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 102: Analytic Geometry and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

Math 101

Description:

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

MATH 104: Algebra, Analytic Geometry and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

MATH 113: Math for Elementary Teachers I

See Preregistration guide for instructors and times

Prerequisites:

MATH 011 or satisfaction of R1 requirement.

Description:

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

MATH 114: Math for Elementary Teachers II

See Preregistration guide for instructors and times

Prerequisites:

MATH 113

Description:

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

MATH 121: Linear Methods and Probability for Business

See Preregistration guide for instructors and times

Prerequisites:

Working knowledge of high school algebra and plane geometry.

Description:

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

MATH 127: Calculus for Life and Social Sciences I

See Preregistration guide for instructors and times

Prerequisites:

Proficiency in high school algebra, including word problems.

Description:

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

MATH 128: Calculus for Life and Social Sciences II

See Preregistration guide for instructors and times

Prerequisites:

Math 127

Description:

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

MATH 128H: Honors Calculus for Life and Social Sciences II

See Preregistration guide for instructors and times.

Prerequisites:

Math 127

Description:

Honors section of Math 128.

MATH 131: Calculus I

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

MATH 132: Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

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

MATH 233: Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

Techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals.

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 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 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

Weimin Chen MWF 11:15-12:05

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

An Introduction to Mathematical Thinking, by William J. Gilbert and Scott A. Vanstone.

Note:

Math 300 students are required to register also for the 1-credit co-seminar Math 391A. Seminar times will be arranged during the first week of classes.

Description:

The goal is that you learn to read, understand, and construct coherent logically correct proofs, so that you may more easily make the transition from calculus to the more theoretical junior-senior courses, especially abstract algebra and modern analysis. Starting with explicit axioms and precisely stated definitions, you will systematically develop basic propositions about induction, equivalence relations, real numbers, infinite sets, group theory, and metric spaces and point set topology. You will be provided with the needed background about logic, sets, and functions. For nearly every class you will create written mathematical proofs. You are expected to participate actively in class, including at the co-seminar.

MATH 300.2: Fundamental Concepts of Mathematics

Eric Sommers TuTh 10:00-11:15

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

TBD

Note:

Math 300 students are required to register for the 1-credit co-seminar Math 391A. Seminar times will be arranged during the first week of classes.

Description:

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

MATH 300.3: Fundamental Concepts of Mathematics

Paul Hacking TuTh 1:00-2:15

Prerequisites:

Math 132 with a grade of C or better

Text:

T. Sundstrom, Mathematical Reasoning: Writing and Proof, version 2.0. Available for free download at: http://scholarworks.gvsu.edu/books/7/

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

Robin Koytcheff MWF 11:15-12:05

Prerequisites:

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

Text:

None.

Recommended Text:

None.

Note:

This course satisfies the Junior Year Writing requirement.

Description:

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

MATH 370.2: Writing in Mathematics

Robin Koytcheff MWF 12:20-1:10

Prerequisites:

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

Text:

None.

Recommended Text:

None.

Note:

This course satisfies the Junior Year Writing requirement.

Description:

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

MATH 411: Introduction to Abstract Algebra I

Gufang Zhao MWF 10:10-11:00

Prerequisites:

Math 235, Math 300

Text:

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

Recommended Text:

Michael Artin, "Algebra", second edition, Pearson.

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 412: Introduction to Abstract Algebra II

Yaping Yang TuTh 8:30-9:45

Prerequisites:

Math 411

Text:

Dan Saracino, "Abstract Algebra: A First Course", Second Edition, Waveland Press.

Description:

This course is a continuation of Math 411. We will study properties of rings and fields. A ring is an algebraic system with two operations (addition and multiplication) satisfying various axioms. Main examples are the ring of integers and the ring of polynomials in one variable. Later in the course we will apply some of the results of ring theory to construct and study fields. At the end we will outline the main results of Galois theory which relates properties of algebraic equations to properties of certain finite groups called Galois groups. For example, we will see that a general equation of degree 5 can not be solved in radicals.

MATH 421: Complex Variables

Weimin Chen MWF 1:25-2:15

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

MATH 425.1: Advanced Multivariate Calculus

Franz Pedit MWF 1:25-2:15

Prerequisites:

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

Text:

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]

Recommended Text:

J. Marsden and A. Tromba, Vector Calculus (any edition is fine)

Note:

Text books are for additional reading.

