# 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

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

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

"Introduction to Mathematical Thinking: Algebra and Number Systems" (paperback) by Will J. Gilbert and Scott A. Vanstone, Prentice Hall, ISBN 0131848682

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

Prerequisites:

Math 132 with a grade of 'C' or better

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). 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

Prerequisites:

Math 132 with a grade of 'C' or better

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). 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

Prerequisites:

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

Description:

Students will develop skills in writing, oral presentation, and teamwork. The first part of the course will focus on pre-professional skills, such as writing a resume, cover letter, and graduate school essay and preparing for interviews. Subsequent topics will include presenting mathematics to a general audience, the role of mathematics in society, mathematics education, and clear communication of mathematical content. The end of the term will be dedicated to the research process in mathematics and will include technical writing, research paper, and professional presentation.

### MATH 370.2: Writing in Mathematics

Prerequisites:

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

Description:

Satisfies Junior Year Writing requirement. Develops research, presentation, and writing skills in mathematics, including LaTex through team work, peer review, and revision. Students write on mathematical subject areas, prominent mathematicians, and famous mathematical problems.

### MATH 370.3: Writing in Mathematics

Prerequisites:

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

Description:

Satisfies Junior Year Writing requirement. Develops research, presentation, and writing skills in mathematics, including LaTex through team work, peer review, and revision. Students write on mathematical subject areas, prominent mathematicians, and famous mathematical problems.

### MATH 405: Mathematical Computing

Prerequisites:

COMPSCI 121 (or INFO 190S/CICS 110), MATH 235, and COMPSCI 250 (or 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

Prerequisites:

Math 235; Math 300 or CS 250.

Description:

This course is an introduction to group theory, which is one of the oldest branches of modern algebra. It was invented by a 19-year-old Evariste Galois with a goal of proving that there is no algebraic formula expressing the roots of an equation of degree 5 in terms of its coefficients. Since then, group theory has become the crucial tool in uncovering hidden symmetries of the world. The emphasis of this class will be on using concrete examples to develop problem-solving and proof-writing skills. We will cover permutations, cyclic and Abelian groups, cosets and Lagrange's theorem, quotient groups, group actions and Burnside's theorem.

### MATH 411.2: Introduction to Abstract Algebra I

Prerequisites:

MATH 235; MATH 300 or CS 250

Description:

Description:
The focus of the course will be on learning group theory. A group is a central concept of mathematics which is used to describe algebraic operations and symmetries of every possible kind, from modular arithmetic to symmetries of geometric objects.

Learning objectives: The emphasis will be on development of careful mathematical reasoning. Theoretical constructions and applications will be tested on many examples, both by hand and using computer algebra systems, specifically Wolfram Mathematica.

The following topics will be covered: Group axioms. Examples of groups. Numbers and matrices. Transformation groups. Multiplication tables. The group of units modulo n. Properties of groups. Generators and Cayley graphs. Subgroups. Symmetric, Dihedral and Cyclic groups. Cyclic subgroups of a group. Order of an element. Properties of permutations. Cayley theorem. Isomorphisms. Rubik's cube and other permutation puzzles. Subgroups of permutations. Sign of a permutation. Cosets. Lagrange Theorem. Normal Subgroups. Quotient group. Homomorphisms. Isomorphism theorems. Direct product of groups. Classification of finite Abelian groups. Group actions. Orbit/stabilizer theorem. Burnside lemma. Crystallographic groups. Conjugacy classes. Cauchy theorem. Sylow theorems (w/o proof). Matrix groups over Fp. Group-theoretic aspects of public-key cryptography. Simple groups. Classification of groups of small order.

### MATH 411.3: Introduction to Abstract Algebra I

Prerequisites:

MATH 235; MATH 300 or CS 250.

Text:

A first course in abstract algebra, by J. B. Fraleigh. We will cover Chapters I,II,III of the textbook. We will also cover parts of Chapter VII.

