Course Descriptions

Lower Division Courses

HONORS 391AH.10: Seminar - Geometry of Pre-Columbian Textiles

Jenia Tevelev Mondays 1:25 PM-2:15 PM

Prerequisites:

Open to Senior, Junior, and Sophomore Commonwealth Honors College students only.

Description:

Pre-Columbian cultures of the Andes, which did not develop a written language, relied heavily on artistic media of textiles and ceramics, as well as large-scale engineering, architectural and agricultural projects, to preserve their cultural, scientific, and mathematical heritage. The goal of this multi-disciplinary course will be to explore rich history and heritage of Andean cultures as viewed through the prism of geometry. Geometry here is understood as an abstraction of space and time: not just as the physical space but also as cultural, societal, technological, spiritual, and artistic environments. Along the way we will learn a fair amount of geometry: analysis of symmetries and transformations, patterns and crystallographic groups. We will learn how to weave on the traditional Andean backstrap loom and how to encode the same designs mathematically or on a computer. The grade in the class will be assigned based on group projects, an essay, and class participation.

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 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 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 190F: 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

Liubomir Chiriac TuTh 2:30-3:45

Prerequisites:

Math 132 with a grade of 'C' or better

Description:

The goal of this course is to help students learn the language of rigorous mathematics. Students will learn how to read, understand, devise and communicate proofs of mathematical statements. A number of proof techniques (contrapositive, contradiction, and especially induction) will be emphasized. Topics to be discussed include 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

Luca Schaffler MWF 10:10-11:00

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

T. Sundstrom, Mathematical Reasoning: Writing and Proof, version 2.1. Available for free download at: http://scholarworks.gvsu.edu/books/9/

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

George Avrunin TuTh 11:30-12:45

Prerequisites:

Math 132 with a grade of C or better

Text:

T. Sundstrom, Mathematical Reasoning: Writing and Proof, version 2.1. Available for free download at: http://scholarworks.gvsu.edu/books/9/

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 370.1: Writing in Mathematics

Patrick Dragon TuTh 10:00-11:15

Prerequisites:

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

Description:

This course will introduce students to technical writing in mathematics. Writing assignments will include proofs, instructional handouts, resumes, cover letters, and a final paper. All assignments will be completed using LaTeX. By the end of the semester, students should be able to clearly convey mathematical ideas through their writing, as geared to a particular audience.

MATH 370.2: Writing in Mathematics

Patrick Dragon TuTh 8:30-9:45

Prerequisites:

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

Description:

This course will introduce students to technical writing in mathematics. Writing assignments will include proofs, instructional handouts, resumes, cover letters, and a final paper. All assignments will be completed using LaTeX. By the end of the semester, students should be able to clearly convey mathematical ideas through their writing, as geared to a particular audience.

MATH 370.3: Writing in Mathematics

Franz Pedit TuTh 1:00-2:15

Prerequisites:

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

Text:

Reading material will be provided by the instructor.

Description:

The main objective of this class is to practice writing about mathematical topics such as its history, important solved and unsolved mathematical problems, and its relation to physics and other sciences. The position we take is that of a science writer who explains those themes to an educated, general public. Examples of such writing will be given in class. There will also be group projects and presentations of these projects in class. In addition, we will learn how to write a cover letter and vita for possible job/internship/grad school applications.
All writing has to be done in the open source word processing system LaTex for which there will be a tutorial in class.

MATH 391T: Seminar- Introduction to K-12 Mathematics Teaching

Michael Hayes MWF 1:25-2:15

Prerequisites:

Open to junior and senior Math majors. MATH 300 and completion of a 400-level or higher Math or Statistics course required. Completion of two or more 400 level or higher Math or Statistics courses strongly recommended.

Note:

If you have any questions about the course, please email Mike at mhayes@math.umass.edu

Description:

This course provides future secondary math teachers an introduction to a range of topics related to the teaching of mathematics in the public schools. The focus will be on increasing the participants’ mathematical content knowledge for teaching by exploring the mathematical content and practices of secondary math. Through these explorations, students will have opportunities to gain some familiarity with the Massachusetts Frameworks, Common Core, standardized and local assessments, curriculum resources, and other topics related to secondary math teaching. As part of the course, students will also explore connections between secondary math and the higher-level mathematics courses they have been taking.