Description:

This course covers the basics of differential and integral calculus in many variables: differentiability, directional and partial derivatives and gradient of functions; inverse and implicit function theorems; critical points, also 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).

MATH 425.2: Advanced Multivariate Calculus

Ava Mauro MWF 9:05-9:55

Prerequisites:

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

Recommended 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.

MATH 455: Introduction to Discrete Structures

Tom Braden TuTh 2:30-3:45

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

Note:

The textbook is available as a pdf or as a $25 print-on-demand paperback, through the UMass library. Instructions for obtaining the book in one of these ways will be posted on the course web page before the start of classes.

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 learning mathematical theories with applications to concrete problems from other disciplines using discrete modeling techniques. Student groups will be formed to investigate a modeling problem and each group will report its findings to the class in a final presentation. This course satisfies the university's Integrative Experience (IE) requirement for math majors.

MATH 456.1: Mathematical Modeling

Bruce Turkington MWF 10:10-11:00

Prerequisites:

Math 233 and Math 235 (and Differential Equations, Math 331, is recommended). Some familiarity with a programming language is desirable (Mathematica, Matlab, C++, Python, etc.)

Text:

No textbook. The lectures will be drawn from various sources. In the group projects the students will need to consult whatever literature is relevant to their research topic.

Description:

In this course we concentrate on building mathematical models using continuous mathematics -- that is, calculus and differential equations. There is a huge variety of such models, since most of physical science is based on exactly this kind of modeling. In the first half of the course the lectures will showcase some of the famous models of science, taken from a wide variety of different fields. These models will be explained from basic principles. The point will be to put the mathematics that students already know to use to make interesting predictions about the behavior of physical, chemical or biological systems. In the second half of the course, students will work on projects in small groups (usually 3 to a group), and they will present their results to the class at the end of the semester.

This course satisfies the University's Integrative Experience (IE) requirement for math majors.

MATH 456.2: Mathematical Modeling

Nestor Guillen 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, C++, Python, etc.)

Text:

Richard Durrett.
Essentials of Stochastic Processes. 2nd print.

Description:

In this course we will study some of the mathematics used in modern modelling, be it continuous deterministic systems (modelled by differential equations) or discrete stochastic systems (modelled by Markov chains). A first part of the course will involve learning some of the theory in the aforementioned topics, and the second part will involve case studies on real life situations where these models are put to practice. Later on the course, students will team up in small groups (2-3) and do presentations on topics selected from a list made available at the beginning of the semester .

This course satisfies the University's Integrative Experience (IE) requirement for math majors.

MATH 471: Theory of Numbers

Liubomir Chiriac TuTh 10:00-11:15

Prerequisites:

Math 233 and Math 235. Math 300 or CS250 as a co-requisite is not absolutely necessary but highly recommended.

Text:

Number Theory: A lively introduction with proofs, applications and stories by James Pommersheim, Tim Marks and Eric Flapan.

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. Many central concepts and theorems will be presented together with their applications to other fields (such as Computer Science, Cryptography, etc.).

The list of topics include (but is not limited to): the Euclidean Algorithm, Linear Diophantine Equations, the Fundamental Theorem of Arithmetic, Modular Arithmetic, Elementary Cryptography (e.g. RSA algorithm), Primitive Roots, Quadratic Reciprocity, Gaussian Integers, Pell's Equation, and some cases of Fermat's Last Theorem.

MATH 475: History of Mathematics

Jenia Tevelev MWF 12:20-1:10

Prerequisites:

Math 233 and Math 300 or CS 250.

Text:

"A History of Mathematics" by V. Katz

Note:

This course satisfies the General Education IE requirement for Mathematics and Statistics.

Description:

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

The math major is made up of technical courses on the theory of mathematics from Calculus to more complex concepts. This course is unique in providing a humanities-based approach to understanding math. For example, students are required to use primary sources on a weekly basis. Students study examples of how mathematical advances were made in response to or alongside developments in other branches of science - such as Ptolemy’s work in trigonometry being motivated by applications in astronomy, and Newton as the father of both calculus and modern physics. Students also learn to understand mathematicians as people of their times - for example, how Babylonian mathematicians were motivated by the needs of the empire, or how Evariste Galois was both a brilliant mathematician and a passionate French revolutionary. Additionally, many math majors go on to teach mathematics after graduation, and in this course the history of math is is studied in the context of the history of education.