Recommended Text:
Description:

This course is an introduction to group theory, which is one of the oldest branches of modern algebra. It was invented by a 19-year-old Evariste Galois with a goal of proving that there is no algebraic formula expressing the roots of an equation of degree 5 in terms of its coefficients. Since then, group theory has become the crucial tool in uncovering hidden symmetries of the world. The emphasis of this class will be on using concrete examples to develop problem-solving and proof-writing skills. We will cover permutations, cyclic and Abelian groups, cosets and Lagrange's theorem, quotient groups, and group actions.

### MATH 421: Complex Variables

Prerequisites:

Math 233

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

Prerequisites:

Math 131 and 132 or equivalent courses with C or better

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

Prerequisites:

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

Text:

Combinatorics and Graph Theory, John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff (second edition)

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, colorings 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

Prerequisites:

Math 233 and Math 235

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

Prerequisites:

Math 233 and Math 235

Description:

We learn how to build, use, and critique mathematical models. In modeling we translate scientific questions into mathematical language and corresponding computational methods, 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. In the Fall of 2023, we will focus on modeling through Machine Learning and in particular on Generative Artificial Intelligence. We will discuss their mathematical, computational and statistical foundations and discuss some prominent generative models and related tools. Student groups will be formed to investigate their assigned machine learning modeling problem and each group will report its findings to the class in a final presentation. The course satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

### MATH 461: Affine and Projective Geometry

Prerequisites:

Math 235 and Math 300

Description:

There are three types of surfaces which look the same at every point and in every direction: the plane, the sphere, and the hyperbolic plane. The hyperbolic plane is a remarkable surface in which the circumference of a circle grows exponentially as the radius increases; it was only discovered in the 18th century. We will begin by studying the geometry of the plane and the sphere and their symmetries. Then we will describe and study the hyperbolic plane. The emphasis will be on developing our geometric intuition in each case.

### MATH 471: Theory of Numbers

Prerequisites:

Math 233 and Math 235 and either Math 300 or CS250.

Description:

This course is a proof-based introduction to elementary number theory. We will quickly review basic properties of the integers including modular arithmetic and linear Diophantine equations covered in Math 300 or CS250. We will proceed to study primitive roots, quadratic reciprocity, Gaussian integers, and some non-linear Diophantine equations. Several important applications to cryptography will be discussed.

### MATH 481: Knot Theory

Prerequisites:

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

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 491A: Seminar - Putnam Exam Prep (1 credit)

Prerequisites:

One variable Calculus, Linear Algebra

Description:

The William Lowell Putnam Mathematics Competition is the most prestigious annual contest for college students. While the problems employ topics from a standard undergraduate curriculum, the ability to solve them requires a great deal of ingenuity, which can be developed through systematic and specific training. This class aims to assist the interested students in their preparation for the Putnam exam, and also, more generally, to treat some topics in undergraduate mathematics through the use of competition problems.

### MATH 491P: GRE Prep Seminar (1 credit)

Prerequisites:

MATH 233 & 235 and either MATH 300 or COMPSCI 250.
Students should have already completed, or be currently taking Math 331.
Students should have already completed, or be currently taking Math 411 or Math 523H.

Description:

This class is designed to help students review and prepare for the GRE Mathematics subject exam, which is a required exam for entrance into many PhD programs in mathematics. Students should have completed the three courses in calculus, a course in linear algebra, and have some familiarity with differential equations. The focus will be on solving problems based on the core material covered in the exam. Students are expected to do practice problems before each meeting and discuss the solutions in class.

### MATH 491S: S-STEM Seminar (1-credit seminar)

Description:

A community building weekly seminar introducing S-STEM scholars to the different directions of research pursued in the Department of Mathematics and Statistics and applications of mathematics and statistics in industry. During fall and spring semesters, the seminar will be a one-credit course that S-STEM scholars can register and receive a grade for. Embedded within the seminars, students will work on short- and long-term goal setting for their program and career aspirations, routinely conduct self-reflections, and have regular peer and facilitator feedback. Seminars will feature collaborations with industry partners who have committed to share insights into important employee skills and knowledge, provide guest speakers, and advice on preparing competitive job applications, including Google, Microsoft, MassMutual, Zapata Computing, and Collins Aerospace. Students who are not S-STEM scholars will be admitted with instructor permission as capacity allows.

