# 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 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 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 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 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 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 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

Kevin Sackel TuTh 8:30-9:45

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 300.2: Fundamental Concepts of Mathematics

Kevin Sackel TuTh 10:00-11:15

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

Eric Sommers TuTh 1:00-2:15

Prerequisites:

Math 132 with a grade of C or better

Text:

Introduction to Mathematical Structures and Proofs, by Larry J. Gerstein. ISBN:9781461442653. eBook or physical book.

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 CS 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

A Havens MWF 11:15-12:05

Prerequisites:

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

Description:

While the mathematicians of the pre-internet age often spread their mathematical ideas within the community via written letters prior to publication, modern mathematical correspondence and exposition is rapidly facilitated by a variety of digital tools. Of great importance to the publishing process in mathematical sciences is the LaTeX markup language, used to typeset virtually all modern mathematical publications, even at the pre-print stage. In this course we will develop facility with LaTeX, and develop a variety of writing practices important to participation in the mathematical community. There will be regular written assignments completed in LaTeX, as well as collaborative writing assignments, owing to the importance of collaborative writing in mathematical research. Writing topics may include proofs, assignment creation, pre-professional writing (resumes/cover letters, research and teaching statements), expository writing for a general audience, recreational mathematics, and the history of mathematics. Short writing assignments on such topics will be assigned in response to assigned readings from a variety of accessible/provided sources. Towards the end of the semester groups will complete a research paper of an expository nature and craft a seminar style presentation. This course meets the junior year writing requirement.

### MATH 370.3: Writing in Mathematics

A Havens MWF 10:10-11:00

Prerequisites:

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

Description:

While the mathematicians of the pre-internet age often spread their mathematical ideas within the community via written letters prior to publication, modern mathematical correspondence and exposition is rapidly facilitated by a variety of digital tools. Of great importance to the publishing process in mathematical sciences is the LaTeX markup language, used to typeset virtually all modern mathematical publications, even at the pre-print stage. In this course we will develop facility with LaTeX, and develop a variety of writing practices important to participation in the mathematical community. There will be regular written assignments completed in LaTeX, as well as collaborative writing assignments, owing to the importance of collaborative writing in mathematical research. Writing topics may include proofs, assignment creation, pre-professional writing (resumes/cover letters, research and teaching statements), expository writing for a general audience, recreational mathematics, and the history of mathematics. Short writing assignments on such topics will be assigned in response to assigned readings from a variety of accessible/provided sources. Towards the end of the semester groups will complete a research paper of an expository nature and craft a seminar style presentation. This course meets the junior year writing requirement.

### MATH 405: Mathematical Computing

Matthew Dobson MWF 9:05-9:55

Prerequisites:

CS 121 or INFO 190S, Math 235, 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

Kristin DeVleming TuTh 10:00-11:15

Prerequisites:

Math 235; Math 300 or CS 250

Description:

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

### MATH 411.2: Introduction to Abstract Algebra I

Wendelin Lutz TuTh 1:00-2:15

Prerequisites:

Math 235; Math 300 or CS 250

Recommended Text:

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

Description:

This course is an introduction to group theory, which is one of the oldest branches of modern algebra, and 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 411.3: Introduction to Abstract Algebra I

Wendelin Lutz TuTh 11:30-12:45

Prerequisites:

Math 235; Math 300 or CS 250

Recommended Text:

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

Description:

This course is an introduction to group theory, which is one of the oldest branches of modern algebra, and 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 412: Introduction to Abstract Algebra II

Jenia Tevelev TuTh 10:00-11:15

Prerequisites:

Math 411

Text:

A first course in abstract algebra by John Fraleigh

Description:

This course is a continuation of Math 411. We will study properties of rings and fields. A ring is an algebraic system with two operations (addition and multiplication) satisfying various axioms. Rings and fields are ubiquitous in mathematics, especially in all branches of modern algebra such as Number Theory, Algebraic Geometry, and Representation Theory. Basic examples of rings are the ring of integers and the ring of polynomials. Later in the course we will apply some of the results of ring theory to construct and study fields. At the end we will outline the main results of Galois theory which relates properties of algebraic equations to properties of certain finite groups called Galois groups. For example, we will see that a general equation of degree 5 can not be solved in radicals. In addition to learning theoretical tools, we will also experiment with rings and fields using the computer algebra system MAGMA.

### MATH 421: Complex Variables

Tom Weston TuTh 1:00-2:15

Prerequisites:

Math 233

Text:

Complex Analysis for Mathematics and Engineering (6th edition) by Mathews and Howell.

Description:

Complex numbers and functions, analytic functions, complex integration, series, residues, conformal mappings. Applications: computation of real integrals, Dirichlet's boundary value problem and its application to physics and engineering.

### 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

Jinguo Lian MWF 1:25-2:15

Prerequisites:

Math 233 and Math 235. Some familiarity with a programming language is desirable (R studio, Python, etc.). Some familiarity with statistics and probability is desirable.

Recommended Text:

ASM Study Manual Program for SRM- Statistics for Risk Modeling, 4th or later edition by Abraham Weishaus.

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

Jinguo Lian MWF 12:20-1:10

Prerequisites:

Math 233 and Math 235. Some familiarity with a programming language is desirable (R studio, Python, etc.). Some familiarity with statistics and probability is desirable.