The homework assignments contain a component where students are required to write short compositions. Many of these assignments will ask students to engage in self-reflection on how their study of the history of mathematics in the current course is influenced by the General Education courses they took. This is not limited to courses carrying the Historical Studies designation, but Economics, Sociology, Science and other modes of human thought all present lenses through which one can study the mathematics and mathematicians that are the focus of the course; the homework assignments will invite students to apply all of those lenses to the topics at hand. Students will also be required to write an interdisciplinary 20-page final essay. Essay topics are developed by the student with assistance from the professor. Students draw not only on their mathematics coursework, but also on the knowledge they have accrued from other GenEd curriculum courses they have experienced in their first two years of college. After seeing how mathematical tools have developed in conversation with history, culture, and science, students can better appreciate the uses and possibilities of advanced mathematics.

A substantial fraction of the course grade is based on a class presentation; this is a major change from standard upper division math/stat requirements. Each group, which typically consists of three students, collaboratively researches and presents an interdisciplinary mathematical topic, chosen by the group from the instructor’s list of suggested topics. This is highly unusual for mathematics classes, where problems are typically presented abstracted from their scientific and cultural roots. These presentations are spaced out throughout the semester, and the students’ work is referenced and discussed in a class discussion later in class.

Additionally, highly unusually for a mathematics course, a large part of the course grade is based on participation in class discussions. Each week, the students are assigned readings. A large amount of weekly class time is devoted to a roundtable discussion of the reading - its implications for modern mathematics, how it was understood at the time, mathematical concepts in the reading, and the close-reading of assigned passages.

See http://people.math.umass.edu/~tevelev/475_2016/ for more information about the course and examples of essays, class presentations, and reading assignments from previous years.

MATH 523H: Int. Mod. Analysis I

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

Prerequisites:

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

Text:

Elementary Analysis: The Theory of Calculus by Kenneth Ross. Springer-Verlag.

Recommended Text:
  • Analysis by its History by Ernest Hairer and Gerhard Wanner. Springer
  • Fundamental Ideas of Analysis by Michael Reed, Wiley, 1998
  • Introduction to Real Analysis by William Trench. (freely available at http://ramanujan.math.trinity.edu/wtrench).
Description:

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

MATH 524: Introduction to Modern Analysis II

Nathan Totz TuTh 1:00-2:15

Prerequisites:

MATH 523H

Description:

Topology of the euclidean space and functions of several variables (implicit function theorem), introduction to Fourier analysis, metric spaces and normed spaces. Applications to differential equations, calculus of variations, and others.

MATH 534H: Introduction to Partial Differential Equations

Andrea Nahmod TuTh 11:30-12:45

Prerequisites:

Math 233, 235, and 331.
(The prerequisites for this class are calculus, differential equations and linear algebra. Having taken complex variables and real analysis is definitely a plus, but not necessary.)

Text:

Main Text:
Partial Differential Equations in Action. From modeling to theory; by Sandro Salsa. Springer, Third Edition.

Optional reference text:
Partial Differential Equations: An Introduction, by Walter Strauss, Wiley, Second Edition.

Description:

An introduction to PDEs (partial differential equations), covering the some of the most basic and ubiquitous equations modeling physical problems and arising in a variety of contexts. We shall study the existence and derivation of explicit formulas for their solutions —when feasible and study their behavior. We will also learn how to read and use specific properties of each individual equation to analyze the behavior of solutions when explicit formulas do not exist. Equations covered include: heat/diffusion equations; the Laplace’s equation; transport equations and the wave equation. Along the way we will discuss topics such as Fourier series, separation of variables, harmonic functions and potential theory, maximum principle, energy methods, etc.

Time-permitting, we will discuss some additional topics (eg.. Schrodinger equations, Fourier transform methods, eigenvalue problems, etc.). The final grade will be determined on the basis of homework, attendance and class participation, a midterm and final projects.

MATH 536: Actuarial Probability

Jinguo Lian MWF 1:25-2:15

Prerequisites:

Math 233 and Stat 515

Text:

ASM Study Manual for Exam P/ Exam 1, 16th or later edition -, Author/Publisher: Ostaszewski / ASM

Recommended Text:

Probability for Risk Management, (Second Edition), 2006, by Hassett, M. and Stewart, D., ACTEX, ISBN: 978-156698-2.

