# Course Descriptions

## Lower Division Courses

### MATH 011: Elementary Algebra

See Preregistration guide for instructors and times

Description:

Beginning algebra enhanced with pre-algebra topics such as arithmetic, fractions, and word problems as need indicates. Topics include real numbers, linear equations and inequalities in one variable, polynomials, factoring, algebraic fractions, problem solving, systems of linear equations, rational and irrational numbers, and quadratic equations.

This course is only offered online through Continuing and Professional Education.

### 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.

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.

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

See Preregistration Guide for instructors and times

Prerequisites:

Math 132 or 136; corequisite: Math 233

Text:

TBA

Description:

(Formerly Math 431) 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 190L: Foundations of Data Science

See SPIRE for instructors and times

Description:

The field of Data Science encompasses methods, processes, and systems that enable the extraction of useful knowledge from data. Foundations of Data Science introduces core data science concepts including computational and inferential thinking, along with core data science skills including computer programming and statistical methods. The course presents these topics in the context of hands-on analysis of real-world data sets, including economic data, document collections, geographical data, and social networks. The course also explores social issues surrounding data analysis such as privacy and design.

### STAT 240: Introduction to Statistics

See Preregistration guide for instructors and times

Description:

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

## Upper Division Courses

### MATH 300.1: Fundamental Concepts of Mathematics

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

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 basic logic (truth tables, negation, quantifiers), set theory (Cantor's notion of size for sets and gradations of infinity, maps between sets, equivalence relations, partitions of sets), and elementary number theory (divisibility, Euclidean algorithm, congruences). Other topics will be included as time allows. Math 300 is designed to help students make the transition from calculus courses to the more theoretical junior-senior level mathematics courses.

### MATH 300.2: Fundamental Concepts of Mathematics

TBA MWF 11:15-12:05

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 basic logic (truth tables, negation, quantifiers), set theory (Cantor's notion of size for sets and gradations of infinity, maps between sets, equivalence relations, partitions of sets), and elementary number theory (divisibility, Euclidean algorithm, congruences). Other topics will be included as time allows. Math 300 is designed to help students make the transition from calculus courses to the more theoretical junior-senior level mathematics courses.

### MATH 300.4: Fundamental Concepts of Mathematics

Eyal Markman TuTh 11:30-12:45

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

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

Description:

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

### MATH 370.1: Writing in Mathematics

Franz Pedit TuTh 1:00-2:15

Prerequisites:

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

Text:

The Poincare Conjecture: In search of the shape of the universe" by Donald O'Shea.

Recommended Text:

The Poincare Conjecture: In search of the shape of the universe" by Donald O'Shea.

Description:

The overall paradigm of the course is to provide the students with a non-compartmentalized view of mathematics. The course is based on material covered in the general audience book The Poincare Conjecture: In search of the shape of the universe" by Donald O'Shea. The content of this book is tantamount to what humans know about the physical world and its mathematical pendant, and hence can be considered a bedrock for anyone who aspires to work as an educator and/or researcher. All students are required to read the book. There will be additional reading assignments, and short lectures by the instructor, on background material as the semester progresses. (Groups of) students will choose topics from the book and will have to write a self contained, educated audience article on the material. All papers have to be written using LaTex word processing (open source). The papers will go through a number of editing cycles and will finally be presented to the class. Some of the class time will be reserved for video taped general mathematical audience lectures by Fields medallists and other prize winning mathematicians on related topics. In addition, the course will reserve one week during which advisors from the career office of the University will provide information about the job application process, resume/cover letter writing, and job interviews. Each student will be requested to hand in a putative job application (cover letter, resume) of their choice.

### MATH 370.2: Writing in Mathematics

TBA 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 and writing skills in mathematics through peer review and revision. Students write on mathematical subject areas, prominent mathematicians, and famous mathematical problems. Prerequisites: MATH 300 and completion of College Writing (CW) requirement.

### MATH 370.3: Writing in Mathematics

TBA 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 and writing skills in mathematics through peer review and revision. Students write on mathematical subject areas, prominent mathematicians, and famous mathematical problems. Prerequisites: MATH 300 and completion of College Writing (CW) requirement.

