# Course Descriptions

## Lower Division Courses

### MATH 100: Basic Math Skills for the Modern World

See Preregistration guide for instructors and times

Description:

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

### MATH 101: Precalculus, Algebra, Functions and Graphs

See Preregistration guide for instructors and times

Prerequisites:

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

Note:

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

Description:

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

### MATH 102: Analytic Geometry and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

Math 101

Description:

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

### MATH 103: Precalculus and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

The trigonometry topics of MATH 104.

### MATH 104: Algebra, Analytic Geometry and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

### MATH 113: Math for Elementary Teachers I

See Preregistration guide for instructors and times

Prerequisites:

MATH 011 or satisfaction of R1 requirement.

Description:

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

### MATH 114: Math for Elementary Teachers II

See Preregistration guide for instructors and times

Prerequisites:

MATH 113

Description:

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

### MATH 121: Linear Methods and Probability for Business

See Preregistration guide for instructors and times

Prerequisites:

Working knowledge of high school algebra and plane geometry.

Description:

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

### MATH 127: Calculus for Life and Social Sciences I

See Preregistration guide for instructors and times

Prerequisites:

Proficiency in high school algebra, including word problems.

Description:

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

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

See Preregistration guide for instructors and times

Prerequisites:

Proficiency in high school algebra, including word problems.

Description:

Honors section of Math 127.

### MATH 128: Calculus for Life and Social Sciences II

See Preregistration guide for instructors and times

Prerequisites:

Math 127

Description:

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

### MATH 131: Calculus I

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

### MATH 131H: Honors Calculus I

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

Honors section of Math 131.

### MATH 132: Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

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

### MATH 132H: Honors Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

Honors section of Math 132.

### MATH 233: Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

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

### MATH 233H: Honors Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

Honors section of Math 233.

### MATH 235: Introduction to Linear Algebra

See Preregistration guide for instructors and times

Prerequisites:

Math 132 or consent of the instructor.

Description:

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

### MATH 235H: Honors Introduction to Linear Algebra

See Preregistration guide for instructors and times

Prerequisites:

Math 132 or consent of the instructor.

Description:

Honors section of Math 235.

### MATH 331: Ordinary Differential Equations for Scientists and Engineers

See Preregistration Guide for instructors and times

Prerequisites:

Math 132

Text:

TBA

Description:

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

### STAT 111: Elementary Statistics

See Preregistration guide for instructors and times

Prerequisites:

High school algebra.

Description:

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

### STAT 240: Introduction to Statistics

See Preregistration guide for instructors and times

Description:

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

## Upper Division Courses

### MATH 300.1: Fundamental Concepts of Mathematics

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 300.2: Fundamental Concepts of Mathematics

A Havens TuTh 2:30-3:45

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 300.3: Fundamental Concepts of Mathematics

Weimin Chen MWF 11:15-12:05

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

How to Prove it, by Daniel J. Velleman, 2nd edition, 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). 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

Franz Pedit MW 4:00-5:15

Prerequisites:

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

Description:

In the year 2000 the Clay Institute listed seven (then) unsolved problems across all areas of mathematics considered the most challenging and important for the new millennium. So far only one of the problems, the Poincare Conjecture, has been solved by Perleman (who refused to collect the one million dollar prize stating that mathematics should never be done for money). In this course we shall focus on this conjecture by studying shapes in dimension 1,2, 3 (and possibly higher) to get a feel of what the conjecture is actually saying. We shall also attempt to get an idea of the notion of curvature of shapes and how Perleman utilized this in his proof of the conjecture.

The course is structured around writing assignments on these topics which will be discussed in class. The assignments will l be graded by the instructor and the course TA. During the last quarter of the semester there will be group project presentations.

All writing has to be done in the word processing system LaTex, which is the only word processing system capable of producing a professional layout. Templates and some basic tutorials will be provided. We shall NOT spend time on resume and job application writing. There is ample opportunity to receive expert help from the career center. A representative of the center will give a presentation of their mission and resources in class.

