Course Descriptions

Lower Division Courses

MATH 011: Elementary Algebra

See Preregistration guide for instructors and times

Description:

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

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

MATH 100: Basic Math Skills for the Modern World

See Preregistration guide for instructors and times

Description:

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

MATH 101: Precalculus, Algebra, Functions and Graphs

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

MATH 102: Analytic Geometry and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

Math 101

Description:

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

MATH 103: Precalculus and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

The trigonometry topics of MATH 104.

MATH 104: Algebra, Analytic Geometry and Trigonometry

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

MATH 113: Math for Elementary Teachers I

See Preregistration guide for instructors and times

Prerequisites:

MATH 011 or satisfaction of R1 requirement.

Description:

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

MATH 114: Math for Elementary Teachers II

See Preregistration guide for instructors and times

Prerequisites:

MATH 113

Description:

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

MATH 121: Linear Methods and Probability for Business

See Preregistration guide for instructors and times

Prerequisites:

Working knowledge of high school algebra and plane geometry.

Description:

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

MATH 127: Calculus for Life and Social Sciences I

See Preregistration guide for instructors and times

Prerequisites:

Proficiency in high school algebra, including word problems.

Description:

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

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

See Preregistration guide for instructors and times

Prerequisites:

Proficiency in high school algebra, including word problems.

Description:

Honors section of Math 127.

MATH 128: Calculus for Life and Social Sciences II

See Preregistration guide for instructors and times

Prerequisites:

Math 127

Description:

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

MATH 131: Calculus I

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

MATH 131H: Honors Calculus I

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

Honors section of Math 131.

MATH 132: Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

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

MATH 132H: Honors Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

Honors section of Math 132.

MATH 233: Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

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

MATH 233H: Honors Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

Honors section of Math 233.

MATH 235: Introduction to Linear Algebra

See Preregistration guide for instructors and times

Prerequisites:

Math 132 or consent of the instructor.

Description:

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

MATH 331: Ordinary Differential Equations for Scientists and Engineers

See Preregistration Guide for instructors and times

Prerequisites:

Math 132 or 136; corequisite: Math 233

Text:

TBA

Description:

(Formerly Math 431) Introduction to ordinary differential equations.First and second order linear differential equations, systems of linear differential equations, Laplace transform, numerical methods, applications. (This course is considered upper division with respect to the requirements for the major and minor in mathematics.)

STAT 111: Elementary Statistics

See Preregistration guide for instructors and times

Prerequisites:

High school algebra.

Description:

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

STAT 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 and 1 credit co-seminar

Eyal Markman TuTh 1:00-2:15

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

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

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 300.2: Fundamental Concepts of Mathematics and 1 credit co-seminar

Paul Hacking MWF 11:15-12:05

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: https://sites.google.com/site/mathematicalreasoning3ed/

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 and 1 credit co-seminar

Eduardo Cattani MWF 9:05-9:55

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: https://sites.google.com/site/mathematicalreasoning3ed/ Printed copy available from Amazon.

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 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 300.4: Fundamental Concepts of Mathematics and 1 credit co-seminar

Jacob Matherne TuTh 11:30-12:45

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

R. Hammack, Book of Proof, Second Edition. Available for free download at http://www.people.vcu.edu/~rhammack/BookOfProof/

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 so that they can successfully transition from more computation-focused courses like calculus to the more theoretical junior-senior level mathematics courses. 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 (possibly some combinatorics) will be included as time allows.

MATH 370: Writing in Mathematics

Adena Calden TuTh 1:00-2:15

Prerequisites:

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

Recommended Text:

Your freshman year writing guide will be a useful reference tool.

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 the research process in mathematics and will include grant writing, research paper, and professional presentation.