MATH 411.1: Introduction to Abstract Algebra I

Noriyuki Hamada MWF 10:10-11:00

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

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

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 412: Introduction to Abstract Algebra II

Tom Weston MWF 12:20-1:10

Prerequisites:

Math 411

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

Owen Gwilliam MWF 9:05-9:55

Prerequisites:

Math 233

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

Alexei Oblomkov TuTh 11:30-12:45

Prerequisites:

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

Text:

Vector Calculus by Marsden and Tromba, Ed., W. H. Freeman, 6th edition.

Description:

The course is an in depth version of a vector calculus course. We will cover intergration and differentiation in multidimensional setting. The Stokes and Green theorem and their multidimensional versions will
be discussed. Some application to engineering and science are covered if time permits.

MATH 425.2: Advanced Multivariate Calculus

Belgin Korkmaz MWF 1:25-2:15

Prerequisites:

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

Text:

Vector Calculus by Marsden and Tromba, 5th Ed., W. H. Freeman ISBN-10: 0716749920; ISBN-13: 978-0716749929

Description:

In this course we will study multivariable differential and integral calculus from a more advanced point of view. We will study limits, continuity, and differentiation of functions of several variables and vector-valued functions. Then we will continue with multivariable integrals (double-triple), line integrals and surface integrals. 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 425.3: Advanced Multivariate Calculus

Belgin Korkmaz MWF 12:20-1:10

Prerequisites:

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

Text:

Vector Calculus by Marsden and Tromba, 5th Ed., W. H. Freeman ISBN-10: 0716749920; ISBN-13: 978-0716749929

Description:

In this course we will study multivariable differential and integral calculus from a more advanced point of view. We will study limits, continuity, and differentiation of functions of several variables and vector-valued functions. Then we will continue with multivariable integrals (double-triple), line integrals and surface integrals. 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 455.1: Introduction to Discrete Structures

Laura Colmenarejo MWF 11:15-12:05

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.

Description:

This is a rigorous introduction to some topics in mathematics that underlie areas in computer science and computer engineering, including graphs and trees, spanning trees, and matchings; the pigeonhole principle, induction and recursion, generating functions, and discrete probability proofs (time permitting). The course integrates learning mathematical theories with applications to concrete problems from other disciplines using discrete modeling techniques. Student groups will be formed to investigate a concept or an application related to discrete mathematics, and each group will report its findings to the class in a final presentation. This course satisfies the university's Integrative Experience (IE) requirement for math majors.

MATH 455.2: Introduction to Discrete Structures

Alejandro Morales 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, generating functions, and discrete probability proofs (time permitting). The course integrates learning mathematical theories with applications to concrete problems from other disciplines using discrete modeling techniques. Student groups will be formed to investigate a concept or an application related to discrete mathematics, and each group will report its findings to the class in a final presentation. This course satisfies the university's Integrative Experience (IE) requirement for math majors.

MATH 456.1: Mathematical Modeling

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

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:

There is no formal text for the class. Reading material and some classnotes will be provided.

Description:

This modeling class will revolve around probability and game theory. We will take simple example and problems from gambling, games, economics, decision theory and biology and show how to model them and analyze them. For example we will compute odds for a variety of games (lottery and casino games), we will analyze the Monty hall problem and other application of Bayes theorem,
we will use game theory to analyze a number of social dilemna (tragedy of the commons, the prisonner's dilemna, etc...). And many others.

We will use some linear algebra and calculus. Differential equations (Math 331) will not be really nedeed in that class but we will discuss difference equations. We will explain from scratch the probability theory and game theory needed for the class.

There will be regular weekly homework for the class as well as other assignment: one self-reflection essay, one book analysis, and a final group project.

MATH 456.2: Mathematical Modeling

Mike Sullivan TuTh 2:30-3:45

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.). Some familiarity with statistics and probability is desirable.

Text:

Richard Durrett's Essentials of Stochastic Process, 2nd or 3rd edition.

Description:

This course is an introduction to mathematical modeling. The main goal of the class is to learn how to translate problems from "real-life" into a mathematical model and how to use mathematics to solve the problem. Topics to be covered include systems of nonlinear differential equations and Markov chains, with emphasis on ideas such as equilibria, stability, and long time behavior, to name a few. Most of the theory in the course will deal with Markov chains. Although Stats 515 is not a pre-req for this class, it would be an advantage to have seen its material beforehand.