Note:

This course requires any calculator accepted by the Society of Actuaries for the Exam P.
This course was formerly numbered Math 438.

Description:

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

MATH 537: Intro. to Math of Finance

Mike Sullivan TuTh 2:30-3:45

Prerequisites:

Math 233 and Stat 515

Text:

(1)The Big Short by Michael Lewis, 2010, W. Norton & Company.
(2)Unpublished e-textbook freely available first week of class.

Recommended Text:

Derivative Markets by Robert L. McDonald, 2nd or 3rd edition.

Note:

A calculator should have a cumulative distribution function for the standard normal variable (also known as the ``Erf" function or ``normalcdf"). The inverse normalcdf feature is also necessary. The TI-83 or higher, for example, will work.

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: Linear Algebra for Applied Mathematics

Robin Young MWF 1:25-2:15

Prerequisites:

Math 233, Math 235, Math 300

Text:

Elementary Linear Algebra, by Kenneth Kuttler. (Creative commons, available for free download. Will be on course website).

Description:

This course aims to give a deeper understanding of linear algebra tools and theory. We will study the decomposition of matrices, particularly the LU, QR, and singular value decompositions. We also study inner product spaces, orthogonality, and spectral theory. Applications will be made to linear systems, least-squares fitting, and dynamical systems. The coursework will be a mix of proof and compution. Computations will be done in the open-source program Scilab, which is similar in design and capability to MATLAB.

MATH 551.1: Intr. Scientific Computing

Stathis Charalampidis TuTh 10:00-11:15

Prerequisites:

MATH 233 and 235 as well as knowledge of a scientific programming language, e.g. Matlab, Fortran, C, C++, Python, Java.

Text:

A First Course in Numerical Methods, by Ascher & Greif (SIAM).

Description:

The course will introduce basic numerical methods used for solving problems that arise in different scientific fields. The following topics (not necessarily in the order listed) will be covered: finite precision arithmetic and error propagation, linear systems of equations, root finding, interpolation, least squares and numerical integration. Students will gain practical programming experience in implementing the methods using MATLAB. The use of MATLAB for homework assignments will be mandatory. We will also discuss some very important practical considerations of implementing numerical methods using such languages as fortran, C or C++.

MATH 551.2: Intr. Scientific Computing

Stathis Charalampidis TuTh 11:30-12:45

Prerequisites:

MATH 233 and 235 as well as knowledge of a scientific programming language, e.g. Matlab, Fortran, C, C++, Python, Java.

Text:

A First Course in Numerical Methods, by Ascher & Greif (SIAM).

Description:

The course will introduce basic numerical methods used for solving problems that arise in different scientific fields. The following topics (not necessarily in the order listed) will be covered: finite precision arithmetic and error propagation, linear systems of equations, root finding, interpolation, least squares and numerical integration. Students will gain practical programming experience in implementing the methods using MATLAB. The use of MATLAB for homework assignments will be mandatory. We will also discuss some very important practical considerations of implementing numerical methods using such languages as fortran, C or C++.

MATH 552: Applications of Scientific Computing

Nathaniel Whitaker MWF 12:20-1:10

Prerequisites:

Math 551 or equivalent or permission of instructor

Text:

Numerical Analysis by Tomothy Sauer( You do not have to buy the latest version)

Description:

This course will cover some modern topics in scientific computing including the numerical solutions of Differential Equations. Other topics include random numbers, Monte-Carlo simulation, Brownian motion, stochastic differential equations, Fast Fourier transform and signal processing, data compression, eigenvalues and optimization.

MATH 563H: Differential Geometry

Franz Pedit MWF 11:15-12:05

Prerequisites:

Very good understanding of Advanced Multivariable Calculus and Linear Algebra (Math 425, 233 and 235).
Intro to Modern Analysis (Math 523H) can be helpful, but not necessary.

Text:

Elementary Differential Geometry by Christian Bär.
Any book with similar title like Elementary Differential Geometry by Barrett O'Neill etc.
Any edition is fine.

Note:

All material will be developed in class. Textbooks are useful for additional reading, explorations etc.

Description:

The course develops the classical concepts of Differential Geometry: curves and surfaces in space, their basic local invariants (fundamental forms, curvatures) and integrability relations (Gauss-Codazzi equations). We will also explore global problems, such as elastic curves (critical for the bending energy of elastic wires) and special surface classes (minimal and constant mean curvature surfaces --soap films and soap bubbles -- critical for the area functional without and with a volume constraint).

