# 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

### STAT 297F: ST-Fundamental Concepts/Stats

Prerequisites:

Open to Math majors only.
Prerequisite: 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.

## Upper Division Courses

### MATH 300.1: Fundamental Concepts of Mathematics

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

Description:

Math 300 is an introduction to rigorous, abstract mathematics. In lower-level courses like calculus, the emphasis is on applying theorems and formulas to solve specific, often numerical, problems. More advanced math classes are concerned with developing the theorems and formulas and solving general classes of problems. In particular, it's important to know why those theorems and formulas are true. In mathematics, the way we know a statement is true is by giving a proof of it, and this course is about learning what proof is, how to read, create, and present proofs, and how to tell a correct proof from an incorrect one. In many ways, this is like learning a language. We need to learn the grammar (logical deduction) and vocabulary (sets, functions, and other basic structures), but it also helps to have something to say. So we will also study some important and beautiful mathematics along the way. Starting with explicit axioms and precisely stated definitions, we will systematically develop basic propositions about integers and modular arithmetic, induction and recursion, equivalence classes and rational numbers, and such other topics as time allows.

### MATH 300.2: Fundamental Concepts of Mathematics

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

Description:

Math 300 is an introduction to rigorous, abstract mathematics. In lower-level courses like calculus, the emphasis is on applying theorems and formulas to solve specific, often numerical, problems. More advanced math classes are concerned with developing the theorems and formulas and solving general classes of problems. In particular, it's important to know why those theorems and formulas are true. In mathematics, the way we know a statement is true is by giving a proof of it, and this course is about learning what proof is, how to read, create, and present proofs, and how to tell a correct proof from an incorrect one. In many ways, this is like learning a language. We need to learn the grammar (logical deduction) and vocabulary (sets, functions, and other basic structures), but it also helps to have something to say. So we will also study some important and beautiful mathematics along the way. Starting with explicit axioms and precisely stated definitions, we will systematically develop basic propositions about integers and modular arithmetic, induction and recursion, equivalence classes and rational numbers, and such other topics as time allows.

### MATH 300.3: Fundamental Concepts of Mathematics

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

Title: How to Prove it: A structured Approach, 2nd edition
Author: Daniel J. Velleman, by Cambridge Univ. Press

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 370.1: Writing in Mathematics

Prerequisites:

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

Description:

This course will introduce students to writing in mathematics, both technical and otherwise. Writing assignments will include proofs, instructional handouts, resumes, cover letters, presentations, and a final paper. All assignments will be completed using LaTeX using offline and online editors. By the end of the semester, students should be able to clearly convey mathematical ideas through their writing, and to tailor that writing for a particular audience. Students will also learn about LaTeX offline and online editors, file sharing and version control (GitHub).

### MATH 370.2: Writing in Mathematics

Prerequisites:

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

Description:

This course will introduce students to writing in mathematics, both technical and otherwise. Writing assignments will include proofs, instructional handouts, resumes, cover letters, presentations, and a final paper. All assignments will be completed using LaTeX. By the end of the semester, students should be able to clearly convey mathematical ideas through their writing, and to tailor that writing for a particular audience. Students will also learn about LaTeX offline and online editors, file sharing and version control (GitHub).

### MATH 370.3: Writing in Mathematics

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

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 411.1: Introduction to Abstract Algebra I

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

Prerequisites:

MATH 235; MATH 300 or CS 250

Text:

Dan Saracino, "Abstract Algebra: A First Course", second edition, Waveland Press

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

Prerequisites:

MATH 235; MATH 300 or CS 250.

Text:

Dan Saracino, "Abstract Algebra: A First Course", second edition, Waveland Press.

Description:

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

### MATH 421: Complex Variables

Prerequisites:

Math 233

Text:

Complex Variables and Applications, 8-th Edition, by James Ward Brown and Ruel V. Churchill, McGraw-Hill.

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. The Argument Principle and Rouche's Theorem. Evaluation of Improper integrals via residues. Conformal mappings.

### MATH 425.1: Advanced Multivariate Calculus

Prerequisites:

Multivariable Calculus (MATH 233) and Linear Algebra (MATH 235).

Recommended Text:

J. Marsden and A. Tromba, Vector Calculus [an earlier edition is fine and may be less expensive: W. H. Freeman, Fifth Edition edition (2003) ISBN-10: 0716749920, ISBN-13: 978-0716749929; or Sixth Edition (2012) ISBN-10: 1-4292-9411-6, ISBN-13: 978-1-4292-9411-9]
H. M. Schey, div, grad, curl and all that [ISBN-13: 978-0393925166; ISBN-10: 039 3925161]
M. Spivak, Calculus on Manifolds [ISBN-13: 978-0805390216; ISBN-10: 0805390219]

Description:

Calculus of several variables, Jacobians, implicit functions, inverse functions; multiple integrals, line and surface integrals, divergence theorem, Stokes' theorem.