### MATH 411.2: Introduction to Abstract Algebra I

Luca Schaffler MWF 12:20-1:10

Prerequisites:

MATH 235; MATH 300 or CS 250

Text:

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

Description:

Introduction to abstract algebra, focusing primarily on the theory of groups. There will be regular problem assignments and quizzes, as well as midterm and final examinations.

### MATH 411.3: Introduction to Abstract Algebra I

Luca Schaffler MWF 11:15-12:05

Prerequisites:

MATH 235; MATH 300 or CS 250

Text:

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

Description:

Introduction to abstract algebra, focusing primarily on the theory of groups. There will be regular problem assignments and quizzes, as well as midterm and final examinations.

### MATH 421: Complex Variables

Jeremiah Birrell TuTh 10:00-11:15

Prerequisites:

Math 233

Text:

Complex Variables (Second Edition) by Stephen D. Fisher

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 Laurant series. Classification of isolated singularities. Evaluation of Improper integrals via residues. Conformal mappings.

### MATH 425.1: Advanced Multivariate Calculus

Ivan Mirkovic TuTh 11:30-12:45

Prerequisites:

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

Text:

Vector Calculus by Marsden and Tromba, 5th Ed., W. H. Freeman

Description:

This is a course in differential and integral multivariate calculus from a more advanced perspective than Math 233. We will begin by studying limits, continuity, and differentiation of functions of several variables and vector-valued functions. We will then study integration over regions, the change of variables formula, and integrals over paths and surfaces. The relationship between differentiation and integration will be explored through the theorems of Green, Gauss, and Stokes. Various physical applications, such as fluid flows, force fields, and heat flow, will be covered. While the text covers functions of up to 3 variables we will sketch how everything works for any number of variables.

### MATH 425.2: Advanced Multivariate Calculus

Rob Kusner MW 2:30-3:45

Prerequisites:

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

Text:

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

H. M. Schey, div, grad, curl and all that [ISBN-13: 978-0393925166; ISBN-10: 0393925161]

M. Spivak, Calculus on Manifolds [ISBN-13: 978-0805390216; ISBN-10: 0805390219]

Description:

This course covers the basics of differential and integral calculus in many variables: differentiability, directional and partial derivatives and gradient of functions; critical points without or with constraints (Lagrange-multipliers/tangential-gradient) and the Hessian; vector fields and differential forms; divergence, curl and exterior derivative; line- and surface-integrals; the fundamental theorem of calculus (Gauss/Green/Stokes/Thomson). If time and taste permit, topics from physics (fluids and electromagnetism) and differential geometry (curves and surfaces in space) may also be explored.

### MATH 437: Actuarial Financial Math

Jinguo Lian MWF 1:25-2:15

Prerequisites:

Math 131, 132, with a C or better in Math 132

Text:

ASM Study Manual for Exam FM, 12th or later Edition by Harold Cherry. It can be purchased at http://www.studymanuals.com/Product/Show/453138484

Note:

Required Calculator: any calculator accepted by the Society of Actuaries would be fine for the course, but I will be working with the TI BA II Plus calculator.

Description:

This 3 credit 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

Annie Raymond TuTh 8:30-9:45

Prerequisites:

Calculus (MATH 131, 132, 233), Linear Algebra (MATH 235), and Math 300 or CS 250. For students who have not taken Math 300 or CS 250, the instructor may permit students with sufficient experience in reading and writing mathematical arguments to enroll.

Text:

Harris, Hirst, and Mossinghoff, Combinatorics and Graph Theory, 2nd edition (free online)

Description:

This is a rigorous introduction to some topics in mathematics that underlie areas in computer science and computer engineering, including graphs and trees, spanning trees, and matchings; the pigeonhole principle, induction and recursion, and generating functions. 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: Mathematical Modeling

TBA TuTh 8:30-9:45

Prerequisites:

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

Description:

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

### MATH 461: Affine and Projective Geometry

Paul Hacking MWF 10:10-11:00

Prerequisites:

Math 235 and Math 300

Text:

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

Description:

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

### MATH 471: Theory of Numbers

TBA TuTh 10:00-11:15

Prerequisites:

Math 300 (or CS 250) and CS 121 as pre-requisites is recommended

Description:

Basic properties of the positive integers including congruence arithmetic, the theory of prime numbers, quadratic reciprocity, and continued fractions. Theory applied to develop algorithms and computational techniques of computer science and to cryptography. To help learn these materials, students will be assigned computational projects using computer algebra software. Prerequisite: MATH 233 and 235. Math 300 or COMPSCI 250 as a co-requisite is not absolutely necessary but highly recommended.