Recommended Text:

ASM Study Manual Program for SRM- Statistics for Risk Modeling, 4th or later edition by Abraham Weishaus.

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 456.3: Mathematical Modeling

Markos Katsoulakis MW 2:30-3:45

Prerequisites:

Math 233, Math 235, Math 331. Familiarity with probability at the level of Stat 315 (formerly Stat 515) or CompSci 240 or higher is strongly advised. Some familiarity with a programming language is necessary (Python, Matlab, Java, C++, etc.).

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. In the Spring of 2024, we will focus on modeling through Machine Learning and in particular on Generative Artificial Intelligence models. During the last decade, generative models have produced breakthrough results in a wide area of applications including image generation, text and speech synthesis, applications in science and engineering such as surrogate and sub-grid scale simulators (e.g. in aerospace, atmosphere ocean science and materials) and discovery of new molecules and proteins for drug design, to name only a few. In this course, we will cover to varying degrees some of the the main families of generative models such as Gaussian Mixture Models as generative models, Normalizing Flows, Generative Adversarial Networks, Variational Auto-encoders, Energy-based Models, Deep Autoregressive Models and Probabilistic Diffusion Models.
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 Math majors.

### MATH 471: Theory of Numbers

Weimin Chen MWF 11:15-12:05

Prerequisites:

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

Text:

Number Theory, A lively Introduction with Proofs, Applications, and Stories, by James Pommersheim, Tim Marks, and Erica Flapan. Wiley 2010.

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 475: History of Mathematics

A Havens MWF 1:25-2:15

Prerequisites:

Math 131, 132, 233, and either Math 300 or CS 250.

Description:

This is an introduction to the history of mathematics from ancient civilizations to present day. Students will study major mathematical discoveries in their cultural, historical, and scientific contexts. This course explores how the study of mathematics evolved through time, and the ways of thinking of mathematicians of different eras - their breakthroughs and failures. Students will have an opportunity to integrate their knowledge of mathematical theories with material covered in General Education courses. Forms of evaluation will include a group presentation, class discussions, and a final paper. Satisfies the Integrative Experience requirement for BA-MATH and BS-MATH majors.

### MATH 522: Fourier Methods

Manas Bhatnagar MWF 11:15-12:05

Prerequisites:

MATH 235, 300, and 331

Description:

The course introduces and uses Fourier series and Fourier transform as a tool to understand varies important problems in applied mathematics: linear ODE & PDE, time series, signal processing, etc. We'll treat convergence issues in a non-rigorous way, discussing the different types of convergence without technical proofs. Topics: complex numbers, sin & cosine series, orthogonality, Gibbs phenomenon, FFT, applications, including say linear PDE, signal processing, time series, etc; maybe ending with (continuous) Fourier transform.

### MATH 523H: Introduction to Modern Analysis I

Franz Pedit MW 4:00-5:15

Prerequisites:

Math 233, Math 235, and Math 300 or CS 250

Note:

There is no particular text book needed for the course. Instructor will suggest some reading material at the beginning of the class.

Description:

This course covers a rigorous development of the real number system and fundamental results of Calculus. We will study the real numbers and their topology, convergence of sequences/series, integration and differentiation, and function sequences/ series. Emphasis will be placed on rigorous proofs.

### MATH 524: Introduction to Modern Analysis II

Franz Pedit MW 2:30-3:45

Prerequisites:

MATH 523H, good knowledge of linear algebra (abstract vector spaces, linear maps etc.)

Note:

Instructor will suggest various reading material at beginning of class. No particular text book will be followed.

Description:

Topology of Euclidean space; metric spaces; normed vector spaces; functions on normed vector spaces: continuity, differentiability; implicit and inverse function theorems; Taylor series, min/max criteria; integration, fundamental theorem of ODEs on Banach spaces.

### MATH 534H: Introduction to Partial Differential Equations

Oussama Landoulsi MW 2:30-3:45

Prerequisites:

Math 233, 235, and 331.

Complex variables (M421) and Introduction to Real Analysis (M523H) are definitely a plus, and helpful, but not absolutely necessary.

Description:

An introduction to PDEs (partial differential equations), covering some of the most basic and ubiquitous linear equations modeling physical problems and arising in a variety of contexts. We shall study the existence and derivation of explicit formulas for their solutions (when feasible) and study their behavior. We will also learn how to read and use specific properties of each individual equation to analyze the behavior of solutions when explicit formulas do not exist. Equations covered include: transport equations and the wave equation, heat/diffusion equations and the Laplace’s equation on domains. Along the way we will discuss topics such as Fourier series, separation of variables, energy methods, maximum principle, harmonic functions and potential theory, etc.
Time-permitting, we will discuss some additional topics (eg.. Schrödinger equations, Fourier transform methods, eigenvalue problems, etc.). The final grade will be determined on the basis of homework, attendance and class participation, midterms and final projects.

### MATH 536: Actuarial Probability

Jinguo Lian MWF 10:10-11:00

Prerequisites:

Math 233 and Stat 315/515

Recommended Text:

ASM Study Manual Program for Exam P, 5th or later Edition by Weishaus.