MATH 411.1: Introduction to Abstract Algebra I

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

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 411.2: Introduction to Abstract Algebra I

Liubomir Chiriac MWF 12:20-1:10

Prerequisites:

MATH 235; MATH 300 or CS 250

Text:

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

Description:

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

MATH 411.3: Introduction to Abstract Algebra I

Liubomir Chiriac MWF 11:15-12:05

Prerequisites:

MATH 235; MATH 300 or CS 250

Text:

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

Description:

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

MATH 421: Complex Variables

Eyal Markman TuTh 10:00-11:15

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

Ivan Mirkovic TuTh 11:30-12:45

Prerequisites:

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

Text:

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

Description:

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

MATH 425.2: Advanced Multivariate Calculus

Rob Kusner MW 2:30-3:45

Prerequisites:

Multivariable Calculus and Linear Algebra

Text:

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

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

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

Description:

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

MATH 437: Actuarial Financial Math

Jinguo Lian MWF 1:25-2:15

Prerequisites:

MATH 131, 132

Text:

ASM Study Manual for Exam FM, 12th Edition by Harold Cherry. You may buy the book online at https://www.actuarialbookstore.com/order_selection.aspx

Note:

I recommend that you should use a TI-BA II Plus calculator during the course.

Description:

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

MATH 455: Introduction to Discrete Structures

George Avrunin TuTh 11:30-12:45

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.

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: Mathematical Modeling

Nathaniel Whitaker MWF 11:15-12:05

Prerequisites:

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

Text:

No Textbook Planned

Description:

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

MATH 461: Affine and Projective Geometry

Jenia Tevelev TuTh 1:00-2:15

Prerequisites:

Math 235 (or equivalent) and Math 300 or consent of the instructor.

Text:

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

Description:

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

MATH 471: Theory of Numbers

Siman Wong MWF 10:10-11:00

Prerequisites:

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

Text:

Elementary Number Theory, Cryptography and Codes
by M. Welleda Baldoni, Ciro Ciliberto, G.M. Piacentini Cattaneo, Daniele Gewurz.
Springer-Verlag, 2009

Description:

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

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

Liubomir Chiriac Wed 4:00-4:50

Prerequisites:

One variable Calculus, Linear Algebra

Recommended Text:

1. The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary, by Kedlaya, Poonen and Vakil.

2. Putnam and Beyond by Gelca and Andreescu.

Description:

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

MATH 491P: S - Problem Seminar (1 credit)

Prerequisites:

Required Prerequisites: Math 233, 235, and 300. Suggested Prerequisites: Math 331 (completed or currently taking); Math 411 or Math 523H (completed or currently taking)

Description:

This class is designed to help students review and prepare for the GRE Mathematics subject exam, which is a required exam for entrance into many PhD program in mathematics. The exam is offered every April, September, and October. We will meet 6-7 times in September and October, with the course ending before the October exam date.

Students should have completed the three courses in calculus, a course in linear algebra, and have some familiarity with differential equations. The focus will be on solving problems based on the core material covered in the exam. Students are expected to do practice problems before each meeting and discuss the solutions in class.

MATH 523H: Introduction to Modern Analysis

Instructor TBA; Meeting Time MWF 12:20-1:10

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 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 532H: Nonlinear Dynamics

Instructor TBA; Meeting Time TuTh 11:30-12:45

Prerequisites:

Math 235 (Linear Algebra), Math 331 (Differential Equations) and the calculus sequence (Math 131, 132, 233), or equivalent background in elementary differential equations, linear algebra, and calculus

Text:

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2nd edition by Steven H. Strogatz, Westview Press, 2014

Description:

This course provides an introduction to systems of differential equations and dynamical systems, as well as will touch upon chaotic dynamics, while providing a significant set of connections with phenomena modeled through these approaches in Physics, Chemistry and Biology. From the mathematical perspective, geometric and analytic methods of describing the behavior of solutions will be developed and illustrated in the context of low-dimensional systems, including behavior near fixed points and periodic orbits, phase portraits, Lyapunov stability, Hamiltonian systems, bifurcation phenomena, and concluding with chaotic dynamics. From the applied perspective, numerous specific applications will be touched upon ranging from the laser to the synchronization of fireflies, and from the outbreaks of insects to chemical reactions or even prototypical models of love affairs. In addition to the theoretical component, a self-contained computational component towards addressing these systems will be developed with the assistance of Matlab (and wherever relevant Mathematica).