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

TBA Wed 4:00-4:50

Prerequisites:

One variable Calculus, Linear Algebra

Description:

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

### MATH 513: Combinatorics

Prerequisites:

Mathematical maturity; calculus; linear algebra; strong performance in some discrete mathematics class, such as COMPSCI 250 or MATH 455. Modern Algebra - MATH 411 - is helpful but not required.

Description:

This course is a basic introduction to combinatorics and graph theory for advanced undergraduates in computer science,
mathematics, engineering and science. Topics covered include: elements of graph theory; Euler and Hamiltonian circuits; graph
coloring; matching; basic counting methods; generating functions; recurrences; inclusion-exclusion; and Polya's theory of counting.

### MATH 523H: Introduction to Modern Analysis

Andrea Nahmod TuTh 10:00-11:15

Prerequisites:

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

Text:

Fundamental Ideas of Analysis by Michael Reed, Wiley, 1998

Description:

This is the first part of the introduction to analysis sequence (523 and 524). This course presents a rigorous development of the real number system, fundamental results of calculus and basic concepts of analysis of functions mostly on the real line.

Covered topics will include the real numbers and their topology, cardinality, convergence of sequences, series of function, , continuity, differentiability, and integration. Emphasis will be placed on rigorous proofs.

### MATH 532H: Nonlinear Dynamics

Panos Kevrekidis TuTh 11:30-12:45

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

Text:

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity), Author: Steven H. Strogatz, Publisher: CRC Press, Edition: 2

Description:

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

### MATH 537: Intro to Mathematics of Finance

HongKun Zhang TuTh 2:30-3:45

Prerequisites:

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

Recommended Text:

Derivative Markets by Robert L. McDonald, 3rd edition.
The 2nd and 3rd editions are on reserve at the library.

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

Eduardo Cattani TuTh 8:30-9:45

Prerequisites:

Math 233, Math 235, and Math 300

Text:

TBA

Recommended Text:

TBA

Description:

This is a second course in Linear Algebra building upon the concepts and techniques introduced in Math 235. We will study the decomposition of matrices, particularly the LU, QR, and singular value decompositions. We also study vector spaces and linear transformations, inner product spaces, orthogonality, and spectral theory. We will emphasize applications of these techniques to various problems including, as time permits: solutions of linear systems, least-square fitting, search engine algorithms, error-correcting codes, fast Fourier transform, dynamical systems.

The coursework will be a mix of proof and computation. For the latter students may choose Matlab or one of the open source programs: Scilab or Octave (both similar to Matlab).

### MATH 545.2: Linear Algebra for Applied Mathematics

Eduardo Cattani TuTh 11:30-12:45

Prerequisites:

Math 233, Math 235, and Math 300

Text:

TBA

Recommended Text:

TBA

Description:

This is a second course in Linear Algebra building upon the concepts and techniques introduced in Math 235. We will study the decomposition of matrices, particularly the LU, QR, and singular value decompositions. We also study vector spaces and linear transformations, inner product spaces, orthogonality, and spectral theory. We will emphasize applications of these techniques to various problems including, as time permits: solutions of linear systems, least-square fitting, search engine algorithms, error-correcting codes, fast Fourier transform, dynamical systems.

The coursework will be a mix of proof and computation. For the latter students may choose Matlab or one of the open source programs: Scilab or Octave (both similar to Matlab).

### MATH 551.1: Intr. Scientific Computing

Matthew Dobson MWF 9:05-9:55

Prerequisites:

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

Text:

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

Important note about the textbook: UMass has an Institutional SIAM Membership. Thus, a free e-book is available through the UMass library. As a side note, make sure that you are connected to the UMass Amherst Libraries network (if not, you can still have off-campus access by clicking "Off-campus login" and entering your SPIRE ID and password). Of course, a physical copy of the book can be purchased directly from the publisher, SIAM at www.siam.org (link is external)

Description:

Simulations and numerical computation drive large portions of technological and scientific developments in the modern world. The course will introduce the foundations for formulating, numerically solving, and assessing the accuracy of solutions to problems that arise in different 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, and numerical integration.