Description:

Math 536 is three credit hours course, which serves as a preparation for the first SOA/CAS actuarial exam on the fundamental probability tools for quantitatively assessing risk, known as Exam P (SOA) or Exam 1 (CAS). The course covers general probability, random variables with univariate probability distributions (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma, and normal), random variables with multivariate probability distributions (including the bivariate normal), basic knowledge of insurance and risk management, and other topics specified by the SOA/CAS exam syllabus.

### MATH 537: Intro. to Math of Finance

Kien Nguyen TuTh 11:30-12:45

Prerequisites:

Math 233 and either Stat 315/515 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

Owen Gwilliam MWF 12:20-1:10

Prerequisites:

Math 233 and 235, both with grade of 'C' or better, Math 300 or CS 250

Text:

Applied Linear Algebra (2nd edition) by Peter J. Olver and Chehrzad Shakiban

Recommended Text:

Linear Algebra and its Applications by Gilbert Strang
Linear Algebra Done Right by Sheldon Axler

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

Owen Gwilliam MWF 10:10-11:00

Prerequisites:

Math 233 and 235, both with grade of 'C' or better, Math 300 or CS 250

Text:

Applied Linear Algebra (2nd edition) by Peter J. Olver and Chehrzad Shakiban

Recommended Text:

Linear Algebra and its Applications by Gilbert Strang
Linear Algebra Done Right by Sheldon Axler

Description:

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

### MATH 545.3: Linear Algebra for Applied Mathematics

Eric Sarfo Amponsah TuTh 10:00-11:15

Prerequisites:

Math 233 and 235, both with grade of 'C' or better, Math 300 or CS 250

Text:

Linear Algebra and Its Applications, 4th ed., By Gilbert Strang,
Other Texts: Elementary Linear Algebra, by Ken Kuttler.

Description:

Math 545 is an advanced linear algebra course that builds on the concepts and techniques introduced in Math 235 (Intro Linear Algebra). We will study the decomposition of matrices, particularly the LU, QR, Cholesky and SVD decompositions. The coursework will be a mix of proof and computation. We will also study vector spaces and linear transformations, inner product spaces, orthogonality, spectral theory, and Jordan form. We will emphasize applications of these techniques to various problems including solutions of linear systems, least-square fitting, fast Fourier transforms, dynamical systems. (Time permitting) The final part covers algorithms for computation of eigenpairs, iterative methods for linear systems, etc.

### MATH 545.4: Linear Algebra for Applied Mathematics

Andreas Buttenschoen TuTh 11:30-12:45

Prerequisites:

Math 233 and 235, both with grade of 'C' or better, Math 300 or CS 250

Recommended Text: Description:

Math 545 is an advanced linear algebra course that builds on the concepts and techniques introduced in Math 235 (Intro Linear Algebra). We will study the decomposition of matrices, particularly the LU, QR, Cholesky and SVD decompositions. The coursework will be a mix of proof and computation. We will also study vector spaces and linear transformations, inner product spaces, orthogonality, spectral theory, and Jordan form. We will emphasize applications of these techniques to various problems including solutions of linear systems, least-square fitting, fast Fourier transforms, dynamical systems. The final part covers algorithms for computation of eigenpairs, iterative methods for linear systems, etc.

### MATH 548: Stochastic Processes and Simulation

Kien Nguyen TuTh 1:00-2:15

Prerequisites:

STATISTC 315, STATISTC 515, or CICS 110 (previously INFO 190S)

Description:

The course will cover the following topics in the core of the theory of Random and Stochastic Processes.We will introduce the students to some fundamental stochastic processes such as discrete state Markov chains, Poisson processes, and Brownian motion, as well as an array of important stochastic models. Computer programming will be a central part of this course.The theoretical part of this course includes analysis of random walks, convergence of discrete and continuous-time Markov processes to stationarity, Poisson processes and other point processes, Brownian motion and a bit Martingale processes. In addition, we also offer a series of lectures on topics of stochastic simulations--introduction to Monte Carlo methods and computer modeling of stochastic systems. Monte Carlo topics that we will cover include random variable generation, expectation estimation with confidence interval formation, importance sampling, stochastic optimization, MCMC algorithms and sampling of Brownian motion.

### MATH 551.1: Intr. Scientific Computing

Hans Johnston TuTh 11:30-12:45

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:

The course will introduce basic numerical methods used for solving problems that arise in a variety scientific fields. Properties such as accuracy of methods, their stability and efficiency will be studied. We will cover finite precision arithmetic and error propagation, linear systems of equations, root finding, interpolation, approximation of functions, numerical integration and numerical methods for differential equations.

Students will gain practical programming experience in implementing the methods using MATLAB, which is available for FREE after following the instructions on UMass IT website. The use of MATLAB for homework assignments is mandatory. We will also discuss some important practical considerations of implementing numerical methods using such languages as FORTRAN or C.

### MATH 551.2: Intr. Scientific Computing

Brian Van Koten MWF 12:20-1:10

Prerequisites:

MATH 233 & 235 and either COMPSCI 121, E&C-ENG 122, PHYSICS 281, or E&C-ENG 242

Knowledge of a programming language, e.g. C, C++, Java, Julia, or Python.