MATH 471: Theory of Numbers

Eyal Markman MW 2:30-3:45

Prerequisites:

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

Text:

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

Description:

This course is a proof-based introduction to elementary number theory. We will quickly review basic properties of the integers including modular arithmetic and linear Diophantine equations covered in Math 300 or CS250. We will proceed to study primitive roots, quadratic reciprocity, Gaussian integers, and some non-linear Diophantine equations. Several important applications to cryptography will be discussed.

MATH 475: History of Mathematics

Jenia Tevelev TuTh 11:30-12:45

Prerequisites:

Math 233 and Math 300 or CS 250.

Text:

"A History of Mathematics" by V. Katz, 3d edition

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.

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.

Forms of evaluation will include a group presentation, homework assignments, class discussions, and a final paper.
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. Students will be required to write an interdisciplinary 15-page final paper. Essay topics are developed by the student with assistance from the professor. 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.

MATH 523H: Int. Mod. Analysis I

Siddhant Agrawal MWF 11:15-12:05

Prerequisites:

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

Text:

Elementary Analysis: The Theory of Calculus, 2nd edition, Kenneth Ross, Springer-Verlag, 2013

Description:

This is the first part of the introduction to analysis sequence (523 and 524). This course deals with basic concepts of analysis of functions mostly on the real line, and we will try to make many of the concepts one learns in calculus rigorous. Covered topics will include series, and sequences, continuity, differentiability, and integration. Prerequisites for the class are Math 233, Math 235, and Math 300 or CS 250.

MATH 524: Introduction to Modern Analysis II

Taryn Flock MWF 1:25-2:15

Prerequisites:

MATH 523H

Recommended Text:

Beals, Richard. Analysis: an introduction Cambridge University Press, 2004.

Description:

This course is the second part of the Introduction to Analysis sequence (Math 523 and Math 524). We will first extend the notions of convergence developed for real numbers in 523 to more general settings-metric spaces. This will reveal the need for a deeper theory of integration -- measure theory -- which we will then explore. Finally, we will apply our understanding to develop Fourier Analysis.

MATH 534H: Introduction to Partial Differential Equations

Andrea Nahmod TuTh 10:00-11:15

Prerequisites:

Math 233, 235, and 331.

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

Recommended Text:

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

Reference text (optional): Partial Differential Equations in Action: From Modelling to Theory by Sandro Salsa, (UNITEXT; Springer) 3rd ed. 2016 Edition.

Description:

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

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

MATH 536: Actuarial Probability

Jinguo Lian MWF 1:25-2:15

Prerequisites:

Math 233 and Stat 515

Recommended Text:

Recommend textbook: ASM Study Manual for Exam P, 2nd or later Edition by Weishaus. 3-month digital license is only $55; 6-month digital license is $69. You may buy the book through http://www.studymanuals.com/Product/Show/453140947.

Description:

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

MATH 537: Intro. to Math of Finance

HongKun Zhang TuTh 2:30-3:45

Prerequisites:

Math 233 and Stat 515

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

Jeremiah Birrell MWF 10:10-11:00

Prerequisites:

Math 233, Math 235, Math 300

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, we will often use MATLAB.

MATH 545.2: Linear Algebra for Applied Mathematics

Jeremiah Birrell MWF 9:05-9:55

Prerequisites:

Math 233, Math 235, Math 300

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, we will often use 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 U. M. Ascher and C. Greif (SIAM).

Description:

The course will introduce basic numerical methods used for solving problems that arise in
a variety of 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. We will cover the following topics (not necessarily in the order listed): Finite Precision Arithmetic
and Error Propagation, Linear Systems of Equations (direct and iterative methods), Root Finding
(fixed point methods such as Newton's method), interpolation, least squares and Numerical Quadrature.

MATH 551.2: Intr. Scientific Computing

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

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, Authors: Uri M. Ascher and Chen Greif, Publisher: Society for Industrial and Applied Mathematics (SIAM), 2011

Description:

The course will introduce basic numerical methods used for solving problems that arise in a variety of 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. We will cover the following topics (not necessarily in the order listed!): finite precision arithmetic and error propagation, root finding, interpolation, approximation of functions, linear systems of equations, numerical integration, numerical methods for differential equations.

