iii) development of basic theory for inferences (estimation, confidence intervals, hypothesis testing, power) for the general linear model with "application" to both full rank regression and correlation models as well as some treatment of less than full rank models arising in the analysis of variance (one and some two-factor models). The applied part of the course is not directed towards extensive data analysis (which is available in many other applied courses). Instead, the emphasis with applications is on understanding and using the models and on some computational aspects, including understanding the documentation and methods used in some of the computing packages. [Stat 706 will pick up some additional regression topics, do more on experimental designs settings and then address mixed models of various forms including estimating variance components, modelling and analyzing linear mixed models broadly, and repeated measures/hierarchical regression models more specifically, and cover generalized linear and nonlinear mixed models.]

STAT 797S: ST - Estimation/Semi Non Paramet Md

Ted Westling TuTh 8:30-9:45

Prerequisites:

STAT 607/608 or permission of instructor.

Description:

Statistical inference in parametric models is generally well-understood, but parametric assumptions are unrealistic in many settings. Semiparametric and nonparametric models provide more flexible alternatives that may better reflect our knowledge of the problem at hand, but statistical inference in these models is often challenging. In this course, we will introduce the statistical theory and methods underlying targeted inference of Euclidean parameters in semiparametric and nonparametric models. We will begin by discussing aspects of semiparametric efficiency theory. We will then introduce several general-purpose methods of targeted estimation in these models. Finally, we will provide an overview of tools for analyzing the behavior of such estimators, emphasizing the role that modern machine learning methods can play. Throughout the course, we will illustrate these methods using problems from causal inference, survival analysis, and missing data. Grades will be based on regular homework assignments and a final project.