Description:

A practical overview of computational methods used in science, statistics, industry, and machine learning. Topics will include: an introduction to python programming and software for scientific computing such as NumPy and LAPACK, numerical linear algebra, optimization and root-finding, approximation of functions by splines and trigonometric polynomials, and the Fast Fourier Transform. Applications may include regression problems in statistics, audio and image processing, and the calculation of properties of molecules. Homework will be assigned frequently. Each assignment will involve both mathematical theory and python programming. There will be no exams. Instead, each student will pursue an open-ended project related to a topic discussed in class.

### MATH 551.3: Intr. Scientific Computing

Maria Correia TuTh 2:30-3:45

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 552: Applications of Scientific Computing

Weiqi Chu TuTh 2:30-3:45

Prerequisites:

Math 233, Math 235, Math 331 or permission of instructor, Math 551 (or equivalent) or permission of instructor.

Knowledge of a programming language, e.g. Matlab, Python, C, or C++.

Description:

Introduction to the application of computational methods to models arising in science and engineering, concentrating mainly on the solution of partial differential equations. Topics include finite differences, boundary value problems, numerical ODEs, and spectral methods.

### MATH 563H: Differential Geometry

Paul Hacking TuTh 11:30-12:45

Prerequisites:

Very good understanding of Multivariable Calculus and Linear Algebra (233 and 235). Math 331 highly recommended.

Text:

There is no required text for this course. I plan to follow the notes of Ted Shifrin available at http://alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

Description:

This course is an introduction to differential geometry, where we apply theory and computational techniques from linear algebra, multivariable calculus, and differential equations to study the geometry of curves and surfaces.

### MATH 590STA: Intro Math Machine Learning

Benjamin Zhang and Ziyu Chen MWF 1:25-2:15

Prerequisites:

We expect a strong command of probability, multivariable calculus, and linear algebra at the level of STAT 315/515, MATH 233, and MATH 545, or permission of the instructor. Basic programming experience is assumed. Recommended: Familiarity of numerical methods at the level of MATH 551.

Recommended Text:

Probabilistic Machine Learning by Murphy and The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman

Description:

This course will provide an introduction to machine learning from a mathematical perspective. The primary objective of this course is to cultivate in students a sense of mathematical curiosity and equip them with the skills to ask mathematical questions when studying machine learning algorithms. Classical supervised learning methods will be presented and studied using the tools from information theory, statistical learning theory, optimization, and basic functional analysis. The course will cover three categories of machine learning approaches: linear methods, kernel-based methods, and deep learning methods, each applied to regression, classification, and dimension reduction. Coding exercises will be an essential part of the course to empirically study and strengths and weakness of methods.

### STAT 310: Fundamental Concepts of Statistics

Qian Zhao TuTh 10:00-11:15

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 315/515, 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 315.1: Statistics I

Yao Li TuTh 10:00-11:15

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 315.2: Statistics I

Wuzhe Xu MWF 12:20-1:10

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 315.3: Statistics I

Wuzhe Xu MWF 1:25-2:15

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 315.4: Statistics I

Yalin Rao MWF 11:15-12:05

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 315.5: Statistics I

Yao Li TuTh 8:30-9:45

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 315.6: Statistics I

Luc Rey-Bellet TuTh 1:00-2:15

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 315.7: Statistics I

Mike Sullivan TuTh 2:30-3:45

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 501: Methods of Applied Statistics

Joanna Jeneralczuk TuTh 11:30-12:45

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 516.1: Statistics II

Ted Westling TuTh 11:30-12:45

Prerequisites:

Stat 315/515 or 315H/515H with a grade of “C" or better

Text:

Mathematical Statistics with Applications (7th Edition). D. D. Wackerly, W. Mendenhall and R. L. Schaeffer

Description:

Continuation of Stat 315/515. 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

Sepideh Mosaferi TuTh 10:00-11:15

Prerequisites:

Stat 315/515 or 315H/515H with a grade of “C" or better

Description:

Continuation of Stat 315/515. 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

Ted Westling TuTh 2:30-3:45

Prerequisites:

Stat 315/515 or 315H/515H with a grade of “C" or better

Text:

Mathematical Statistics with Applications (7th Edition). D. D. Wackerly, W. Mendenhall and R. L. Schaeffer

Description:

Continuation of Stat 315/515. 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

Sepideh Mosaferi TuTh 1:00 - 2:15

Prerequisites:

Stat 315/515 or 315H/515H with a grade of “C" or better

Text:

Mathematical Statistics with Applications (7th Edition). D. D. Wackerly, W. Mendenhall and R. L. Schaeffer

Description:

Continuation of Stat 315/515. 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

Daeyoung Kim MWF 10:10-11:00

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 315/515 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 525.2: Regression Analysis

Jonathan Larson MWF 12:20-1:10

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 315/515 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 525.3: Regression Analysis

Yalin Rao MWF 1:25-2:15

Prerequisites:

Stat 516 or equivalent : Previous coursework in Probability and Statistics, including knowledge of estimation, confidence intervals, and hypothesis testing and its use in at least one and two sample problems. You must be familiar with these statistical concepts beforehand. Stat 315/515 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 526: Design Of Experiments

Zijing Zhang Th 6:00-8:30

Prerequisites:

Stat 516 or equivalent coursework in statistics, encompassing proficiency in estimation, hypothesis testing, and confidence intervals

Text:

Applied Linear Statistical Models, 5th Edition; Authors: Kutner, Nachtsheim, Neter, Li; ISBN-13 Number 9780073108742.