### MATH 425.2: Advanced Multivariate Calculus

Prerequisites:

Multivariable calculus (Math 233) and Linear algebra (Math 235)

Text:

J. Marsden and A. Tromba, Vector Calculus [an earlier edition is fine and may be less expensive: W. H. Freeman, Fifth Edition edition (2003) ISBN-10: 0716749920, ISBN-13: 978-0716749929; or Sixth Edition (2012) ISBN-10: 1-4292-9411-6, ISBN-13: 978-1-4292-9411-9]

Note:

There will also be posted notes to complement the material in the book.

Description:

Calculus of several variables.
While MATH233 covers the case of up to three variables we will try to build intuition and methods for functions of any number of variables. The emphasizes will on integration over shapes'' though we will recall where needed the differentiation of mappings.
Some topics: change of variables, parametrizations of shapes, Jacobians, implicit functions, inverse functions; multiple integrals, line and surface integrals, divergence theorem, Stokes' theorem, fundamental theorem of multivariable calculus.

### MATH 425.3: Advanced Multivariate Calculus

Prerequisites:

Multivariable calculus (Math 233) and Linear algebra (Math 235)

Recommended Text:

J. Marsden and A. Tromba, Vector Calculus [an earlier edition is fine and may be less expensive: W. H. Freeman, Fifth Edition edition (2003) ISBN-10: 0716749920, ISBN-13: 978-0716749929; or Sixth Edition (2012) ISBN-10: 1-4292-9411-6, ISBN-13: 978-1-4292-9411-9]
H. M. Schey, div, grad, curl and all that [ISBN-13: 978-0393925166; ISBN-10: 039 3925161]

Description:

Calculus of several variables, Jacobians, implicit functions, inverse functions; multiple integrals, line and surface integrals, divergence theorem, Stokes' theorem.

### MATH 437: Actuarial Financial Math

Prerequisites:

Math 131 and 132 or equivalent courses with C or better

Description:

Foundational material in mathematical finance. Course covers interest rates, annuities, bonds, forwards, futures, options and other derivative securites. (Basis of actuarial exam in financial math exam fm/2).

### MATH 455: Introduction to Discrete Structures

Prerequisites:

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

Text:

Harris, Hirst, Mossinghurst, Combinatorics and Graph Theory (Second Edition).

Recommended Text:

A pdf of this book can be downloaded free from the University Library.

Note:

A pdf of this book can be downloaded free from the University Library.

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

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.

### MATH 456.2: Mathematical Modeling

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 such problems. The course will culminate in a final modeling project that will involve optimizing different logistical aspects of some inspiring community partner.

### MATH 461: Affine and Projective Geometry

Prerequisites:

Math 235 and Math 300

Text:

J. Stillwell, The Four Pillars of Geometry, Springer Verlag, 2005.

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

Prerequisites:

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

Text:

Number Theory, A lively Introduction with Proofs, Applications, and Stories, by James Pommersheim, Tim Marks and Erica Flapan.

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 490A: Intro Abstract Algebra for Future Teachers

Prerequisites:

Math 235 and either Math 300 or CMPSCI 250, or permission of the instructor

Text:

Ronald S. Irving, Integers, Polynomials, and Rings. You can read this book online through the library.

Description:

Abstract algebra forms a key part of the ideas behind high school mathematics and is the basis for several parts of the Massachusetts Test for Educator Licensure for secondary school math teachers. This course will cover the parts of abstract algebra most important for building a deep understanding of the ideas of high school mathematics and their interconnections. It will focus on the properties of rings (especially the integers and polynomial rings over fields), and fields. During the course, we will be making some of the connections between these topics and high school mathematics; this is definitely a course in abstract algebra, not a course on how to understand or teach high school mathematics, but I hope that the things you learn in this course will deepen your understanding of, and change the way you think about, some important parts of high school algebra.

### MATH 491A: Seminar: Putnam Exam Preparation (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: S - Problem Seminar (1 credit)

Prerequisites:

Required Prerequisites: Math 233, 235, and 300. Suggested Prerequisites: Math 331 (completed or currently taking); Math 411 or Math 523H (completed or currently taking)

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 513: Combinatorics

Prerequisites:

CMPSCI 250 or MATH 455 with a grade of 'B' or better.
Students requesting permission to enroll must request an override to COMPSCI 575 via the online form www.cics.umass.edu/overrides .
Students may only request an override to one of COMPSCI 575 OR MATH 513; not both.

Note:

Open to Math majors only.