MATH 551.3: Intr. Scientific Computing

Hans Johnston 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 a variety 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. 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

Stathis Charalampidis TuTh 8:30-9:45

Prerequisites:

Math 233, Math 235, Math 551 (or equivalent) or permission
of instructor; knowledge of scientific programming language is
required.

Text:

Finite difference methods for ordinary and partial differential equations, by R. J. LeVeque (SIAM).

Description:

This course complements the topics covered in MATH 551. In particular, the following topics (not necessarily in
the order listed) will be covered: finite difference schemes for steady-state boundary value problems, numerical
methods for time-dependent ordinary and partial differential equations, numerical methods for computing eigenvalues,
eigenvectors and singular values as well as fast poisson solvers and the fast Fourier transform (FFT). If time permits,
we will discuss iterative methods for linear systems (including modern methods such as the multigrid method) and parametric
continuation techniques (pseudo-arclength and deflation methods). The use of MATLAB for homework assignments will be
mandatory, although any other scientific language for solving the homework problems will be accepted.

Main Text: [1] Finite difference methods for ordinary and partial differential equations, by R. J. LeVeque (SIAM).

Supplementary Texts:
[1] A First Course in Numerical Methods, by U. M. Ascher and C. Greif (SIAM).
[2] A Multigrid tutorial, by W. L. Briggs, V. E. Henson and S. F. McCormick (SIAM).

MATH 563H: Differential Geometry

Belgin Korkmaz MWF 10:10-11:00

Prerequisites:

Very good understanding of Advanced Multivariable Calculus and Linear Algebra (Math 425, 233 and 235).

Text:

Differential Geometry of Curves and Surfaces by Manfredo P. Do Carmo, Dover Publications, 2016. ISBN-10: 0486806995 ISBN-13: 978-0486806990

Description:

The course covers standard materials in the theory of curves in the plane and the space, and the theory of surfaces in the space. We will develop their local invariants (curvature and torsion for curves, fundamental forms and curvature for surfaces.) We will also explore the interplay between local and global properties.

STAT 494CI: Cross-Disciplinary Research

John Staudenmayer MWF 9:05-9:55

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

Recommended Text:

Introduction to Probability and Statistics,
by Mendenhall, Beaver and Beaver, 14 th edition, Publishers: Brooks/Cole

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

Panagiota Birmpa MWF 9:05-9:55

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is required for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

Description:

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

Panagiota Birmpa MWF 10:10-11:00

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is required for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

Description:

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

STAT 515.3: Statistics I

Jianyu Chen TuTh 2:30-3:45

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is required for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

Description:

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

STAT 515.4: Statistics I

Jianyu Chen TuTh 1:00-2:15

Prerequisites:

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is required for this course. However, some necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

Description:

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

STAT 515.5: 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.

Text:

Mathematical Statistics with Applications, Authors: Wackerly, Mendenhall, Schaeffer (ISBN-13: 978-0495110811), Edition: 7th.

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

Zheni Utic TuTh 8:30-9:45

Prerequisites:

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

Text:

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

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

Zheni Utic TuTh 10:00-11:15

Prerequisites:

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

Text:

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

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

Vincent Lyzinski MWF 1:25-2:15

Prerequisites:

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

Text:

Mathematical Statistics with Applications, by D. D. Wackerly, W. Mendenhall and R. L. Schaeffer, 7th edition.

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

Erin Conlon MW 2:30-3:45

Prerequisites:

Stat 516

Text:

Applied Linear Regression Models, by Kutner, Nachtsheim and Neter (4th edition) or Applied Linear Statistical Models by Kutner, Nachtsheim, 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.

Description:

Regression is the most widely used statistical technique. In addition to learning about regression methods, this course will also reinforce basic statistical concepts and introduce students to "statistical thinking" in a broader context. This is primarily an applied statistics course. While models and methods are written out carefully with some basic derivations, the primary focus of the course is on the understanding and presentation of regression models and associated methods, data analysis, interpretation of results, statistical computation and model building. Topics covered include simple and multiple linear regression; correlation; the use of dummy variables; residuals and diagnostics; model building/variable selection, regression models and methods in matrix form. With time permitting, further topics include an introduction to weighted least squares, regression with correlated errors and nonlinear (including binary) regression.