Note:

This class meets on the Newton Mount Ida Campus of UMass-Amherst. For those unable to attend in person, remote participation is available through synchronous sessions via Zoom.

Description:

An applied statistics course on planning, statistical analysis, and interpretation of experiments of various types. Coverage includes factorial designs, randomized blocks, incomplete block designs, nested and crossover designs. Computer analysis of data using the programming software SAS (no prior SAS experience assumed).

### STAT 530: Analysis of Discrete Data

Daeyoung Kim MWF 12:20-1:10

Prerequisites:

Statistics 525

Recommended Text:

1. Friendly, M. and Meyer, D. (2016). Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data. Chapman & Hall.
2. Agresti, A. (2013). Categorical Data Analysis, 3rd ed., NY: Wiley.
3. Agresti, A. (2007). Introduction to Categorical Data Analysis, 2nd ed., NY: Wiley.

Description:

Discrete/Categorical data are prevalent in many applied fields, including biological and medical sciences, social and behavioral sciences, and economics and business. This course provides an applied treatment of modern methods for visualizing and analyzing broad patterns of association in discrete/categorical data. Topics include forms of discrete data, visualization/exploratory methods for discrete data, discrete data distributions, correspondence analysis, logistic regression models, models for polytomous responses, loglinear and logit models for contingency tables, and generalized linear models. This is primarily an applied statistics course. While models and methods are written out carefully with some basic mathematical derivations, the primary focus of the course is on the understanding of the visualization and modeling techniques for discrete data, presentation of associated models/methods, data analysis, interpretation of results, statistical computation and model building.

### STAT 535: Statistical Computing

Carlos Soto MW 2:30-3:45

Prerequisites:

Stat 516 and CompSci 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 590T: Clinical Trials

Jonathan Larson MWF 10:10-11:00

Prerequisites:

STATISTC 315 (or STATISTC 515) and 516

Description:

This course will cover all aspects of conducting a clinical trial, from design to reporting. Although the course will focus mainly on statistical considerations, we will also discuss ethical, methodological, and regulatory considerations. The goal is to prepare students to serve as statisticians on research teams conducting clinical trials. Lectures are concurrent with STAT 690CT.

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

Krista J Gile and Anna Liu W 8:40-9:55

Prerequisites:

Graduate standing, STAT 315 (or 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 606: Stochastic Processes and Applications

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

Prerequisites:

Stat 605 or Stat 607, that is a strong background in probability. A good working knowledge of linear algebra and analysis will be helpful as well.

Text:

Detailed class notes are provided. Recommended readings can be found in the syllabus.

Description:

This course is an introduction to stochastic processes. The course will cover Monte Carlo methods, Markov chains in discrete and continuous time, random walks, martingales, and Brownian motion. Theory and applications will each play a major role in the course. Applications will range widely and may include problems from population genetics, statistical physics, chemical reaction networks, and queueing systems, for example.

### MATH 612: Algebra II

Kristin DeVleming TuTh 8:30-9:45

Prerequisites:

Math 611 (or consent of the instructor).

Description:

A continuation of Math 611. Topics in group theory (e.g., Sylow theorems, solvable and simple groups, Jordan-Holder and Schreier theorems, finitely generated Abelian groups). Topics in ring theory (matrix rings, prime and maximal ideals, Noetherian rings, Hilbert basis theorems). Modules, including cyclic, torsion, and free modules, direct sums, tensor products. Algebraic closure of fields, normal, algebraic, and transcendental field extensions, basic Galois theory. Prerequisite: Math 611 or equivalent.

### MATH 621: Complex Analysis

Alexei Oblomkov MWF 12:20-1:10

Prerequisites:

Advanced Calculus. Students are expected to have a working knowledge of complex numbers and functions at the level of Math 421 for example.

Description:

Complex number field, elementary functions, holomorphic functions, integration, power and Laurent series, harmonic functions, conformal mappings, applications.

### MATH 624: Real Analysis II

Andrea Nahmod TuTh 2:30-3:45

Prerequisites:

Math 523H, Math 524 and Math 623.

Description:

This is the second part of a 2-semester introduction to Real Analysis (namely Math 623 in the Fall, and Math 624 in the Spring) which covers parts of Vol. III and of Vol. IV of Stein&Shakarchi texts.

Math 624 is a continuation of Math 623. We start where Math 623 left off in the Fall and cover in particular the following topics: signed measures; Hilbert spaces and L2 theory; compact operators; the Fourier transform; Banach spaces; elementary operator theory and linear functionals; Lp spaces theory: duality, interpolation, fundamental inequalities and approximation theorems. Time permitting we will discuss some applications in harmonic analysis and some distribution theory.