### MATH 551.2: Intr. Scientific Computing

Matthew Dobson MWF 10:10-11:00

Prerequisites:

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

Text:

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

Important note about the textbook: UMass has an Institutional SIAM Membership. Thus, a free e-book is available through the UMass library. As a side note, make sure that you are connected to the UMass Amherst Libraries network (if not, you can still have off-campus access by clicking "Off-campus login" and entering your SPIRE ID and password). Of course, a physical copy of the book can be purchased directly from the publisher, SIAM at www.siam.org (link is external)

Description:

Simulations and numerical computation drive large portions of technological and scientific developments in the modern world. The course will introduce the foundations for formulating, numerically solving, and assessing the accuracy of solutions to problems that arise in different 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, and numerical integration.

### MATH 591CF: Seminar - Cyber Security Faculty Lecture Series

Krista J Gile Wed 1:25-2:15

Description:

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

### STAT 501: Methods of Applied Statistics

Joanna Jeneralczuk TuTh 11:30-12:45

Prerequisites:

Knowledge of high school algebra, junior standing or higher.

Text:

TBA

Description:

A non-calculus-based applied statistics course for graduate students and upper level undergraduates with no previous background in statistics who will need statistics in their future studies and their work. The focus is on understanding and using statistical methods in research and applications. Topics include: descriptive statistics, probability theory, random variables, random sampling, estimation and hypothesis testing, basic concepts in the design of experiments and analysis of variance, linear regression, and contingency tables. The course has a large data-analytic component using a statistical computing package.

### STAT 515.1: Introduction to Statistics I

TBA TuTh 2:30-3:45

Prerequisites:

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

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, the central limit theorem, and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.

### STAT 515.2: Introduction to Statistics I

Jianyu Chen MWF 9:05-9:55

Prerequisites:

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

Description:

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

### STAT 515.3: Introduction to Statistics I

Jianyu Chen MWF 10:10-11:00

Prerequisites:

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

Description:

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

### STAT 515.4: Introduction to Statistics I

TBA TuTh 1:00-2:15

Prerequisites:

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

Description:

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

### STAT 515.6: Introduction to Statistics I

Markos Katsoulakis TuTh 11:30-12:45

Prerequisites:

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

Description:

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

### STAT 516.1: Statistics II

Erin Conlon MWF 11:15-12:05

Prerequisites:

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

Text:

Mathematical Statistics with Applications, 7th Edition, by Wackerly, Mendenhall and Scheaffer

Description:

Continuation of Stat 515. Overall objective of the course is the development of basic theory and methods for statistical inference. Topics include: Sampling distributions; General techniques for statistical inference (point estimation, confidence intervals, tests of hypotheses); Development of methods for inferences on one or more means (one-sample, two-sample, many samples - one-way analysis of variance), inference on proportions (including contingency tables), simple linear regression and non-parametric methods (time permitting).

### STAT 516.2: Statistics II

Erin Conlon MWF 1:25-2:15

Prerequisites:

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

Text:

Mathematical Statistics with Applications, 7th Edition, by Wackerly, Mendenhall and Scheaffer

Description:

Continuation of Stat 515. Overall objective of the course is the development of basic theory and methods for statistical inference. Topics include: Sampling distributions; General techniques for statistical inference (point estimation, confidence intervals, tests of hypotheses); Development of methods for inferences on one or more means (one-sample, two-sample, many samples - one-way analysis of variance), inference on proportions (including contingency tables), simple linear regression and non-parametric methods (time permitting).

### STAT 516.3: Introduction to Statistics I

Instructor TBA
MWF 12:20-1:10

Prerequisites:

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

Text:

Mathematical Statistics with Applications, 7th Edition, by Wackerly, Mendenhall and Scheaffer

Description:

Continuation of Stat 515. Overall objective of the course is the development of basic theory and methods for statistical inference. Topics include: Sampling distributions; General techniques for statistical inference (point estimation, confidence intervals, tests of hypotheses); Development of methods for inferences on one or more means (one-sample, two-sample, many samples - one-way analysis of variance), inference on proportions (including contingency tables), simple linear regression and non-parametric methods (time permitting).