MATH 537: Intro to Mathematics of Finance

Mike Sullivan MW 2:30-3:45

Prerequisites:

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

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, 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 545.1: Linear Algebra for Applied Mathematics

Qian-Yong Chen MWF 1:25-2:15

Prerequisites:

Introductory course such as Math 233, 235 and 300 or equivalents, or consent of the instructor.

Text:

Linear Algebra and Its Applications, 4th ed., By Gilbert Strang. 2006, Cengage.
ISBN-10: 0030105676 ISBN-13: 9780030105678.

Elementary Linear Algebra, by Ken Kuttler;

Linear Algebra, by Cherney, Denton and Waldron.

Description:

This is a course in Advanced Linear Algebra and Applications. We will cover LU decomposition,
Vector and Inner Product Spaces, Orthogonality and Least Squares,
Determinants and Eigenvalues. Other decompositions such as SVD and QR, and, if time permitting,
numerical issues.
There will be elements of proof and computation in the course. The students will be required
to use numerical linear algebra packages in Matlab - there will be some project based assignments.
Homework will be assigned every one or two weeks. Late homework will NOT be
accepted. The final grade will be based on both exam and homework assignments.

MATH 545.2: Linear Algebra for Applied Mathematics

Eduardo Cattani MWF 11:15-12:05

Prerequisites:

Math 233, Math 235, and Math 300

Text:

Applied Linear Algebra, by Peter J. Olver and Chehrzad Shakiban. Pearson Prentice Hall.
ISBN: 0131473824

Description:

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

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

MATH 551.1: Intr. Scientific Computing

Stathis Charalampidis MWF 9:05-9:55

Prerequisites:

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

Text:

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

Description:

This 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 such numerical methods using MATLAB. The use of MATLAB for homework
assignments will be mandatory, although any other scientific language for solving the homework problems will be accepted.
We will also discuss some very important practical considerations of implementing numerical methods using other languages
such as fortran, C or C++.

MATH 551.2: Intr. Scientific Computing

Nathaniel Whitaker MWF 1:25-2:15

Prerequisites:

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

Text:

Numerical Analysis, Timothy Sauer(Any Edition)

Description:

The course will introduce basic numerical methods used for solving problems that arise in different scientific fields. Properties such as accuracy of methods, their stability and efficiency will be studied. Students will gain practical programming experience in implementing the methods. We will cover the following topics (not necessarily in the order listed): Finite Precision Arithmetic and Error Propagation, Linear Systems of Equations, Root Finding, Interpolation, least squares, Numerical Integration, Numerical Solution of Ordinary Differential Equations.

STAT 501: Methods of Applied Statistics

Joanna Jeneralczuk TuTh 11:30-12:45

Prerequisites:

Knowledge of high school algebra, junior standing or higher.

Text:

Textbook: 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 packages Minitab and R .

STAT 515.1: Introduction to Statistics I

Instructor TBA; Meeting Time 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.

Text:

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

Description:

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

STAT 515.2: Introduction to Statistics I

Mike Sullivan MWF 12:20-1:20

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. Scheaffer

Description:

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

STAT 515.3: Introduction to Statistics I

Anna Liu MWF 1:25-2:15

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.

Text:

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

Description:

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

STAT 515.4: Introduction to Statistics I

Instructor TBA; Meeting Time 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.

Text:

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

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: Introduction to Statistics I

Mike Sullivan MWF 11:15-12:05

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. Scheaffer

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

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 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 525.1: Regression Analysis

Krista J Gile 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. Stat 515 is NOT sufficient background for this course. Familiarity with basic matrix notation and operations is helpful.