### MATH 370.2: Writing in Mathematics

Leili Shahriyari TuTh 10:00-11:15

Prerequisites:

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

Description:

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

### MATH 370.3: Writing in Mathematics

Leili Shahriyari TuTh 11:30-12:45

Prerequisites:

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

Description:

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

### MATH 405: Mathematical Computing

Hans Johnston TuTh 2:30-3:45

Prerequisites:

COMPSCI 121 (or INFO 190S/CICS 110), MATH 235, and COMPSCI 250 (or MATH 300)

Description:

This course is about how to write and use a modern programming language to explore and solve problems in pure and applied mathematics.  We will use Python, and the first part of the course will review core language features and apply them to problems in mathematics.  We will introduce specialized mathematical packages such as numpy.  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 use code to solve and explore mathematical questions in several project areas.  Students will work on projects both individually and in small groups.

### MATH 411.1: Introduction to Abstract Algebra I

Paul Gunnells TuTh 8:30-9:45

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 11:30-12:45

Prerequisites:

Math 235; Math 300 or CS 250.

Description:

This course is an introduction to group theory, which is one of the oldest branches of modern algebra, 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 10:00-11:15

Prerequisites:

MATH 235; MATH 300 or CS 250

Description:

This course is an introduction to group theory, which is one of the oldest branches of modern algebra, 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 421: Complex Variables

Eyal Markman TuTh 11:30-12:45

Prerequisites:

Math 233

Text:

Complex Variables and Applications, 8th Edition,
James W. Brown and Ruel V. Churchill, McGraw-Hill, 2009.

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 437: Actuarial Financial Math

Jinguo Lian MWF 1:25-2:15

Prerequisites:

Math 131 and 132 or equivalent courses with C or better

Recommended Text:

ASM Study Manual for Exam FM 16th or later Edition by Cherry & Shaban, ISBN 978-1-64756-753-8.

Note:

TI-BA II Plus Calculator is required.

Description:

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

### MATH 455: Introduction to Discrete Structures

Louis Gaudet TuTh 1:00-2:15

Prerequisites:

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

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 (if time permits) combinatorial geometry. The course integrates mathematical theories with applications to concrete problems from other disciplines using discrete modeling techniques. Small student groups will be formed to investigate a modeling problem independently, and each group will report its findings to the class in a final presentation. Satisfies the Integrative Experience for BS-Math and BA-Math majors.

### MATH 456.1: 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 456.2: Mathematical Modeling

Patrick Flaherty TuTh 11:30-12:45

Prerequisites:

Math 233 and Math 235

Recommended Text:

"The Doctrine of Chances" by Stewart Ethier

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 461: Affine and Projective Geometry

Jie Min TuTh 8:30-9:45

Prerequisites:

Math 235 and Math 300

Text:

John Stillwell, The Four Pillars of Geometry (accessible through library)

Description:

This course explores various approaches to geometry, as we trace the evolution of mathematical thinking and rigor from ancient to modern: 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, where projective geometry will be studied in some detail.

### MATH 471: Theory of Numbers

Siman Wong MWF 10:10-11:00

Prerequisites:

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

Text:

TBA

Description:

The goal of this course is to give a rigorous introduction to elementary number theory. While no prior background in number theory will be assumed, the ability to read and write proofs is essential for this course. The list of topics include (but is not limited to): Euclidean Algorithm, Linear Diophantine Equations, the Fundamental Theorem of Arithmetic, congruence arithmetic, continued fractions, the theory of prime numbers, primitive roots, and quadratic reciprocity, with an emphasis on applications to and connections with cryptography. Homework will consist of both rewritten assignments and computer projects.

### MATH 481: Knot Theory

R. Inanc Baykur TuTh 1:00-2:15

Prerequisites:

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

Description:

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

### MATH 490RH: Mathematics of Risk Management

Patrick Flaherty TuTh 1:00-2:15

Prerequisites:

STAT 315/515, CICS 110 or equivalent, MATH 235, or permission of instructor

Text:

Doctrine of Chances by Stewart Ethier 978-3540787822
A Course in Game Theory by Tom Ferguson 978-9813227347

Description:

This course covers probabilistic aspects of risk management intended for those familiar with probability theory. Games of chance are used as models of real-world situations of decision-making under uncertainty. Students will gain a deeper understanding of the mathematical foundations of probability theory and stochastic processes. They will apply concepts in game theory and probability theory to real-world problems in risk management.