The prerequisites for this class are Math 623 covering most of chapters 1, 2, 3(part) and 6 (part) of Stein-Shakarchi’s Real Analysis book (Vol. III) (namely having a working knowledge of Measure theory: Lebesgue measure and Integrable functions (Chapter 1); Integration theory: Lebesgue integral, convergence theorems and Fubini theorem (Chapter 2); Differentiation and Integration. Functions of bounded variation (Chapter 3) and some abstract measure theory (first part of Chapter 6) as well as a working knowledge of undergraduate Analysis (as for example taught in classes like M523H and M524H).

### MATH 646: Applied Math and Math Modeling

Qian-Yong Chen TuTh 1:00-2:15

Prerequisites:

Math 523 or equivalent, or permission of the instructor. Knowledge of basic coding is required. Python is preferred, MATLAB is another option.

Text:

Applied Mathematics by David Logan (3rd or 4th edition).
3rd edition: ISBN-10: 0471746622; ISBN-13: 978-0471746621.
4th edition: ISBN 978-1-118-47580-5

Recommended Text:

Lin and Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences,
ISBN: 978-0-89871-229-2,
eISBN: 978-1-61197-134-7

Description:

This course covers classical methods in applied mathematics and math modeling. The topics include dimensional analysis, asymptotics, regular and singular perturbation theory for ordinary differential equations, variation of calculus, random walks and the diffusion limit, classical solution techniques for PDE, common methods for parameter estimation like Maximum Likelihood Estimation (MLE), Maximum a Posteriori (MAP) estimation, Bayesian estimation.
The techniques will be applied to models arising throughout the natural sciences. The course grade will be based on homework (one assignment every two weeks) and a group project (each group consists of two students).

### MATH 652: Int Numerical Analysis II

Brian Van Koten MWF 1:25-2:15

Prerequisites:

Math 651 or permission of the instructor

Description:

Presentation of the classical finite difference methods for the solution of the prototype linear partial differential equations of elliptic, hyperbolic, and parabolic type in one and two dimensions. Finite element methods developed for two dimensional elliptic equations. Major topics include consistency, convergence and stability, error bounds, and efficiency of algorithm.

### MATH 672: Algebraic Topology

Martina Rovelli TuTh 11:30-12:45

Prerequisites:

Math 671, Math 611 or equivalent.

Description:

An introduction to the basic tools of algebraic topology, which studies topological spaces and continuous maps by producing associated algebraic structures (groups, vector spaces, rings, and homomorphism between them). Emphasis will be placed on being able to compute these invariants, not just on their definitions and associated theorems.

### MATH 690STC: Generating Functions

Paul Gunnells MW 8:40-9:55

Description:

Generating functions are a basic counting technique in combinatorics with many applications to different fields, including geometry, number theory, and representation theory. This course will be a fast-paced introduction to the subject with an emphasis on examples. Topics will include ordinary and exponential generating functions, rational generating functions, algebraic generating functions, combinatorics of gaussian integrals and matrix models, and applications to counting graphs, hypergraphs, and maps on surfaces.

### MATH 705: Symplectic Topology

Weimin Chen MWF 1:25-2:15

Prerequisites:

A solid understanding of Math 703. Basic elements of Riemannian geometry, Kahler geometry, and characteristic classes are preferable, but not absolutely required.

Text:

Instructor will provide lecture notes.

Description:

This course is an introduction to symplectic and contact geometry, as outlined below.

Part 1. Symplectic Geometry
1. Basic notions and examples.
2. Linear symplectic geometry.
1) Symplectic vector spaces
2) Symplectic vector bundles
3. Moser's argument.
1) Weinstein’s neighborhood theorems
2) Stability theorems
4. Symplectic circle actions.
5. Symplectic cutting and symplectic blowing-up.

Part 2. Contact Geometry
1. Basic notions and examples.
2. Stability and neighborhood theorems.
3. Contact structures on 3-manifolds
1) Legendrian and transverse knots
2) Overtwisted v.s. tight contact structures and symplectic fillings
3) Surfaces in a contact 3-manifold

Final Grade is based on a few homework assignments, a final presentation, and in-class participation.

### MATH 706: Stochastic Calculus

Matthew Dobson MWF 11:15-12:05

Description:

This course provides an introduction to the theory of stochastic differential equations oriented towards topics useful in applications (Brownian motion, stochastic integrals, and diffusion as solutions of stochastic differential equations), and the study of diffusion in general (forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus, as well as Girsanov's theorem, Feynman-Kac formula, Martingale representation theorem).  Applications to mathematical finance will be included as time permits.

### MATH 708: Complex Algebraic Geometry

Eyal Markman TuTh 1:00-2:15

Prerequisites:

Holomorphic functions of one complex variable (at the level of Math 621), Differentiable Manifolds and their deRham cohomology (at the level of Math 703).

Text:

Complex Geometry, an introduction, by Daniel Huybrechts, Springer Univeritext, 2005.

Recommended Text:

Principle of algebraic geometry, by P. Griffiths and J. Harris

Description:

An introductory course to complex algebraic geometry. The basic techniques of Kahler geometry, Hodge theory, line and vector bundles, needed for the study of the geometry and topology of complex projective algebraic varieties, will be introduced and illustrated in basic examples.

Outline of topics. Complex Manifolds, Sheaf cohomology, Kahler manifolds, Hodge Theory, the Hard Lefschetz Theorem, Holomorphic Vector bundles, Kodaira's Vanishing and Embedding theorems, other topics as time permits.