### MATH 523H: Introduction to Modern Analysis

Prerequisites:

Math 300 or CS 250

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

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

Text:

S. Strogatz,
Nonlinear Dynamics and Chaos with applications to Physics, Biology, Chemistry and Engineering
Westview Press, 2nd Edition, 2015.

Description:

This course is intended to provide an introduction to systems of differential equations and dynamical systems, as well as to touch upon chaotic dynamics, while providing a significant set of connections with phenomena modeled through these approaches in Physics, Chemistry and Biology. From the mathematical perspective, geometric and analytic 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 concluding with chaotic dynamics. From the applied perspective, numerous specific applications will be touched upon ranging from the laser to the synchronization of fireflies, and from the outbreaks of insects to chemical reactions or even prototypical models of love affairs. In addition to the theoretical component, a self-contained computational component towards addressing these systems will be developed with the assistance of Matlab (and wherever relevant Mathematica). However, no prior knowledge of these packages will be assumed.

### MATH 537.1: Intro to Mathematics of Finance

Prerequisites:

Math 233 and either Stat 515 or MIE 273

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

Prerequisites:

Math 233 and either Stat 515 or MIE 273

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

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

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 545.3: Linear Algebra for Applied Mathematics

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.

Recommended Text:

Sheldon Axler, "Linear Algebra Done Right", 3rd edition.

Description:

Basic concepts (mainly over the field of 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, normal. Diagonalization of real symmetric matrices, generalizations (like singular value decomposition) and applications (for instances, to the geometry of "propellors" – a current research topic).

### MATH 551.1: Intr. Scientific Computing

Prerequisites:

MATH 233 & 235 and either COMPSCI 121, E&C-ENG 122, PHYSICS 281, or E&C-ENG 242. Knowledge of a scientific programming language, e.g. MATLAB, Fortran, C, C++, Python, Java.

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 & 235 and either COMPSCI 121, E&C-ENG 122, PHYSICS 281, or E&C-ENG 242. Knowledge of a scientific programming language, e.g. MATLAB, Fortran, C, C++, Python

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. Prerequisites: MATH 233 and 235, or consent of instructor, and knowledge of a scientific programming language.

### MATH 551.3: Intr. Scientific Computing

Prerequisites:

MATH 233 & 235 and either COMPSCI 121, E&C-ENG 122, PHYSICS 281, or E&C-ENG 242. Knowledge of a scientific programming language, e.g. MATLAB, Fortran, C, C++, Python, Java.

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 310.1: Fundamental Concepts/Stats

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 310.2: Fundamental Concepts/Stats

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

Prerequisites:

Knowledge of high school algebra, junior standing or higher.

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

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is recommended for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

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

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is recommended for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

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

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is recommended for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

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

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is recommended for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

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

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is recommended for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

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

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is recommended for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

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

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

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

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

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. You must be familiar with these statistical concepts beforehand. Stat 515 by itself is NOT a 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 525.2: Regression Analysis

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. You must be familiar with these statistical concepts beforehand. Stat 515 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).
NOTE on the book(s). The first 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 Stat 526.
If you are going to take Stat 526, you should buy the Applied Linear Statistical Models.

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 SAS (no previous computer experience assumed). Requires prior coursework in Statistics, preferably Stat 516, and basic matrix algebra. Satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

### STAT 535.1: Statistical Computing

Prerequisites:

Stat 516 and CS 121

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 535.2: Statistical Computing

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 Mount Ida 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 590C: Intro to Causal Inference

Prerequisites:

STAT 515, 516, and 525

Text:

"Causal Inference: What If", Miguel Hernán and James M. Robins. Online edition freely available: https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/

Recommended Text:

"Causality", Judea Pearl. "Graphical Models", Steffen L. Lauritzen. "Observational Studies", Paul R. Rosenbaum. "Targeted Learning: Causal inference for observational and experimental data", Mark J. van der Laan and Sherri Rose.