### STAT 525: Regression Analysis

Anna Liu 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. Stat 515 is NOT sufficient background for this course. Familiarity with basic matrix notation and operations is helpful.

Text:

Applied Linear Regression Models, by Kutner, Nachshem and Neter (4th edition) or Applied Linear Statistical Models by Kutner, Nachtshem, Neter and Li (5th edition). Both published by McGraw-Hill/Irwin. 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 our ST526 course. (A) Students planning to take STAT 526 should buy the ALSM textbook.

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 535: Statistical Computing

Patrick Flaherty MWF 11:15-12:05

Prerequisites:

Prior knowledge of statistical methods and programming experience (STAT525 or equivalent).

Description:

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

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

Krista J Gile Thurs 1:00-2:15

Prerequisites:

STAT 515, 516, 525, or equivalent, and permission of instructor. Graduate standing strongly recommended.

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 611: Algebra I

Paul Gunnells MWF 9:05-9:55

Prerequisites:

Undergraduate algebra (equivalent of our Math 411-412)

Description:

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

I. Group Theory and Representation Theory.

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

II. Linear Algebra and Commutative Algebra.

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

III. Field Theory and Galois Theory

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

### MATH 621: Complex Analysis

Siman Wong TuTh 10:00-11:15

Prerequisites:

Advanced Calculus. Students are expected to have a working knowledge of complex numbers and functions at the level of M421 for example.

Text:

Complex Analysis, by Serge Lang. Fourth edition, Springer-Verlag, 2003.

Description:

We will cover the basic theory of functions of one complex variable, at a pace that will allow for the inclusion of some non-elementary topics at the end. Basic Theory: Holomorphic functions, conformal mappings, Cauchy's Theorem and consequences, Taylor and Laurent series, singularities, residues, Riemann mapping theorem; other topics (such as elliptic functions and the Prime Number Theorem) as time permits.

### MATH 623: Real Analysis I

Robin Young MWF 10:10-11:00

Prerequisites:

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

Text:

Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis) (Bk. 3), Authors: Elias M. Stein; Rami Shakarchi, Publisher: Princeton University Press ISBN 978-0-691-11386-9

Description:

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

### MATH 645: ODE and Dynamical Systems

Yao Li TuTh 1:00-2:15

Prerequisites:

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

Text:

Differential Dynamical Systems, by James D. Meiss; SIAM, 2007

Description:

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

### MATH 651: Numerical Analysis I

Qian-Yong Chen MWF 12:20-1:10

Prerequisites:

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

Text:

Kendall E Atkinson, An Introduction to Numerical Analysis}, 2nd edition, John Wiley & Sons

Description:

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

### MATH 671: Topology I

R. Inanc Baykur TuTh 11:30-12:45

Prerequisites:

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

Text:

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

Recommended Text:

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

Description:

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

### MATH 691Y: Applied Math Project Seminar

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

Prerequisites:

Graduate Student in Applied Math MS Program

Description:

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

### MATH 697CP: ST - Convex Polytopes

Alejandro Morales MWF 11:15-12:05

Prerequisites:

Math 455
co-requisite Math 797U Lie algebras is recommended for later parts of the course.

Recommended Text:

Ziegler, Günter M. Lectures on polytopes. Vol. 152. Springer, 2012 (Ch. 0, 2, 7, 8)
Beck, Matthias, and Robins, Sinai. Computing the continuous discretely, second edition, Springer, 2015.
Barvinok, Alexander, Lattice Points, Polyhedra, and Complexity, IAS/Park City Mathematics Series, 2004.
Stanley, Richard P., Two poset polytopes, Discrete Comput. Geom. 1:9-23 (1989).
Postnikov, Alexander, Permutohedra, associahedra, and beyond, International Mathematics Research

Description:

This course is an introduction to the theory of convex polytopes and their applications to algebraic combinatorics. The course will cover basic facts and properties of polytopes including faces of polytopes, valuation theory, Ehrhart theory, triangulations, and zonotopes. We will also tentatively cover the following families of polytopes with interest in other fields including root polytopes, flow polytopes, polytopes from partially ordered sets, and generalized permutahedra.