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

Franz Pedit Mon 5:30-6:30

Prerequisites:

One variable Calculus, Linear Algebra

Recommended Text:

Instructor hands out problems on a weekly basis.

Description:

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

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

Siman Wong Fri 1:25-2:30

Prerequisites:

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

Note:

If you wish to enroll in this course, please fill out a request here at the link below by April 30, 2024:

Description:

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

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

Maryclare Griffin Thu 2:30-3:45

Description:

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

### MATH 513: Combinatorics

Mark C. Wilson TuTh 1:00-2:15

Prerequisites:

COMPSCI 250 or MATH 455 with a grade of 'B' or better.

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. Prerequisites: mathematical maturity, calculus, linear algebra, discrete mathematics course such as CompSci 250 or Math 455. Math 411 recommended but not required.

### MATH 523H: Introduction to Modern Analysis

Sohrab Shahshahani TuTh 10:00-11:15

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

Sohrab Shahshahani TuTh 8:30-9:45

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. Proficiency in linear algebra is very important.

Description:

This course provides an introduction to systems of differential equations and dynamical systems, as well as chaotic dynamics. Geometric and analytical methods of describing the behavior of solutions will be developed and illustrated in the context of low-dimensional systems, including behavior near fixed points and periodic orbits, phase portraits, Lyapunov stability, Hamiltonian systems, bifurcation phenomena, and chaotic dynamics.

### MATH 537: Intro to Mathematics of Finance

Mike Sullivan TuTh 10:00-11:15

Prerequisites:

Math 233 and either Stat 515 or MIE 273

Description:

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

### MATH 545.1: Linear Algebra for Applied Mathematics

Andreas Buttenschoen TuTh 2:30-3:45

Prerequisites:

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

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 545.2: Linear Algebra for Applied Mathematics

Eric Sarfo Amponsah TuTh 10:00-11:15

Prerequisites:

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

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 545.3: Linear Algebra for Applied Mathematics

Andreas Buttenschoen TuTh 4:00-5:15

Prerequisites:

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

Description:

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 551.1: Intr. Scientific Computing

Weiqi Chu MWF 10:10-11:00

Prerequisites:

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

Description:

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

### MATH 551.2: Intr. Scientific Computing

Matthew Dobson MWF 9:05-9:55

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 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 551.3: Intr. Scientific Computing

Matthew Dobson MWF 11:15-12:05

Prerequisites:

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

Description:

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.

### STAT 310.1: Fundamental Concepts/Stats

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, 516, 525, and 535. It is intended to be the first course in statistics taken by math majors interested in statistics. Concepts covered include point estimation, interval estimation, prediction, testing, and regression, with focus on sampling distributions and the properties of statistical procedures. The course will be taught in a hands-on manner, introducing powerful statistical software used in practical settings and including methods for descriptive statistics, visualization, and data management.

### STAT 310.2: Fundamental Concepts/Stats

Sepideh Mosaferi TuTh 8:30-9:45

Prerequisites:

MATH 132

Description:

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

### STAT 315.1: Introduction to Statistics I

Qian-Yong Chen MW 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 315.2: Introduction to Statistics I

Instructor TBA 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 315.3: Introduction to Statistics I

Instructor TBA MWF 10:10-11:00

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: Introduction to Statistics I

Yao Li 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 315.5: Introduction to Statistics I

Kien Nguyen 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: Introduction to Statistics I

Kien Nguyen 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 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

Haben Michael TuTh 2:30-3:45

Prerequisites:

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

Recommended Text:

Mathematical Statistics with Applications, 7th edition by Wackerly, Mendenhall, 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 315/515/515H 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

Jonathan Larson MWF 12:20-1:10

Prerequisites:

Stat 315/515/515H 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 525.1: Regression Analysis

Haben Michael TuTh 10:00-11:15

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 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).