Description:

Seeking answers to questions of causality is a fundamental part of the scientific process and the advancement of human knowledge. Answers to causal questions are imperative to supporting decision-making in areas such as healthcare and public policy. This course provides an introduction to causal inference in statistics. We will introduce the potential outcomes framework to causal modeling, and use it to study core causal models including randomized experiments, backdoor adjustment, instrumental variables, difference-in-difference, regression discontinuity, and mediation analysis. Directed Acyclic Graphs will be introduced as an alternative approach to causal reasoning and as a tool for assessing conditional independence assumptions.  In each model, we will study the causal and observed data structures, the causal estimand(s) of interest, the causal identification conditions and the associated graphical model, the identification result, statistical inference for the identified parameter, and R code implementing statistical inference. We will use case studies from the real scientific literature to illustrate each model. In the final project, students will apply the techniques learned in class to conduct causal analysis for a scientific question of their choosing and write up their results.

### STAT 598C: Statistical Consulting Practicum (1 cr)

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.

### MATH 605: Probability Theory I

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.

Text:

Probability Essentials, by Jean Jacod and Philip Protter, Universitext, Springer

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

Prerequisites:

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

Description:

Introduction to groups, rings, and fields. Direct sums and products of groups, cosets, Lagrange's theorem, normal subgroups, quotient groups. Polynomial rings, UFDs and PIDs, division rings. Fields of fractions, GCD and LCM, irreducibility criteria for polynomials. Prime field, characteristic, field extension, finite fields. Some topics from Math 612 included.

### MATH 623: Real Analysis I

Prerequisites:

Working knowledge of undergraduate Analysis (with rigorous proofs) as well as basics of metric spaces and linear algebra as for example taught in classes like M523H and M524 at UMass Amherst.

Description:

This is the first part of a 2-semester introduction to Real Analysis: Math 623 in the Fall, and in the Spring Math 624 which covers part of Vol. IV of Stein & Shakarchi also. In the Fall semester we will cover the following material from Stein-Shakarchi's Vol III:

1) Measure theory: Lebesgue measure and integrable functions on Euclidean spaces (Chapter 1)
2) Integration theory: Lebesgue integral, convergence theorems and Fubini theorem (Chapter 2)
3) Differentiation and Integration. Functions of bounded variation (Chapter 3)
4) Abstract measure theory over more general spaces (first part of Chapter 6)

The topics covered in Math 623 lay at the foundation not just Analysis but also of many other areas of mathematics and are essential to all mathematicians.

### MATH 645: ODE and Dynamical Systems

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

Prerequisites:

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

Description:

The analysis and application of the fundamental numerical methods used to solve a common body of problems in science. Linear system solving: direct and iterative methods. Interpolation of data by function. Solution of nonlinear equations and systems of equations. Numerical integration techniques. Solution methods for ordinary differential equations. Emphasis on computer representation of numbers and its consequent effect on error propagation.

### MATH 655: Biomed and Health Data Analysis

Description:

In this course, we will review, develop, and evaluate some computational biology methods. We will implement most of these methods in Python. Although programming skills, machine learning, or computational biology background are preferred, they are not required for this course. Importantly, this is a research-based course; it is an introduction on how to do research in computational biology. We all work as a team to learn novel methods in computational biology and hopefully find ways to improve them. We will read some recently published papers, which include four cutting-edge papers on computational oncology, implement the methods that have been introduced in these papers, and reproduce their results. Except the first few lectures, a team of students will present the papers and their implementation of methods. Students should be interested in Python programming, computational biology, and doing research as a team member. Students will be evaluated based on their participation, presentations, and works, including their codes and HWs.

### MATH 671: Topology I

Prerequisites:

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

Description:

Topological spaces. Metric spaces. Compactness, local compactness. Product and quotient topology. Separation axioms. Connectedness. Function spaces. Fundamental group and covering spaces.