MATH 571: Intro Math Cryptography

Paul Gunnells TuTh 10:00-11:15

Prerequisites:

Math 300 and Math 471.

Text:

An Introduction to Mathematical Cryptography, Hoffstein, Pipher, Silverman, Springer-Verlag, 2008

Description:

The main focus of this course is on the study of cryptographical algorithms and their mathematical background, including elliptic curve cryptography and the Advanced Encryption Standard. Lectures will emphasize both theoretical analysis and practical applications. To help master these materials, students will be assigned computational projects using computer algebra software.

STAT 494CI: Cross-Disciplinary Research

John Staudenmayer MWF 12:20-1:10

Prerequisites:

Instructor Consent Required. Note: Previous coursework in probability and statistics, including regression, is required.

Description:

Students will work in teams to collaborate with researchers in other disciplines. Each research project will have a team of two students, one faculty statistician, and one researcher from another discipline. Students will be assigned to teams according to their skills and interests. Each team will work together for one semester and be responsible for its own schedule, work plan, and final report. In addition, the whole class will meet weekly for teams to update each other on their progress and problems. Students will learn about several areas of application and the statistical methods employed by each team. Students in the course will probably learn new statistical methods, a discipline where statistics is applied, how to work collaboratively, how to use R, and how to present oral and written reports.

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: Statistics I

Sohrab Shahshahani TuTh 8:30-9:45

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.

Text:

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

Description:

This courses 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: Statistics I

Brian Burrell 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.

Text:

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

Description:

This courses 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. We will cover much of chapters 2-7 in the text (with some omissions) and probably some portions of chapter 8.

STAT 515.3: Statistics I

Jianyu Chen 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 courses provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat 516). 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.

We will cover much of chapters 2-7 in the text (with some omissions) and probably some portions of chapter 8.

STAT 515.4: Statistics I

Jianyu Chen 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 courses provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat 516). 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.

We will cover much of chapters 2-7 in the text (with some omissions) and probably some portions of chapter 8.

STAT 516.1: Statistics II

Zheng Wei TuTh 1:00-2:15

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 516.2: Statistics II

Byungtae Seo MWF 10:10-11:00

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: Statistics II

Anna Liu 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 516.4: Statistics II

Byungtae Seo MWF 9:05-9:55

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 525.1: Regression Analysis

Daeyoung Kim TuTh 1:00-2:15

Prerequisites:

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

Note:

Senior math major undergraduate students only

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. The course will teach and use the SAS software.

STAT 525.2: Regression Analysis

Michael Lavine MWF 9:05-9:55

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, by Sanford Weisberg, published by Wiley, ISBN: 978-1-118-38608-8. There are both hard copy and electronic versions available. You may use either.

Description:

Regression analysis answers questions about the dependence of a response variable on one or more predictors, including prediction of future values of a response, discovering which predictors are important, and estimating the impact of changing a predictor or a treatment on the value of the response. This course focuses on linear regression, which is the basis for many modern, advanced regression techniques, including those used by statisticians, machine learners, and data scientists.

In addition to the usual topics in linear regression, this course also emphasizes (1) graphical methods, because it’s important to visualize your data and not just rely on numerical output from computer packages, and (2) diagnostics, because it’s important to check that any regression analysis accurately represents your data. The course will teach and use the R statistical language.

STAT 597A: ST - Stat Computing

Zheng Wei TuTh 10:00-11:15

Prerequisites:

Prerequisite: Stat 516
Corequisite: Stat 525

Text:

Lecture notes

Recommended Text:

The Art of R Programming: A Tour of Statistical Software Design by Norman Matloff

Description:

The 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 R package creation. The class will be taught in the R language.

STAT 597TS: ST-Time Series (1 Credit)

Peng Wang Tu 4:00-5:15

Prerequisites:

Stat 525 or equivalent

Description:

This one credit undergraduate course aims to introduce basic concepts and modeling techniques for time series data. It emphasizes implementation of the modeling techniques and their practical application in analyzing actuarial and financial data. The open source program R will be used. Chapter 7, 8 and 9 of the textbook will be covered, if time allows. This course satisfies the VEE (Validation by Educational Experience) requirement set by the SOA (Society of Actuaries) in time series of the Applied Statistical Methods topic. Specifically, SOA requires the following educational experience in time series and forecasting:
- Linear time series models
- Moving average, autoregressive and/or ARIMA models
- Estimation, data analysis and forecasting with time series models
- Forecast errors and confidence intervals
This course will cover the above topics and more advanced models such as exponential smoothing, Box-Jenkins and ARCH/GARCH, if time permits.