Description:

Cross-listed with CompSci 575. A basic introduction to combinatorics and graph theory for advanced students in computer science, mathematics, and related fields. Topics include elements of graph theory, Euler and Hamiltonian circuits, graph coloring, matching, basic counting methods, generating functions, recurrences, inclusion-exclusion, Polya's theory of counting.

### 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:

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2nd edition by Steven H. Strogatz, Westview Press, 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: Intro to Mathematics of Finance

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).

Recommended Text:

Derivative Markets by Robert L. McDonald, 3rd edition.

Note:

Lecture notes will be provided

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

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

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.

Text:

A First Course in Numerical Methods, Authors: Uri M. Ascher and Chen Greif, Publisher: Society for Industrial and Applied Mathematics (SIAM), 2011.

Note: An electronic version of the textbook is free from SIAM for students.

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

Prerequisites:

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

Text:

Numerical Analysis, Timothy Sauer

Description:

The course will introduce numerical methods used for solving problems that arise in many scientific fields. Properties such as accuracy of methods, their stability and efficiency will be studied. Students will gain practical programming experience in implementing the methods using MATLAB or Scilab. We will cover the following topics (not necessarily in the order listed): Finite Precision Arithmetic and Error Propagation, Linear Systems of Equations, Root Finding, Interpolation, least squares, Numerical Integration.

### MATH 591CF: S-Cybersecurity Lecture Series

Description:

This course is a one-credit seminar on security research across departments at UMass. Each presentation will cover an active research topic at UMass in a way that assumes only a basic background in security. External speakers may also be invited. Note that this course is not intended to be an introduction to cybersecurity, and will not teach the fundamentals of security in a way that would be useful as a foundation for future security coursework. The intended audience is graduate and advanced undergraduate students, as well as faculty. Meets with COMPSCI 591CF and E&C-ENG 591CF. May be taken repeatedly for credit up to 2 times. This course does not count toward any requirements for the Math major or minor.

### 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.

### STAT 515.1: Introduction to Statistics I

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

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

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

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

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 515.6: Introduction to Statistics I

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

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 516.4: 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. 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

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 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. 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

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 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)

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 and Stochastics by Erhan Cinlar

Recommended Text:

1) Probability Essentials by Jean Jacod and Philip Protter
2) A first look at rigorous probability by Jeffrey Rosenthal
3) Probability: Theory and Examples by Rick Durrett
4) A probability path by Sidney Resnick

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

Prerequisites:

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

Text:

Dummit and Foote, Abstract Algebra, 3rd ed.

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.

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.

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

Prerequisites:

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

Text:

Sheldon Axler, "Measure, Integration & Real Analysis", Springer GTM

Recommended Text:

I'll primarily use Royden (2nd or 3rd edition, NOT 4th!), and Stein & Shakarchi (vol 3). I'll also refer to Bressoud, "A Radical Approach to Lebesgue Integration"

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

Prerequisites:

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

Text:

Differential Dynamical Systems, Revised Edition, by James D. Meiss; SIAM, 2017

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 671: Topology I

Prerequisites:

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

Text:

John M. Lee, "Introduction to Topological Manifolds", second edition.

Recommended Text:

James Munkres, "Topology", second edition.
Allen Hatcher, "Algebraic Topology", available online at the author's webpage.

Description:

This fast-paced course (and its sequel, Math 672) is an introduction to topology, from point-set to geometric and algebraic topology.
Part I: Basic point-set topology, constructions of topological spaces, connectedness, compactness, countability and separation axioms, topological manifolds.
Part II: Introduction to algebraic topology, cell complexes, homotopy, fundamental group, covering spaces.
Grade will be based on regularly assigned homework, as well as exams.

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

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

Prerequisites:

Graduate Student in Applied Math MS Program

Text:

None

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 697B: Introduction to Riemann Surfaces

Description:

Riemann surfaces are one of the most fundamental objects in mathematics and physics. They arise as zeros of equations in two complex variables, the complex 1-dimensional manifolds (complex curves). They also arise from conformal geometry, namely 2-dimensional oriented real manifolds with a conformal class of Riemannian metrics. That these two view points are equivalent, is already a non-trivial result. Thus, any surface you see in 3-space is in fact an example of a Riemann surface. Special such surfaces, obeying variational constraints, arise in geometry as minimal surfaces and in physics as string propagations. If the Riemann surface is compact, a deep results says that it can be described by complex algebraic equations and we are in the realm of algebraic geometry. At which point we could also contemplate Riemann surfaces over any field, e.g. Diophantine equations, Langlands program etc.