STAT 525.2: Regression Analysis

Krista J Gile TuTh 2:30-3:45

Prerequisites:

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

Text:

Applied Linear Regression Models by Kutner, Nachsteim and Neter (4th edition) or, Applied Linear Statistical Models by Kutner, Nachtsteim, Neter and Li (5th edition). Both published by McGraw-Hill/Irwin. NOTE on the book(s). The first 14 chapters of Applied Linear Statistical Models (ALSM) are EXACTLY equivalent to the 14 chapters that make up Applied Linear Regression Models, 4th ed., with the same pagination. The second half of ALSM covers experimental design and the analysis of variance, and is used in our STAT 526. If you are going to take STAT 526, you should buy the Applied Linear Statistical Models (but it is a large book).

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 12:20-1:10

Prerequisites:

Stat 516

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 597G: ST- Intro/Statistical Learning

Anna Liu TuTh 10:00-11:15

Description:

Introduction to some statistical regression and classification techniques including logistic regression, nearest neighbor methods, discriminant analysis, kernel smoothing, smoothing spline, local regression, generalized additive models, decision trees, random forests, and support vector machines. Clustering methods such as K-means and hierarchical clustering will be introduced. Finally, there will also be topics on resampling based model evaluation methods and regularization based model selection methods.

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

Peng Wang Tue 4:00-5:15

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 and Anna Liu Fri 1:25-2:15

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

Paul Gunnells TuTh 11:30-12:45

Prerequisites:

Math 611 (or consent of the instructor)

Text:

Abstract Algebra, by Dummit and Foote, 3rd edition

Description:

A continuation of Math 611. Topics covered will include field theory and Galois theory and commutative algebra. Prequisite: Math 611 or equivalent.

MATH 624: Real Analysis II

Robin Young TuTh 10:00-11:15

Prerequisites:

Math 523H, Math 524 and Math 623.

Description:

Continuation of Math 623. Introduction to functional analysis; elementary theory of Hilbert and Banach spaces; functional analytic properties of Lp-spaces, appli-cations to Fourier series and integrals; interplay between topology, and measure, Stone-Weierstrass theorem, Riesz representation theorem. Further topics depending on instructor.

MATH 672: Algebraic Topology

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

Prerequisites:

Math 671, Math 611 or equivalent.

Text:

Allen Hatcher, "Algebraic Topology", also available online at the author's webpage.

Description:

This fast-paced course is an introduction to the basic tools of algebraic topology, which studies topological spaces and continuous maps by producing associated algebraic structures (groups, rings, vector spaces, and homomorphism between them). Emphasis will be placed on being able to compute these invariants. Topics include: Cell complexes, homotopy, fundamental group, Van-Kampen's theorem, covering spaces (all reviewed from Math 671), simplicial complexes, singular and cellular homology, exact sequences, Mayer-Vietoris, cohomology, universal coefficients theorem, Künneth formulas, Poincaré and Lefschetz dualities.
Grade will be based on regularly assigned homework, as well as exams.

MATH 691T: S-Teaching in Univ Cr

TBD Mon 4:00-5:15 (tentative)

Description:

The purpose of this seminar is to prepare graduate students to teach their own section of calculus in the Fall. Participants will present portions of calculus lectures in the seminar, observe the presentations of other participants, and provide feedback on the presentations.

MATH 691Y: Applied Math Project Sem.

Qian-Yong Chen Fri 1:15-2:30

Prerequisites:

Graduate Student in Applied Math MS Program

Description:

Continuation of Project

MATH 697AM: ST-Appl Math and Math Modeling

Yao Li MW 8:40-9:55

Prerequisites:

Undergraduate real analysis

Text:

Lin and Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences

Recommended Text:

David Logan, Applied Mathematics

Description:

The course covers several classical methods and popular topics in applied mathematics and mathematical modeling. We will go through the following topics. 1, Dimensional analysis and scaling; 2, Deterministic systems and chaos; 3, Regular and singular perturbation theory for ordinary differential equations; 4, Random walks and the diffusion limit, and classical solution techniques for PDE; 5, Methods of model simplifications. The techniques will be applied to various applications in physics, chemistry, and biology.