### MATH 690STB: Math (Cell) Biology

Prerequisites:

Math 645 (co-requisite) or the consent of the instructor.

Text:

None required. A text + lecture notes will be made available to the students.

Description:

This course explores mathematical vignettes motivated by the biophysics of cell shape, cell motility, cell signalling, and pattern formation in cells. We consider how cells interact with each other, and how they coordinate to form tissues. The two primary goals are: (1) learn to use the tools and techniques to formulate models of biological systems, and (2) learn to use mathematical analysis techniques to provide insights into the underlying biological mechanisms.

The two primary goals are: (1) learn to formulate models of biological systems, and (2) learn mathematical analysis tools and techniques to provide insights into the underlying biological mechanisms. Here we concentrate on ordinary and partial differential equation models (i.e.\ deterministic models), and the Cellular-Potts model to describe multiscale tissues. This course will include a tutorial and hands-on exploration of the open source software, Morpheus, which can simulate computational models of cells and tissues.

From a mathematical perspective, we will showcase several important models (with application beyond cellular biology) where analysis provide insights and helps to understand the underlying mechanisms. Many of these models are useful in many other areas of science (e.g.\ ecology, population biology, social aggregation). Hence this course will also serve as a survey of partial differential equations that are important to STEM.

### MATH 691T: S-Teachng In Univ C

TBD Mon 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 703: Topics in Geometry I

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: Intro - Algebraic Number Theory

Prerequisites:

Math 611, 612 or equivalent

Text:

Algebraic Number Theory by J.S.Milne. Available from https://www.jmilne.org/math/CourseNotes/ANT.pdf

Description:

An algebraic number field is a field obtained by adjoining to the rational numbers the roots of an irreducible rational polynomial. Algebraic number theory is the study of properties of such fields. This course will cover the basics of algebraic number theory, with topics to be studied including the following: rings of integers, factorization in Dedekind domains, class numbers and class groups, units in rings of integers, valuations and local fields, and zeta- and L-functions.

### MATH 721: Riemann Surfaces

Description:

This course introduces Riemann surfaces from the points of view of 1-dimensional complex manifolds and also 2-dimensional real oriented conformal manifolds. Topics covered included the structure of holomorphic maps between Riemann Surfaces (Riemann-Hurwitz Theorem), holomorphic line;vector bundles, Chern classes, the Picard group of holomorphic line bundles, the Abel-Jacobi map, and the basic theorems of Riemann Surface theory: Mittag-Leffler, Riemann-Roch, Serre duality, Kodaira embedding and Serre's GAGA principle.

### MATH 731: Partial Differential Equations I

Prerequisites:

A solid working knowledge of linear algebra and calculus (in one and higher variables) is a prerequisite for this class. This includes basic ODE theory, vector calculus, and integration by parts (using the divergence and Stokes' theorems in higher dimensions). Modern Real Analysis (Measure Theory, Hilbert Spaces, L^p-theory, Fourier analysis, etc) at the first-year graduate level is assumed. Math 623 and Math 624 (or equivalents) are prerequisites for this class.

Description:

Introduction to the modern methods in partial differential equations. Calculus of distributions: weak derivatives, mollifiers, convolutions and Fourier transform. Prototype linear equations of hyperbolic, parabolic and elliptic type, and their fundamental solutions. Initial value problems: Cauchy problem for wave and diffusion equations; well-posedness in the Hilbert-Sobolev setting. Boundary value problems: Dirichlet and Neumann problems for Laplace and Poisson equations; variational formulation and weak solutions; basic regularity theory; Green functions and operators; eigenvalue problems and spectral theorem.