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  Stat 516, and basic matrix algebra.  Satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

### STAT 525.2: Regression Analysis

Haben Michael TuTh 11:30-12:45

Prerequisites:

Stat 516 or equivalent : Previous coursework in Probability and Statistics, including knowledge of estimation, confidence intervals, and hypothesis testing and its use in at least one and two sample problems. You must be familiar with these statistical concepts beforehand. Stat 515 by itself is NOT a sufficient background for this course! Familiarity with basic matrix notation and operations is helpful.

Text:

Applied Linear Regression Models by Kutner, Nachsteim and Neter (4th edition) or Applied Linear Statistical Models by Kutner, Nachtsteim, Neter and Li (5th edition).

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 Stat 516, and basic matrix algebra.  Satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

### STAT 526: Design Of Experiments

Jonathan Larson MWF 1:25-2:15

Prerequisites:

STAT 516 and COMPSCI 121, INFO 190S, or CICS 110.

Description:

Planning, statistical analysis and interpretation of experiments. Designs considered include factorial designs, randomized blocks, latin squares, incomplete balanced blocks, nested and crossover designs, mixed models. Has a strong applied component involving the use of a statistical package for data analysis. Prerequisite: previous coursework in statistics.

### 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 535.1: Statistical Computing

Carlos Soto TuTh 11:30-12:45

Prerequisites:

Stat 516 and CICS 110/Info 190S or 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 MCMC, simulation, sampling, and optimization. The class will be taught in a modern statistical computing language (R).

### STAT 535.2: Statistical Computing

Shai Gorsky Wed 6:00-8:30

Prerequisites:

Stat 516 and CICS 110/Info 190S or CS 121

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:

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 540: Statistical Methods/DataSci

Maryclare Griffin TuTh 10:00-11:15

Prerequisites:

Stat 525

Note:

Course combined with Stat 630

Description:

Introduction to some modern statistical regression and classification techniques including logistic regression, nearest neighbor methods, discriminant analysis, kernel smoothing, smoothing spline, local regression, generalized additive models, decision trees, random forests, support vector machines and deep learning. Clustering methods such as K-means and hierarchical clustering will be introduced. Finally, there will also topics on resampling-based model evaluation methods and regularization-based model selection methods. The course emphasizes the mathematics behinds these methods sufficient to understand the differences among the methods as well as the practical implementation of them.

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

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

Prerequisites:

Graduate standing, STAT 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

Luc Rey-Bellet TuTh 11:30-12:45

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.

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

Alexei Oblomkov TuTh 8:30-9:45

Prerequisites:

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

Description:

The course will focus on rings and modules, including a review of linear algebra, multilinear algebra, basic commutative algebra, and introduction to homological algebra. We will move fast, and a lot of homework should be expected. The non-commutative aspects (Galois theory, representation theory of finite groups, etc.) will be covered in Math 612.

### MATH 623: Real Analysis I

Andrea Nahmod TuTh 1:00-2:15

Prerequisites:

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

Description:

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

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

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

### MATH 645: ODE and Dynamical Systems

Leili Shahriyari TuTh 2:30-3:45

Prerequisites:

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

Description:

Classical theory of ordinary differential equations and some of its modern developments in dynamical systems theory, including linear systems and their applications. We will use Python programming to implement mathematical models and investigate their behaviors.

### MATH 651: Numerical Analysis I

Brian Van Koten MWF 1:25-2:15

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, and 523, or equivalent classes.

Text:

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

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 679: Numerical Algorithms and Practices

Eric Polizzi TuTh 1:00-2:15

Description:

This course covers various topics Scientific Computing including: basic numerical techniques of linear algebra and their applications, data formats and practices, matrix computations with an emphasis on solving sparse linear systems of equations and eigenvalue problems. Students will learn about the state-of-the-art programming practices in numerical linear algebra, and will be introduced to numerical parallel algorithms and parallel programming with OpenMP, MPI and hybrid. For students to be successful in this course they should know Linear Algebra basics, and have interests in math and programing.

### MATH 690STE: Zeta Functions of Algebraic Varieties

Siman Wong MWF 11:15-12:05

Prerequisites:

Math 611 and 612

Description:

Given a collection of polynomial equations defined over Q, we can associate to it a family of generating functions, called zeta functions.  They are built using a topological construction based on local information (specifically solutions of these equations modulo prime powers).  But there are deep and important conjectures predicting that these functions encode global information --- the Q-solutions of these equations.  Much of the subject of modern Arithmetic Geometry is about understanding this interplay between local and global objects.