MATH 697CM: ST-Combinatorial Optimization

Annie Raymond TuTh 8:30-9:45

Prerequisites:

Math 235, Math 455 or Math 513/CS 575

Description:

In this course, we will consider maximization and minimization problems in graphs and networks. We will cover a broad range of topics such as matchings in bipartite graphs and in general graphs, assignment problem, polyhedral combinatorics, total unimodularity, matroids, matroid intersection, min arborescence, max flow/min cut, max cut, traveling salesman problem, stable sets and perfect graphs. One of our main tools will be integer programming, and we will also sometimes rely on semidefinite programming. Many of these problems come from real-world applications, so we will also sometimes discuss the algorithms necessary to solve them. This is a rigorous mathematical introduction to combinatorial optimization with proofs.

MATH 697U: ST-Stochastic Processes and Appl

Brian Van Koten MW 2:30-3:45

Prerequisites:

Probability, for example Stat 605 or Stat 607. Linear algebra.

Description:

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

MATH 704: Tpcs in Geometry II

Weimin Chen MWF 11:15-12:05

Prerequisites:

Math 703: Topics in Geometry I, and working knowledge in point-set topology and algebraic topology (as in Math 671-2).

Text:

There is no required text.

Recommended Text:

1. Foundations of Differential Geometry, Vol 1 and 2, by S. Kobayashi and K. Nomizu, John Wiley \& Sons, 1963.
2. Differential Geometry: Bundles, Connections, Metrics and Curvature, by Clifford H. Taubes, Oxford Graduate Texts in Mathematics 23, Oxford Univ. Press, 2011.

Description:

This course aims to give an introduction to the fundamental topics in modern differential geometry, as organized in the following four units.

1. Theory of fiber bundles and connections.
2. Riemannian geometry.
3. Characteristics classes via Chern-Weil theory.
4. Hermitian and Kahler geometry.

We will present the basic concepts and theorems in each unit listed above, illustrated with interesting examples and detailed proofs of some selected results to demonstrate
the various basic techniques in these subjects. We also hope to enhance the learning experience with homework assignments/projects, which form the basis of the course grade.

MATH 725: Intro Functional Analysis

Andrea Nahmod TuTh 11:30-12:45

Prerequisites:

Math 623 and Math 624

Description:

Functional analysis deals with the structure of infinite dimensional vector spaces and (mostly) linear on such spaces. Many such spaces are spaces of functions, hence the name functional analysis, but much of the theory will developed for abstract spaces (spaces with a norm or a scale product). We shall assume that the reader has taken Math 624 (or an equivalent course) and is familiar with the basic objects of functional analysis: Banach spaces and Hilbert spaces, linear functionals and duals, bounded linear operators. Our main goal is to develop a series of tools instrumental in the applications of functional analysis to PDE's, probability, ergodic theory, etc... Among the topics covered in this class are:
The fundamental theorems of functional analysis: Hahn-Banach theorem, Inverse mapping and closed graph theorems. Compact operators, Fredholm operators and applications; Spectral theory for linear bounded and unbounded operators,
Banach algebras, Semigroups. We will also cover the theory of distributions and some important Sobolev spaces properties.

MATH 797AS: ST- Algebraic Surfaces

Paul Hacking TuTh 10:00-11:15

Prerequisites:

Commutative algebra (e.g. from MATH 611-612), Basic algebraic geometry (e.g. MATH 708 from Spring 2018).

Text:

There is no required text but there are several useful references recommended below.

Recommended Text:

Principles of Algebraic Geometry, P. Griffiths and J. Harris, Wiley 2011.
Compact Complex Surfaces, W. Barth, K. Hulek, Chris Peters, and A.van de Ven, Springer, 2003.
Complex Algebraic Surfaces, A. Beauville, Cambridge University Press, 1996.
Algebraic Surfaces and Holomorphic Vector Bundles, R. Friedman, Springer 1998.
Chapters on Algebraic surfaces, M. Reid, https://arxiv.org/abs/alg-geom/9602006, 1996.

Description:

This course is a second course in algebraic geometry. The prerequisites are a basic knowledge of algebraic geometry and commutative algebra. Some prior experience with sheaf cohomology would be useful but not essential. We will study complex algebraic surfaces, introducing the main computational tools of algebraic geometry along the way. Complex surfaces play a central role in algebraic, differential, and symplectic geometry, and number theory.