STAT 598C: Statistical Consulting Practicum (1 Credit)

Krista J Gile W 11:15-12:05

Prerequisites:

Graduate standing, STAT 515, 516, 525 or equivalent, and consent of instructor.

Description:

This course provides a forum for training in statistical consulting. Application of statistical methods to real problems, as well as interpersonal and communication aspects of consulting are explored in the consulting environment. Students enrolled in this class will become eligible to conduct consulting projects as consultants in the Statistical Consulting and Collaboration Services group in the Department of Mathematics and Statistics. Consulting projects arising during the semester will be matched to students enrolled in the course according to student background, interests, and availability. Taking on consulting projects is not required, although enrolled students are expected to have interest in consulting at some point. The class will include some presented classroom material; most of the class will be devoted to discussing the status of and issues encountered in students’ ongoing consulting projects.

Graduate Courses

MATH 612: Algebra II

Siman Wong MWF 10:10-11:00

Prerequisites:

Math 611 (or consent of the instructor)

Text:

Dummit and Foote, Abstract Algebra

Recommended Text:

Lang, Algebra;
Atiyah and MacDonald, Introduction to commutative algebra;
Serre, Linear Representations of Finite Groups

Description:

This fast-paced course is a continuation of Math 611. It 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

Tom Weston 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; other topics as time permits.

MATH 624: Real Analysis II

Andrea Nahmod TuTh 2:30-3:45

Prerequisites:

Math 523 and Math 623 (Lebesgue integral, measure theory in Euclidean space and in other spaces, familiarity with metric spaces).
(Math 524 is a plus but not required).

Text:

1) Functional Analysis: Introduction to Further Topics in Analysis (Princeton Lecture Series IV), by Elias M. Stein & Rami Shakarchi

2) Real Analysis: Measure Theory, Integration, and Hilbert Spaces" (Princeton Lecture Series III) by Stein and Shakarchi will be also used.

Description:

This course is a continuation of Math 623. Topics to be covered include: Signed measures. Hilbert spaces. Banach spaces and elementary operator theory and linear functionals. $L^{P}$-spaces: duality, interpolation and approximation theorems. Time permitting we will discuss some further material introductory to Math 731 (PDE) such as distribution theory, Fourier analysis and Sobolev spaces.

MATH 691Y: Applied Math Project Sem.

Nathaniel Whitaker F 2:30-3:45

Prerequisites:

Graduate Student in Applied Math MS Program

Text:

None

Description:

Continuation of Project

MATH 697MS: ST - Multiscale Methods

Matthew Dobson MWF 10:10-11:00

Prerequisites:

Math 523 or 623, Math 331.

Text:

Pavliotis and Stuart, Multiscale Methods: Averaging and Homogenization

Description:

This course will study problems with multiple scales in time and/or space and derive simplified equations that feel the fine-scale effects in an averaged way. Multiscale structure is widely found in mathematics applied to biological, chemical, and engineering applications, and the study of such structures is a rapidly developing
field. We will study multiscale discrete and continuum models starting with ordinary differential equations and progressing to include Markov processes, stochastic differential equations, and partial differential equations.

In order to keep prerequisites minimal, an introduction to stochastic differential equations, partial differential equations and Markov processes will be given before their treatment, and the focus will be on the unified technique of formal expansions.

MATH 697NA: ST - Numerical Algorithms

Eric Polizzi TuTh 2:30-3:45

Description:

Objectives: Provide a practical understanding of matrix computations for science, engineering and industrial applications;
Provide solid foundations in computational linear algebra; Introduction to parallel computing and programming practices

Contents: Introduction to Scientific Computing- 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 - Parallel architectures and parallel programming with OpenMP, MPI and hybrid -. Numerical parallel algorithms

MATH 704: Topics in Geometry II

Paul Gunnells TuTh 8:30-9:45

Prerequisites:

Topics In Geometry 703 or knowledge of abstract manifolds, vector bundles, ODEs on manifolds and basics of Lie theory.