Text:

Applied Linear Regression Models, by Kutner, Nachshem and Neter (4th edition) or Applied Linear Statistical Models by Kutner, Nachtshem, Neter and Li (5th edition). Both published by McGraw-Hill/Irwin. The first 14 chapters of Applied Linear Statistical Models (ALSM) are EXACTLY equivalent to the 14 chapters that make up Applied Linear Regression Models, 4th ed., with the same pagination. The second half of ALSM covers experimental design and the analysis of variance and is used in our ST526 course. (A) Students planning to take STAT 526 should buy the ALSM textbook.

Description:

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

STAT 525.2: Regression Analysis

Michael Lavine MW 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. Stat 515 is NOT sufficient background for this course. Familiarity with basic matrix notation and operations is helpful.

Text:

Applied Linear Regression, 4th Edition, by S Weisberg

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 535: Statistical Computing

Anna Liu MWF 11:15-12:05

Prerequisites:

Prior knowledge of statistical methods and programming experience (STAT525 or equivalent). Intended for graduate students and seniors.

Text:

Lecture notes

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 597L: ST-Dynamic Linear Models

Michael Lavine MWF 12:20-1:10

Prerequisites:

Stat 525 (linear regression) or equivalent

Text:

Petris, Petrone, and Campagnoli, Dynamic Linear Models with R, ISBN 978-0-387-77238-7, can be found at http://www.springer.com/us/book/9780387772370

Description:

State space models in general, and dynamic linear models in particular, are useful for many types of data and have proven especially popular for time series. After a general introduction to state space models, this course focuses on dynamic linear models, emphasizing their Bayesian analysis. When possible, we show how to calculate estimates and forecasts in closed form; but for more complex models, we use simulation and the dlm package in R. The course includes many detailed examples based on real data sets. No prior knowledge of Bayesian statistics or time series analysis is required, although familiarity with basic statistics and R is assumed.

STAT 597P: ST - R Programming for Data Analytics and Visualization (1 cr)

Peng Wang Wed 4:00-5:15

Prerequisites:

STATISTC 240, 515, or 516. Open to Seniors, Juniors and Graduate students only. Previous programming experience (e.g. Matlab or Python) helpful, but not required.

Text:

none

Description:

This is an introductory class to R programming language designed for senior undergrads and junior graduate students. It lays out all the fundamentals of R, such as syntax, data structure, function design, package design, etc. Some important advanced features and packages will also be introduced, including dplyr, ggplot2, Rmarkdown and shiny. The objective is to give a comprehensive view about R, to provide as many guidance for future studying and practicing, and at the same time to distribute as many raw materials as possible for a jump start.

STAT 598C: Statistical Consulting Practicum (1 cr)

Krista J Gile Thurs 10:00-11:15

Prerequisites:

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

Description:

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

Graduate Courses

MATH 611: Algebra I

Tom Weston TuTh 10:00-11:15

Prerequisites:

Undergraduate algebra (equivalent of our Math 411-412)

Text:

Dummit and Foote, Abstract Algebra

Description:

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

I. Group Theory and Representation Theory.

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

II. Linear Algebra and Commutative Algebra.

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

III. Field Theory and Galois Theory

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

MATH 623: Real Analysis I

Andrea Nahmod TuTh 11:30-12:45

Prerequisites:

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

Text:

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

Description:

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

MATH 645: ODE and Dynamical Systems

Matthew Dobson MWF 11:15-12:05

Prerequisites:

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

Text:

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

Description:

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

MATH 651: Numerical Analysis I

Yao Li MW 2:30-3:45

Prerequisites:

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

Recommended Text:

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

Description:

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

MATH 671: Topology I

Tom Braden TuTh 2:30-3:45

Prerequisites:

Advanced calculus at the level of M523.

Text:

Topology, James Munkres - 2nd Edition (Required); Algebraic Topology , Allen Hatcher (recommended), available free online at Hatcher's website (Cornell Math Department).