The goal of this course is to survey these important ideas and problems through concrete examples.  We will study the Weil conjectures for varieties over finite fields, connections with character sums, construction of global zeta functions, and if time permits and depending on the interests/background of the audience, modern conjectures about special values of L-functions.  While the focus is on the arithmetic of the varieties, this class should be of interests to those who would like to learn the connection between number theory, algebraic geometry and representation theory.

### MATH 690STG: Real and Artificial Neural Networks

Yao Li TuTh 1:00-2:15

Prerequisites:

STAT 315/515, MATH 331, working knowledge of MATLAB and Python

Description:

The course covers a variety of biological neuronal network and artificial neural network topics. We will begin with an introduction to mathematical neuroscience, covering mathematical models for single neurons and neuronal networks. We then delve into how artificial neural networks draw inspiration from biological counterparts. Selected topics include the anatomy and function of the primary visual cortex (V1) and its connection to convolutional neural networks (CNNs), as well as machine learning with spiking neural networks (SNNs).

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

Instructor TBD Mon 4:00-5:15

Prerequisites:

Open to Graduate Teaching Assistants in Math and Statistics

Description:

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

### MATH 703: Topics in Geometry I

Franz Pedit MW 2:30-3:45

Prerequisites:

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

Recommended Text:

Spivak: Differential Geometry I-V
Warner: Introduction to Manifolds and Lie groups
Nicolaescu: Lectures on the Geometry of Manifolds

Note:

We will not follow a particular book. The instructor will hand out useful notes at the beginning of the course. For students who like to consult books on manifolds, see recommended texts.

Description:

An introduction to the basic concepts of Differential Geometry, Differential Topology and Lie Theory. Topics include: A review of differential maps between Euclidean spaces, Inverse and Implicit Function Theorems. Differentiable manifolds, definition and examples. Regular and critical values, Sard's Theorem, Submanifolds, immersions and embeddings, Vector bundles, tangent and cotangent bundles. Vector fields, ODE's on manifolds, Lie bracket, integrable distributions, Frobenius Theorem. Differential forms, Exterior differential.

### MATH 714: Arithmetic of Elliptic Curves

Paul Gunnells TuTh 10:00-11:15

Description:

Elliptic curves, as the only smooth projective algebraic curves equipped with a group law, play a central role in modern arithmetic geometry. The goal of this course is to learn the tools and techniques required to study these groups over the rational numbers by first studying them over finite fields, p-adic fields and archimedean fields.

### MATH 717: Representation Theory

Eric Sommers TuTh 1:00-2:15

Prerequisites:

Math 612. Students who have a good knowledge of group theory and Galois theory, as well as familiarity with modules and multilinear algebra (tensor, symmetric and exterior algebras) may request permission to join the class.

Recommended Text:

"Abstract Algebra", Dummit and Foote
"Linear Representations of Finite Groups", by J. P. Serre
"The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions", by Bruce Sagan
"Representation Theory: A First Course", by Fulton and Harris

Description:

Representation theory studies the ways that groups, algebras and other algebraic structures can act by compatible linear transformations on a vector space. The first half of the course will cover representations of finite groups, including the classification of the irreducible representations of the symmetric group and connections to symmetric functions. The remainder of the course will cover various topics. Possible topics include modular representation theory, representations of finite groups of Lie type, Hecke algebras and their representations, and the irreducible representations of Weyl groups via the construction of Springer.

### MATH 731: Partial Differential Equations I

Robin Young TuTh 10:00-11:15

Prerequisites:

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

Description:

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

### MATH 790STE: Topological Data Analysis

R. Inanc Baykur TuTh 10:00-11:15

Prerequisites:

Undergraduate linear algebra (Math 235) and multivariable calculus (Math 233). Point-set topology and elementary algebraic topology (Math 671) is recommended, but not essential.