Text:

Introduction fo Smooth Manifold, John M. Lee, second edition. Riemannian Manifolds - An Introduction to Curvature, by John M. Lee

Description:

This course is the continuation of Math 703. We will discuss differential forms, integration on manifolds and deRham cohomology, as well as basic Riemannian geometry (connections and curvature).

MATH 797FR: ST - Financial Math and Risk Management

HongKun Zhang TuTh 1:00-2:15

Prerequisites:

Stochastic Calculus

Description:

This is the second course of the series. We will introduce the concepts of arbitrage, state price densities and equivalent martingale measures. European and American claims. Optimal stopping. We will study admissible strategies, pricing and hedging in Markovian models. Admissible strategies. Pricing and hedging in Markovian models. We will consider different ways of of modeling markets with uncertain volatility. We will cover stochastic volatility models, auto-regressive models as well as recently de- rived nonlinear pricing models. We will emphasize, in particular, worst-case scenario risk-management techniques, and managing volatility risk with options. The main probability tool we will use is the Ex- treme Value Theory. Finally, we will cover more practical risk-management techniques and guidelines such as the “Value at Risk” outlined in the J.P. Morgan technical document on measuring financial risk.

MATH 797MC: ST - Mapping Class Groups

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

Prerequisites:

* Basic algebra and complex analysis (undergraduate level)
* Point-set topology (671)
* Algebraic topology (cellular decomposition, homotopy, covering spaces, homology)
* Differentiable manifolds (703-704)

Text:

We will draw the material from several books and research articles.

Recommended Text:

* Benson Farb and Dan Margalit, "A primer on mapping class groups"
* Joan Birman, “Braids, links and mapping class groups”
* William Thurston, "Three dimensional geometry and topology"
* Andrew Casson, “Automorphisms of surfaces after Nielsen and Thurston”
* Wilhelm Magnus, Abraham Karrass and Donald Solitar, “Combinatorial group theory”
* Yukio Matsumoto, “An introduction to Morse theory”
* Burak Ozbagci and Andras Stipsicz, “Surgery on contact 3-manifolds and Stein surfaces”
* Benson Farb, “Problems on mapping class groups and related topics"

Note:

The course grade will be based on homework (70%) and final presentations (30%). Homework will be typically due every one or two weeks. Final presentations will consist of a 30-40 min in-class presentation (15%), accompanied by an expository paper prepared with TeX (15%).

Description:

This is an introductory course on the theory of mapping class groups of surfaces, which connects to several fields of mathematics, such as geometry, topology, algebra and combinatorics. After presenting the rich algebraic structure and the intrinsic geometric nature of mapping class groups, the course will discuss various facets and applications of this newly emerging beautiful subject.

MATH 797MD: ST - Moduli Space and Invariant Theory

Jenia Tevelev MWF 9:05-9:55

Prerequisites:

Math 612, Math 621, and at least one semester of Algebraic Geometry, for example MATH 797W: ST-Algebraic Geometry (or consent of the instructor).

Text:

I have notes on my website from the previous time I taught this course. I probably won't follow them too closely but they will give you some idea what to expect, see http://people.math.umass.edu/~tevelev/moduli797.pdf

Description:

A moduli space parametrizes or classifies all geometric objects of some sort. For example, elliptic curves are classified by the J-invariant, so the moduli space of elliptic curves is an affine line (with coordinate J). The Jacobian of a Riemann surface is also a moduli space: it parametrizes line bundles on the Riemann surface. The study of moduli spaces is an old subject and many methods were developed to understand them including GIT (geometric invariant theory), variation of Hodge structures, stacks, etc. Reading modern literature on moduli theory can be quite hard because it requires deep understanding of these advanced topics. Instead of following this ``ontogeny recapitulates phylogeny'' philosophy, we will introduce interesting examples of moduli spaces and then develop whatever machinery is necessary to work with them. Along the way we will learn a lot of Algebraic Geometry.

MATH 797PM: ST - Predictive Modeling and Uncertainty Quantification

Markos Katsoulakis TuTh 2:30-3:45

Prerequisites:

Instructor consent and graduate courses in probability theory (STAT 605), numerical analysis for ODE/PDE (MATH 652) and familiarity with the basic concepts of statistical inference (STAT608).