### MATH 703: Topics in Geometry I

Weimin Chen MWF 1:25-2:15

Prerequisites:

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

Recommended Text:

Introduction to Smooth Manifolds, by John M. Lee

Description:

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

### MATH 731: Partial Differential Equations I

Sohrab Shahshahani MW 8:40-9:55

Prerequisites:

A solid background in multivariable and vector calculus as well as real analysis (including Lebesgue integration, measure theory, Hilbert spaces, and L^p spaces) is required. It will also be assumed that students have basic familiarity with undergraduate level ODEs and PDEs.

Text:

Partial Differential Equations: Second Edition, by Lawrence Evans.

Description:

This is a course in linear partial differential equations. We will discuss the Laplace, heat, and wave equations on Euclidean space, using purely analytical methods. If time allows we will also consider other elliptic, parabolic, and hyperbolic equations, possibly with a view toward nonlinear problems. Along the way may also discuss distributions and Sobolev spaces which are important tools in the modern study of partial differential equations. A good understanding of the material in the graduate real analysis class (623 and possibly 624) as well as fluency in multivariable calculus (in particular the divergence and Stokes theorems and integration by parts) are required.

### MATH 797DE: ST - Dynamical Sys and Ergodic Theory

HongKun Zhang TuTh 1:00-2:15

Prerequisites:

preferred with Math 623 and Math 645, but not required.

Description:

Dynamical systems is an exciting and very active field in pure and applied mathematics, that involves tools and techniques from many areas such as analyses, probability and number theory. A dynamical system can be obtained by iterating a function or letting evolve in time the solution of equation. Even if the rule of evolution is deterministic, the long term behavior of the system is often chaotic. Different branches of dynamical systems, in particular ergodic theory, provide tools to quantify this chaotic behavior and predict it in average. At the beginning of this lecture course we will give a strong emphasis on presenting many fundamental examples of dynamical systems, such as circle rotations, the baker map on the square and the continued fraction map. Driven by the examples, we will introduce some of the phenomena and main concepts which one is interested in studying. In the second part of the course, we will formalize these concepts and cover the basic definitions and some fundamental theorems and results in topological dynamics, in symbolic dynamics and in particular in ergodic theory. During the course we will also mention some applications to other areas of mathematics, such as number theory, and to Monte Carlo method, etc

### MATH 797EC: ST - Elliptic Curves

Tom Weston TuTh 1:00-2:15

Prerequisites:

Math 612 and Math 672 or consent of the instructor

Text:

Joseph Silverman, The Arithmetic of Elliptic Curves, 2nd Edition. Springer-Verlag, Berlin, 2009.

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 797RT: ST - Intro Representation Theory

Ivan Mirkovic TuTh 2:30-3:45

Prerequisites:

Algebra 611-612.

Recommended Text:

Instead of book we will use notes and internet resources.

Description:

At a basic level the linear representations of groups allow one to study arbitrary groups using matrix groups and linear algebra. This course will cover the fundamentals of the representation theory of finite groups, including character theory, induced representations and applications to the study of classes of finite groups.

More generally, the field of representation theory enacts the principle that any object X of interest in mathematics, physics and related disciplines should be
organized according to its symmetry structure S. The standard
implementation of this idea
starts with linearizing the object, i.e., one considers
a vector space V which naturally contains information about
the object X. Then the vector space V will be a
representation'' of the symmetry structure S, meaning that S
will act on V by linear operators.
The goal is to understand this linear algebra object (the representation of S on V) by decomposing it into its simplest constituents (called irreducible representations'').

The simplest symmetry structures are of course groups and
then their infinitesimal versions, the Lie algebras.
The applications are in geometry (harmonic analysis''), number theory
(Galois representations'' and Langlands program ''),
physics (collisions of elementary particles)
etc.