Homework will be assigned regularly and graded.

### MATH 718: Lie Algebras

Eric Sommers TuTh 11:30-12:45

Prerequisites:

Math 611 required, Math 612 recommended

Text:

Introduction to Lie Algebras and Representation Theory, by James E. Humphreys (3rd edition)

Description:

The goal of the course is the classification of semisimple Lie algebras over the complex numbers and an introduction to their representation theory. The classification is essentially the same as that for simply-connected compact Lie groups, which are central objects in mathematics and physics. Topics covered include representations of sl(2), Jordan decomposition, structure theorems, Weyl groups, roots systems, Dynkin diagrams, complete reducibility, finite-dimensional representations and their characters formulas. Students with a good background in both linear algebra and group theory may contact the instructor to enroll without the Math 611 prerequisite.

### MATH 725: Intr-Fnctnl Anls I

Robin Young TuTh 10:00-11:15

Prerequisites:

Math 623 or 705

Description:

Banach and Hilbert spaces, continuous linear operators, spectral theory, Banach algebras.

### MATH 790STB: Probabilistic Methods in Nonlinear Evolution Equations

Andrea Nahmod TuTh 11:30-12:45

Prerequisites:

Math 623-624. Basic knowledge of probability such as that taught in Math 605. Basic knowledge of PDEs, including solving via Banach fixed point argument/Picard iterations.
Acquaintance with distributions, Sobolev spaces and weak convergence of measures would also be useful.
Consult with the instructor if needed

Description:

The study of randomness in partial differential equations (PDEs) goes back more than seventy years and include examples such as the modeling of random vibrations of strings, or the scattering of waves by objects that are imbedded in random media. Nonlinear dispersive PDEs naturally appear as models describing wave phenomena in quantum mechanics, nonlinear optics, plasma physics, water waves, and atmospheric sciences. Due to their ubiquitousness they have been at the center of profound research both from the applied community as well as from the theoretical one. One way in which randomness enters the field of nonlinear dispersive PDE is via the random data Cauchy initial value problem for (deterministic) equations, such as the nonlinear Schrodinger (NLS) and the nonlinear wave equations (NLW). The interest comes from two fundamental problems: (1) invariance of measures such as Gibbs measures which are physical equilibria for these systems; arising naturally in statistical mechanics and closely related also to QFT models such as the F4, and (2) the study of generic behavior of solutions in the probabilistic sense, and how they are expected to be better than worst case (exceptional) scenarios. The study of this subject in the context of dispersive PDEs can be traced back to Lebowitz-Rose-Speer (1988, 1989) and Bourgain (1994, 1996) concerning the Gibbs measure for NLS. Since then there have been substantial developments of their ideas by many different researchers, extending them in different directions (geometric, infinite volume, other dispersive relations). In recent years, especially since 2018, this field has seen significant progress and many new ideas and methods have been introduced that go beyond the original ideas of Bourgain, including hyperbolic versions of paracontrolled calculus (Gubinelli-Koch-Oh and Bringmann), the method of random averaging operators and the theory of random tensor (both by Deng-Nahmod-Yue). These new methods have led to the resolution of several important open questions in this field, and are expected to play more important roles in future developments. The aim of this course is to provide the foundations upon which these recent developments have built upon, and in particular have a working knowledge of Bourgain's seminal works in the subject.

### STAT 608.1: Mathematical Statistics II

John Staudenmayer MWF 11:15-12:05

Prerequisites:

STAT 607 or permission of the instructor.

Description:

This is the second part of a two semester sequence on probability and mathematical statistics. ST607 covered probability, basic statistical modelling, and an introduction to the basic methods of statistical inference with application to mainly one sample problem. In ST608 we pick up some additional probability topics as needed and examine further issues in methods of inference including more on likelihood based methods, optimal methods of inference, more large sample methods, Bayesian inference and decision theoretic approaches. The theory is utilized in addressing problems in nonparametric methods, two and multi-sample problems, and categorial, regression and survival models. As with ST607 this is primarily a theory course emphasizing fundamental concepts and techniques.

### STAT 608.2: Mathematical Statistics II

Hyunsun Lee M 6:00-8:30

Prerequisites:

STAT 607 or equivalent, or permission of the 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 is the second part of a two semester sequence on probability and mathematical statistics. Stat 607 covered probability, discrete/continuous distributions, basic convergence theory and basic statistical modelling. In Stat 608 we cover an introduction to the basic methods of statistical inference, additional probability topics and examine further issues in methods of inference including likelihood based methods, optimal methods of inference, large sample methods, Bayesian inference and Resampling methods. The theory is utilized in addressing problems in parametric/nonparametric methods, two and multi-sample problems, various hypothesis testing and regression. As with Stat 607, this is primarily a theory course emphasizing fundamental concepts and techniques.

### STAT 610: Bayesian Statistics

Erin Conlon Sat 1:00-3:30

Prerequisites:

Graduate students only. A one-year graduate level calculus-based statistical theory course such as STAT 607-608 or STAT 315/515-516 or the equivalent is required, experience with regression at the level of STAT 625 is required, knowledge of matrix algebra, and prior experience with R including coding and data analysis (for example, at the level of STAT 535).