Description:

In this course we will discuss an array of topics that straddle probabilistic modeling and simulation, uncertainty quantification and statistical learning methods. We focus on developing systematic mathematical and computational tools for building data-driven, predictive models for complex systems and dynamics. In particular, we will discuss material that includes: uncertainty quantification, local and global sensitivity analysis methods for dynamical systems, data assimilation and approximate inference methods, stochastic optimization algorithms and model selection. A significant component of the course focuses on related software such as DAKOTA and others.

STAT 605: Probability Theory I

Yao Li TuTh 8:30-9:45

Prerequisites:

Math 623 (Real Analysis) or permission of instructor. In order to understand the material in this course, knowledge of measure theory is required (Math 623 or equivalent).

Text:

A Course in Probability Theory, Third Edition by Kai-Lai Chung.

Recommended Text:

Probability (GTM 95) by A.N. Shiryaev.

Note:

Most homework problems will be from Chung's book. Some materials may come from GTM 95.

Description:

This course aims to develop the probability basis that is required in modern statistical theories and stochastic processes. Knowledge of measure theory is required to understand the materials in this course. Topics of this course include measure and integration foundations of probability, distribution functions, convergence of random variables, laws of large numbers and central limit theory. If time permits, I will cover some basic martingale theory and random walks.

STAT 608: Mathematical Statistics II

Krista J Gile MW 2:30-3:45

Prerequisites:

STAT 607 or permission of the instructor.

Text:

Statistical Inference, 2nd edition,
by Casella and Berger

Description:

This course is the second half of the STAT 607-608 sequence, which together provide the foundational theory of mathematical statistics. STAT 607 emphasizes concepts in probability, while 608 builds on those concepts to build statistical theory. STAT 608 topics include point and interval estimation, hypothesis testing, large sample results in estimation and testing, decision theory, Bayesian methods, and analysis of discrete data. Other areas may include nonparametric methods, sequential methods, regression, and analysis of variance.

STAT 691P: Project Seminar

John Staudenmayer MWF 12:20-1:10

Prerequisites:

Permission of instructor.

Text:

None.

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 697D: ST - Appl Stat and Data Analysis

Krista J Gile MWF 11:15-12:05

Prerequisites:

co-requisites: Regression (525 or 597R), Mathematical Statistics II (516 or 608)

Description:

This course gives students a brief overview of several topics of practical importance to statisticians doing data analysis. It focuses on topics not typically covered in the required curriculum, but of use to students earning advanced degrees in statistics.

Each topic provides a foundation from which students may extend their understanding, should they need to use the method in practice, or wish to consider more detailed study or research.

The course begins with a very fast introduction to R (students unfamiliar with R are encouraged to contact the professor to begin this process before the semester). Each topic covered includes both a technical overview and an application, implemented in software. Specific topics may include: Simulation studies, randomization methods, Markov chain Monte Carlo, missing data, casual modeling, survival analysis, network analysis, exploratory data analysis, and cross-validation. Other topics may arise from student interest or consulting problems.

One hour each week will meet concurrently with the Statistical Consulting Practicum.

Students will complete projects of their choosing.

STAT 697TS: ST - Time Series Analysis and Appl

Daeyoung Kim TuTh 11:30-12:45

Prerequisites:

Two prerequisites are required - 1) Probability and Statistics at a calculus based graduate level such as Stat 607 and Stat 608 (concurrent), 2) a previous course on regression analysis covering multiple linear regression (e.g., Stat 505, BioEpi 744, RESEC 702) with some exposure to regression models in matrix form. Prior computing experience with R is desirable.

Text:

Time Series Analysis and Its Applications, 3rd ed., by Shumway, Robert H. and Stoffer, David S.

Description:

Time series analysis is an effective statistical methodology for modelling time series data (a series of observations collected over time) and forecasting future observations in many areas, economics, the social sciences, the physical and environmental sciences, medicine, and signal processing. For example, monthly unemployment rates in economics, yearly birth rates in social science, global warming trends in environmental studies, and magnetic resonance imaging of brain waves in medicine. This course presents the fundamental principles of time series analysis including mathematical modeling of time series data and methods for statistical inference. Topics covered will include modeling and inference in the following models : autoregressive (AR) and autoregressive moving average (ARMA) models, (nonseasonal/seasonal) autoregressive integrated moving average (ARIMA) models, unit root and differencing, spectral analysis, (generalized) autoregressive conditionally heteroscedastic models and state-space models.