Description:

This course is a gentle introduction to Topological Data Analysis (TDA), a fast-evolving field that focuses on identifying and analyzing the shape (topology) of data. TDA provides tools and concepts to analyze and understand complex high-dimensional datasets. The course aims to discuss essential methods, aiming for a robust understanding and application of these concepts, including in machine learning.

### STAT 607.1: Mathematical Statistics I

John Staudenmayer MWF 10:10-11:00

Prerequisites:

Advanced calculus and linear algebra, or consent of instructor.

Text:

Casella and Berger: Statistical Inference, second edition.

Recommended Text:

Wasserman, All of Statistics

Description:

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

### STAT 607.2: Mathematical Statistics I

Hyunsun Lee Mon 6:00-8:30

Prerequisites:

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

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:

The first part of a two-semester graduate level sequence in probability and statistics, this course develops probability theory at an intermediate level (i.e., non measure-theoretic - Stat 605 is a course in measure-theoretic probability) and introduces the basic concepts of statistics.

Topics include: general probability concepts; discrete probability; random variables (including special discrete and continuous distributions) and random vectors; independence; laws of large numbers; central limit theorem; statistical models and sampling distributions; and a brief introduction to statistical inference. Statistical inference will be developed more fully in Stat 608.
This course is also suitable for graduate students in a wide variety of disciplines and will give strong preparation for further courses in statistics, econometrics, and stochastic processes, time series, decision theory, operations research, etc.

You will be expected to read sections of the text book in parallel with topics covered in lectures, since important part of graduate study is to learn how to study independently.

### STAT 625.1: Regression Modeling

Lulu Kang MW 2:30-3:45

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., Stat 516 or equivalent. You must be familiar with these statistical concepts beforehand. Stat 515 by itself is NOT a sufficient background for this course! Familiarity with basic matrix notation and operations is helpful.

Description:

Regression 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

Shai Gorsky Tue 6:00-8:30

Prerequisites:

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

Note:

This 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:

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 630: Statistical Methods/DataSci

Maryclare Griffin TuTh 10:00-11:15

Prerequisites:

Stat 525 or 625

Note:

Course combined with Stat 540

Description:

Introduction to some modern statistical regression and classification techniques including logistic regression, nearest neighbor methods, discriminant analysis, kernel smoothing, smoothing spline, local regression, generalized additive models, decision trees, random forests, support vector machines and deep learning. Clustering methods such as K-means and hierarchical clustering will be introduced. Finally, there will also topics on resampling-based model evaluation methods and regularization-based model selection methods. The course emphasizes the mathematics behinds these methods sufficient to understand the differences among the methods as well as the practical implementation of them.

### STAT 631: Categorical Data Analysis

Zijing Zhang Thu 6:00-8:30

Prerequisites:

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

Text:

Categorical Data Analysis, 3rd edition, by Alan Agresti, Wiley. ISBN-13: 978-0470463635.

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:

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 690STA: Appl Semiparametric Regression

John Staudenmayer MWF 11:15-12:05

Prerequisites:

Stat 625

Text:

Harezlak, Ruppert, and Wand: Semiparametric Regression with R (Use R!)

Recommended Text:

Ruppert, Wand, and Carroll: Semiparametric Regression

Description:

Using data to estimate relationships between predictors and responses is an important task in statistics and data science. When datasets are large, modern methods have been developed that allow us to estimate those relationships without making strong assumptions about those relationships-  i.e. we can let the data determine how E(y|x) relates to x. In statistics, these methods are generally referred to as 'nonparametric regression.'

This applied graduate course will focus on learning to use nonparametric regression to analyze data. We will read a book, 'Semiparametric Regression with R,' and implement / understand the methods in that book. We will address simple and multiple regression data, binary/count data, spatial data, and correlated/time series data. The course will require a substantial project that will be done in a group of size 3 or more.

### STAT 691P: S - Project Seminar

Erin Conlon Sat 1:00-3:30

Prerequisites:

Permission of instructor.

Note:

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

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 725: Estmtn Th and Hypo Tst I

Daeyoung Kim MW 2:30-3:45

Prerequisites:

Stat 607-608

Recommended Text:

Elements of Large-Sample Theory (by Erich Lehmann),
Theory of Point Estimation (by Erich Lehmann and George Casella),
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 Application