### STAT 605: Probability Theory I

Instructor TBA
TuTh 2:30-3:45

Prerequisites:

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

Text:

A probability path by Sidney I. Resnick, Modern Birkhäuser Classics, Birkhäuser; 2014 edition,
ISBN-10: 0817684085 ISBN-13: 978-0817684082

Recommended Text:

Probability Essentials by Jean Jacod and Philip Protter, Universitext, Springer; 2nd edition (October 4, 2013) ISBN-10: 3540438718 ISBN-13: 978-3540438717
Probability: Theory and Examples by Rick Durrett, Cambridge Series in Statistical and Probabilistic Mathematics Cambridge University Press; 4 edition (August 30, 2010) ISBN-10: 0521765390 ISBN-13: 978-0521765398

Description:

Math 605: In this course we will build up the tools and foundations of probability theory needed for understanding and using statistical theories, stochastic simulation, and stochastic processes. Topics covered in this class are measure and integration (construction of probability spaces), distribution functions, random variables and their simulation, convergence of random variables, laws of large numbers and Monte-Carlo methods, concentration inequalities, central limit theorem, information theory, random walks.
A class in real analysis (integration theory, Math 623) is not required for this class as we will review, as needed, the basic constructions of probability spaces. It can be beneficial to take these two classes concurrently for the student who wants and in-depth understanding of the mathematical foundations of probability.
The primary goal of the class is to understand and master the basic probability tools and concepts needed in modern applications such as in stochastic simulation, data science and machine learning, engineering, and economics. Motivated students with various backgrounds are welcome.
The class is the first part of the sequence Math605/606 and Math 606 will cover the theory of stochastic processes and stochastic simulation: Martingale theory, Poisson processes, Markov chains in discrete and continuous time, Markov chain Monte-carlo, Brownian motion.

### STAT 607: Mathematical Statistics I

Daeyoung Kim TuTh 10:00-11:15

Prerequisites:

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

Text:

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

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: Regression Modeling

Krista J Gile TuTh 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., ST516 or equivalent. You must be familiar with these statistical concepts beforehand. ST515 by itself is NOT a sufficient background for this course! Familiarity with basic matrix notation and operations is helpful.

Text:

Applied Linear Regression Models, by Kutner, Nachshem and Neter (4th edition) or Applied Linear Statistical Models by Kutner, Nachtshem, Neter and Li (5th edition). Both published by McGraw-Hill/Irwin. 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 our ST526 course. (A) Students planning to take STAT 526 should buy the ALSM textbook.

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 697S: ST - Statistical Network Inference

Vincent Lyzinski MWF 11:15-12:05

Prerequisites:

Math 545 or equivalent; A working knowledge of probability such as STAT 515/605 or STAT 607; A working knowledge of statistics such as STAT 516/608 or equivalent

Text:

No required textbook

Description:

Across a broad array of scientific fields (e.g., neuroscience, sociology, physics, etc.), it is increasingly common to model complex interactions and dependencies via networks/graphs. With this influx of network-valued data, statistical modeling and inference of networks has become increasingly prevalent. In this course, we will investigate recent advances in statistical inference on networks. We will discuss the development of progressively more nuanced statistical models for networks, focusing on the recent advances in developing classical inference tasks within a network framework (e.g., hypothesis testing, clustering, classification, etc.). The class will be partially driven by the interests of the students, with students leading regular discussions of relevant papers from the literature.

### STAT 725: Estmtn Th and Hypo Tst I

Daeyoung Kim TuTh 11:30-12:45

Prerequisites:

Stat 607-608, Stat 705 or concurrent registration in Stat 705 or permission of instructor.

Recommended Text:

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

Description:

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

### STAT 797N: ST - Non-Parametric Regress/Data

John Staudenmayer MWF 1:25-2:15

Prerequisites:

Stat 607/608, a course in regression, *or* permission of the instructor

Recommended Text:

Semiparametric Regression (ISBN-10: 0521785162)
by Ruppert, Wand, and Carroll

Description:

Non-parametric regression techniques and concepts such as splines, kernels, regularization, and cross-valdiation are important for the development and understanding of modern machine / statistical learning and also extremely useful and flexible tools for data analysis. Students in this course will learn how to use non-parametric techniques to analyze data and how the methods work. The course will focus on practical methods for data analysis, not just theory.

Topics to include:
1. Kernel density estimation and kernel smoothing.
2. Spline smoothing
3. Extensions to spline models:
mixed models and penalized splines