### MATH 790STC: Characteristic Classes and K-Theory

Prerequisites:

Math 672 or equivalent

Description:

This class is a second course in algebraic topology, taking the next steps after (co)homology and homotopy.  The central objects of study are vector bundles, which are families of vector spaces parametrized by a topological space.  Associated to a vector bundle are cohomology classes called characteristic classes, which provide a measure of how "twisted" the bundle is.  The first part of the course will focus on motivating examples, the axiomatic approach, and culminate with the notion of a classifying space, which provides a concrete source for characteristic classes.
The second part of the course will develop the natural context for studying vector bundles: K-theory, as a generalized cohomology theory.  We will also develop special features of K-theory, notably Bott periodicity and the Chern character, which relates K-theory to characteristic classes.  Additional topics such as cobordism, the Atiyah-Singer index theorem, or Adams operations and the Hopf invariant one problem may be discussed subject to time and student interest.

### STAT 607.1: Mathematical Statistics I

Prerequisites:

Advanced calculus and linear algebra, or consent of instructor.

Description:

Probability theory, including random variables, independence, laws of large numbers, central limit theorem. STAT 607 is the first semester of a two-semester sequence, followed by STAT 608 which focuses on statistical models; introduction to point estimation, confidence intervals, and hypothesis testing.

### STAT 607.2: Mathematical Statistics I

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

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 Mount Ida Campus of UMass-Amherst.

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 625.1: Regression Modeling

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.

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

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 Mount Ida 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 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 631: Categorical Data Analysis

Prerequisites:

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 R programming experience.

Text:

Textbook: Categorical Data Analysis by Alan Agresti, Wiley. 3rd edition. ISBN-13: 9780470463635.

Note:

This class meets on the Newton Mount Ida Campus of UMass-Amherst.
Students may also attend class meetings synchronously via Zoom.

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 639: Time Series Analysis and Applications

Prerequisites:

Probability and Statistics at a calculus based graduate level such as Stat 607 and Stat 608 (concurrent), and a previous course on regression analysis covering multiple linear regression (e.g., Stat 625) with some exposure to regression models in matrix form. Prior computing experience with R is desirable.

Text:

Shumway & Stoffer. Time Series Analysis and Its Applications: With R Examples (Springer Texts in Statistics) 4th ed. 2017 Edition. ISBN-13: ‎ 978-3319524511.

Description:

This course presents the fundamental principles of time series analysis including
mathematical modeling of time series data and methods for statistical inference.
Topics covered will include: modeling and inference for linear autoregressive time
series models, autoregressive (AR) and autoregressive moving average (ARMA)
models, (nonseasonal/seasonal) autoregressive integrated moving average (ARIMA)
models, unit root and differencing, spectral analysis,
(generalized) autoregressive conditionally heteroscedastic models,
Kalman filtering and smoothing, and state-space models.

### STAT 690C: Intro to Causal Inference

Prerequisites:

Stat 607, 608, and 625, or equivalent

Text:

"Causal Inference: What If", Miguel Hernán and James M. Robins. Online edition freely available: https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/

Recommended Text:

"Causality", Judea Pearl. "Graphical Models", Steffen L. Lauritzen. "Observational Studies", Paul R. Rosenbaum. "Targeted Learning: Causal inference for observational and experimental data", Mark J. van der Laan and Sherri Rose.

Description:

Seeking answers to questions of causality is a fundamental part of the scientific process and the advancement of human knowledge. Answers to causal questions are imperative to supporting decision-making in areas such as healthcare and public policy. This course provides an introduction to causal inference in statistics. We will introduce the potential outcomes framework to causal modeling, and use it to study core causal models including randomized experiments, backdoor adjustment, instrumental variables, difference-in-difference, regression discontinuity, and mediation analysis. Directed Acyclic Graphs will be introduced as an alternative approach to causal reasoning and as a tool for assessing conditional independence assumptions.  In each model, we will study the causal and observed data structures, the causal estimand(s) of interest, the causal identification conditions and the associated graphical model, the identification result, statistical inference for the identified parameter, and R code implementing statistical inference. We will use case studies from the real scientific literature to illustrate each model. In the final project, students will apply the techniques learned in class to conduct causal analysis for a scientific question of their choosing and write up their results.

### STAT 691P: S - Project Seminar

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 Mount Ida 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 705: Linear Models I

Prerequisites:

Calculus based Probability 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 focuses on the theory of linear models and related topics. 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.