Text:

Bayesian Methods for Data Analysis, 3rd Edition, Carlin and Louis (2008), Taylor and Francis/CRC Press. ISBN Number: 9781584886976.

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 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 630: Statistical Methods/DataSci

Shai Gorsky Tu 6:00-8:30

Prerequisites:

Open to Graduate Students only. Undergraduates may enroll with permission of instructor.

Probability and Statistics at a calculus-based level such as Stat 607 and Stat 608 (concurrent) or Stat 315/515 and Stat 516 (concurrent), and knowledge of regression at the level of Stat 525 or Stat 625. Students must have an understanding of linear algebra at the level of Math 235. Students must have prior experience with a statistical programming language such as R, Python or MATLAB.

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 provides an introduction to the statistical techniques that are most applicable to data science. Topics include regression, classification, resampling, linear model selection and regularization, tree-based methods, support vector machines and unsupervised learning. The course includes a computing component using statistical software.

### STAT 632: ST- Applied Multivariate Stats

Anna Liu Mon 4:30-5:45 (Mt Ida campus) and Wed 2:30-3:45 (Amherst campus)

Prerequisites:

Probability and Statistics at a calculus-based level such as Stat 607 and Stat 608 (concurrent) or
Stat 315 (previously Stat 515) and Stat 516. Prior experience with R/Python/MATLAB is strongly
recommended.

Text:

“Applied Multivariate Statistical Analysis”, 6th edition, by R. A. Johnson and D. W. Wichern,
Prentice Hall. ISBN-13: 978-0131877153.

Note:

This course may be taken in a hybrid remote/in-person mode. Please enroll and contact the instructor if you would like to take the course in a hybrid remote/in-person mode.
This class meets Mondays on the Newton Mount Ida Campus of UMass-Amherst, and Wednesdays on the Amherst Campus of UMass-Amherst,

Description:

This course provides an introduction to the more commonly used multivariate statistical methods. Topics include principal component analysis, factor analysis, clustering, discrimination and classification, multivariate analysis of variance (MANOVA), and repeated measures analysis. The course includes a computing component. At the end of the course, the student will understand the various methods of multivariate data analysis, determine the appropriate multivariate statistical method to be used for a given data set based on the study objectives, write programs using the R programming language to carry out multivariate data analyses, understand how to verify assumptions that are needed for the various multivariate data analysis methods and understand how to interpret the results of multivariate data analyses.

### STAT 633: Data Visualization

Shai Gorsky W 6:00-8:30

Prerequisites:

Open to Graduate Students only. Undergraduates may enroll with permission of instructor.

Prerequisites: Probability and Statistics at a calculus-based level such as Stat 607 and Stat 608 (concurrent) or Stat 315/515 and Stat 516 (concurrent). Students must have prior experience with a statistical programming language such as R, Python or MATLAB.

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 increasing production of descriptive data sets and corresponding software packages has created a need for data visualization methods for many application areas. Data visualization allows for informing results and presenting findings in a structured way. This course provides an introduction to graphical data analysis and data visualization. Topics include exploratory data analysis, data cleaning, examining features of data structures, detecting unusual data patterns, and determining trends. The course will also introduce methods to choose specific types of graphics tools and understanding information provided by graphs.

### STAT 690STB: Accelerated Bayesian Statistic

Lulu Kang TuTh 1:00-2:15

Prerequisites:

STATISTC 607 & 608 or STATISTC 315/515 & 516; STATISTC 525 or 625; previous experience with Bayesian inference, such as STATISTIC 610 or BIOSTATS 710

Text:

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D., Vehtari, A., and Rubin, D. B. (2013) Bayesian Data Analysis, Third Edition, Chapman & Hall/CRC.

Recommended Text:
• Peter D. Hoff (2009) A First Course in Bayesian Statistical Methods, Springer.
• Jim Albert (2007) Bayesian Computation with R, Springer.
• R. Christensen, W. Johnson, A. Branscum, T. E. Hanson (2010) Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians, CRC Press.

• Dalgaard, Peter (2008) Introductory Statistics with R, Springer. (ebook at UMass)

Description:

This course gives students a rigorous introduction to the theory of Bayesian Statistical Inference and Data Analysis, including prior and posterior distributions, Bayesian estimation and testing, Bayesian computation theories and methods, and implementation of Bayesian computation methods using popular statistical software. The early part of the course focuses on fundamental Bayesian inference and data analysis. The second part covers more advanced topics including various sampling methods and regression models. Compared to the existing course on Bayesian statistics, including STAT 610 and BIOSTATS 730, this course covers more comprehensive topics on Bayesian statistical models and computation. It also emphasizes more on theoretical basis of various Bayesian models and some advanced computing methods. It prepares students for research in statistics and related areas as well as application of Bayesian data analysis for complex real-world problems.

### STAT 690T: Clinical Trials

Jonathan Larson MWF 10:10-11:00

Prerequisites:

STATISTC 607 & 608

Description:

This course will cover all aspects of conducting a clinical trial, from design to reporting. Although the course will focus mainly on statistical considerations, we will also discuss ethical, methodological, and regulatory considerations. The goal is to prepare students to serve as statisticians on research teams conducting clinical trials.