Tentative syllabus:

1. Sheaves and cohomology. Hodge theory.
2. Line bundles, divisors, morphisms to projective space.
3. Birational geometry of surfaces.
4. Characterization of the projective plane. del Pezzo surfaces.
5. Ruled surfaces.
6. K3 surfaces.
7. Elliptic fibrations.
8. Surfaces of general type.

MATH 797CV: ST- Calculus of Variations

Matthew Dobson MWF 10:10-11:00

Prerequisites:

Math 623 or 731 or instructor permissions. Students should have knowledge of L^p spaces and familiarity with undergraduate level ODE and PDE.

Text:

B. Dacorogna, Introduction to the Calculus of Variations

Description:

The calculus of variations is the study of the minimization of integrals with respect to a function, whose integrand depends on the function and its derivatives. It is a powerful tool for solving PDE with an associated energy functional and arises in the theory of minimal surfaces.

This course will consider both the classical methods and the direct methods in the theory of the calculus of variations. Applications will be made to classical mechanics as well as to the development of numerical methods. We will also introduce the basic theory of gamma convergence and variational coarse-graining techniques.

MATH 797P: Stochastic Calculus

HongKun Zhang TuTh 1:00-2:15

Recommended Text:

The reference book we will use is "Stochastic differential equations" by Bernt Oksendal.

Description:

We first review some basic probability and useful tools, including random walk, Law of large numbers and central limit
theorem. Conditional expectation and martingales. The topics of the course include the theory of stochastic differential equations oriented towards topics useful in applications, such as Brownian motion, stochastic integrals, and diffusion as solutions of stochastic differential equations. Then we study about diffusion in general: forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus, as well as Girsanov's theorem, Feynman-Kac formula, Martingale representation theorem. We will also include some applications to mathematical finance or networks as time permits.

MATH 797W: ST-Algebraic Geometry

Jenia Tevelev TuTh 2:30-3:45

Prerequisites:

Math 611/612 or the consent of the instructor

Text:

Basic algebraic geometry-1. Varieties in projective space. Igor Shafarevich. Third edition. Springer, 2013. ISBN: 978-3-642-37955-0

Recommended Text:

Computations in algebraic geometry with Macaulay 2, edited by David Eisenbud, Daniel R. Grayson, Michael E. Stillman, and Bernd Sturmfels. Springer-Verlag, 2001. ISBN 3-540-42230-7

The red book of varieties and schemes, David Mumford, Second, expanded edition. Lecture Notes in Mathematics, 1358. Springer- Verlag, 1999.

Ideals, Varieties, and Algorithms, An Introduction to Computational Algebraic Geometry and Commutative Algebra, Third Edition, by David Cox, John Little, and Donal O'Shea, Springer, New York, 2007.

Description:

This will be the first course in algebraic geometry - the study of geometric spaces locally defined by polynomial equations. It is a central subject in mathematics with strong connections to differential geometry, number theory, and representation theory. We will pursue an algebraic approach to the subject, when local data is studied via the commutative algebra of quotients of polynomial rings in several variables. The emphasis will be on basic constructions and examples. Topics will include projective varieties, resolution of singularities, divisors and differential forms. Examples will include algebraic curves of low genus and surfaces in projective 3-space. In addition to theoretical approach, we will also learn how to use computer algebra software, specifically the Macaulay 2 package, to help with basic calculations in commutative algebra and algebraic geometry.

Forms of evaluation: biweekly homeworks (25%), in-class midterm (25%), take-home midterm (25%) and computer algebra project (25%).

STAT 608: Mathematical Statistics II

Daeyoung Kim TuTh 11:30-12:45

Prerequisites:

STAT 607 or permission of the instructor.

Text:

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

Description:

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

STAT 691P: Project Seminar

John Staudenmayer MWF 9:05-9:55

Prerequisites:

Permission of instructor.

Description:

This course is designed for students to complete the master's project requirement in statistics, with guidance from faculty. The course will begin with determining student topics and groups. Each student will complete a group project. Each group will work together for one semester and be responsible for its own schedule, work plan, and final report. Regular class meetings will involve student presentations on progress of projects, with input from the instructor. Students will learn about the statistical methods employed by each group. Students in the course will learn new statistical methods, how to work collaboratively, how to use R and other software packages, and how to present oral and written reports.

STAT 697D: ST- Appl Stat and Data Analysis

Anna Liu and Krista J Gile TuThFri 1:25-2:15

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.