This course will explore these different facets of Riemann surfaces. The necessary concepts such as vector bundles and holomorphic structures will be developed as the course progresses. The main results proven in the course include the integrability of almost complex structures in complex dimension one, Riemann-Roch for vector bundles, Serre's GAGA principle, and the Abel-Jacobi theorem describing the moduli space of holomorphic line bundles. Possible applications (or final project topics) include the classification of holomorphic vector bundles over the Riemann sphere and elliptic curves, algebro-geometric integrable systems, moduli spaces of higher rank holomorphic vector bundles, and non-Abelian Hodge theory.

Prerequisites:

good knowledge of abstract (linear) algebra, complex variables, basic topology, perhaps some exposure to basic concepts of manifold theory (e.g. Spivak's book on Calculus on manifolds or Hitchin's notes on Differentiable Manifolds).

Literature:

Hermann Weyl: The Concept of a Riemann Surface (good historical reading).
Griffiths and Harris: Principles of Algebraic Geometry (selected chapters).
Knoeppel, Pedit, and Pinkall: Riemann Surfaces from a Differential Geometric View Point (pdf lecture notes).
Nigel Hitchin: pdf lecture notes on Geometry of Surfaces, Differentiable Manifolds, and Algebraic Curves.
Simon Donaldson: Riemann Surfaces, Oxford Graduate Texts in Mathematics.
R. Narasimhan: Compact Riemann Surfaces, Lectures in Mathematics. ETH Zuerich.
Otto Forster: Lectures on Riemann Surfaces, Springer-Verlag 1981.

### MATH 697PA: ST-Math Foundtns/ProbabilistAI

Description:

The course will primarily focus on the mathematical foundations of probabilistic Artificial Intelligence. The topics covered will include: Fundamentals of Information Theory, Markov Chain Monte Carlo Approximate Inference and Variational Inference Graphical Models (directed and undirected) Hidden Markov Models, Neural Networks and other Black Box methods Support Vector Machines, Adversarial learning, Game Theory and Generative Adversarial Networks, Reinforcement Learning Sensitivity Analysis, Uncertainty Quantification.

### 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.

Text:

Introduction to Smooth Manifolds, by John M. Lee

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 731: Partial Differential Equations I

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.

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 797EC: ST-Elliptic Curves

Description:

Elliptic curves, as the only smooth projective algebraic curves equipped with a group law, play a central role in modern arithmetic geometry.

### MATH 797RT: ST-Intro/Representation Theory

Prerequisites:

Knowledge of group theory and commutative algebra at the level of Math 611-612 and of topology at the level of Math 671, plus familiarity with manifolds.

Description:

The first two-thirds of the course will be a survey of Lie groups and algebraic groups, with a goal toward gaining familiarity with the main ideas and theorems useful for applications to differential geometry (Lie groups) and to number theory and representation theory (algebraic groups). The last part of the course will highlight some of those applications, including the Bott-Borel-Weil Theorem in both the Lie group and algebraic group setting.

### STAT 607.1: Mathematical Statistics I

Prerequisites:

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

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

Prerequisites:

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

Note:

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

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

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 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 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 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

Prerequisites:

Permission of instructor.

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 697BD: ST-Biomedical and Health Data Analysis

Prerequisites:

Knowledge of calculus and linear algebra are required.
Knowledge of statistics (Stat 516, Stat 608, or equivalent) preferred, but not required.
Knowledge of regression (Stat 525, Stat 625, Stat 697R, or equivalent) preferred, but not required.

Description:

In this course, we will apply several novel machine learning algorithms, including normalization methods, classification and regression analysis on cancer patient data sets to arrive at personalized cancer treatments. We will develop several algorithms for analyzing cancer data sets, including gene expression data sets. 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 cutting-edge methods in computational biology and hopefully find ways to improve them. We will read some recently published papers and implement methods that have been introduced in these papers. 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. There is no exam or final project. Students will be evaluated based on their participation, presentations, and works, including their codes and HWs.

### STAT 697L: ST-Categorical Data Analysis

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 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

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

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 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 725: Estmtn Th and Hypo Tst I

Prerequisites:

Stat 607-608 or permission of instructor.

Recommended Text:

A Course in Large Sample Theory (by Thomas S. Ferguson), Asymptotic Statistics (by A. W. van der Vaart)

Description:

This course treats the advanced theory of statistics, going into a more advanced treatment of some topics first seen in Stat 607-608, from the viewpoint of large-sample (asymptotic) theory. Topics include Mathematical and Statistical Preliminaries; (Weak/Strong) Convergence; Central Limit Theorems (including Lindeberg-Feller Central Limit Theorem and Stationary m-Dependent Sequences); Delta Method and Applications; Order Statistics and Quantiles; Maximum Likelihood Estimation; Set estimation and Hypothesis Testing; U-statistics; Bootstrap and Applications