Description:

The first part of the course concerns general topology, often called point-set topology. At the most basic level this is just the study of continuous functions between spaces and properties that are preserved by them. The language of point-set topology underlies modern formulations of many areas of geometry and analysis. In the second part of the course we will do some elementary algebraic topology, including defining the fundamental group, one of the most basic and useful topological invariants of a space.

MATH 691Y: Applied Math Project Seminar

Qian-Yong Chen Fri 2:30-3:45

Prerequisites:

Graduate Student in Applied Math MS Program

Description:

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

MATH 697AM: ST - Foundations/Analysis Machine Learning

Nestor Guillen TuTh 8:30-9:45

Prerequisites:

Minimal requirements: Undergraduate real analysis (basics of metric spaces, integration), basic probability (distributions, random variables), strong background in calculus and linear algebra. Basic programming skills (ideally Python or C++, but other languages are also ok ),

Ideal requirements: Familiarity with one or more of the following topics: measure theory, differentiable manifolds, linear programming, spectral graph theory, calculus of variations.

Text:

The Elements of Statistical Learning (Springer Series in Statistics), 2nd edition. Authors: Trevor Hastie, Robert Tibshirani, and Jerome Friedman.

Description:

In this course we will cover some of fundamental ideas from analysis, statistics, and optimization that are relevant to methods in machine learning and statistical inference. The class will cover not only the most well known linear methods, but also the more recently developed nonlinear methods that use the intuition from classical topics in PDE and the calculus of variations, such as the theory minimal surfaces, optimal transport, and gradient flows. The class will be more theoretical than an ordering machine learning class, however, there will still be plenty of coding as we put the theory into practice.

The target audience includes but is not limited to:
(1) Mathematics graduate students interested in areas such as: convex analysis, statistics, probability, optimization, elliptic PDE, calculus of variations, graph theory, and even Riemannian geometry.
(2) Computer science and electrical engineering graduate students interested in image/signal processing, statistical inference, analysis on networks, linear programming, nonlinear optimization.

MATH 703: Topics in Geometry I

Weimin Chen MWF 12:20-1:10

Prerequisites:

Solid understanding of abstract linear algebra, topology and calculus in n dimensions.

Text:

TBA

Description:

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

MATH 713: Intro Algebraic Number Theory

Paul Gunnells TuTh 8:30-9:45

Prerequisites:

Math 611, 612 or equivalent.

Description:

An introduction to algebraic number theory. Topics include rings of integers, Dedekind domains, ideal theory in algebraic number fields, class groups, units, factorization in Galois extensions, and an introduction to L-functions.

MATH 731: Partial Differential Equations I

Sohrab Shahshahani MW 8:40-9:55

Prerequisites:

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

Text:

The main reference for the course is Partial Differential Equations by L. C. Evans. Additional references will be introduced soon.

Description:

This is a graduate level class in linear partial differential equations. We will try to motivate the equations we study and the questions we ask about the behavior of solutions by means of examples from geometry and physics. The main focus will be the Laplace, heat, and wave equations and we will also discuss more general elliptic, parabolic, and hyperbolic equations (mostly of second order). Along the way we will also introduce important general tools and concepts such as Fourier analysis, Sobolev spaces, and weak solutions. Basic familiarity with real analysis (including basic functional analysis and knowledge of Hilbert spaces) is expected.

MATH 797RE: ST - Model, Simulation and Uncert Quant

Markos Katsoulakis TuTh 10:00-11:15

Prerequisites:

1. Stat607 or Math605,
2. Math623 or Math605 or equivalent (check with instructor)
3. Math532H or Math645 or any class in stochastic processes (not necessarily from math+stat)

Description:

We discuss first what are rare events, why are they important, how are they modeled and why their simulation is a significant high performance computing challenge. We will discuss some of the existing methods and will apply them in prototype systems in applications selected from (among others) queueing theory, molecular dynamics, biochemical reaction networks and finance. Furthermore, we will discuss mathematical theories for rare events and in particular elements of the theory of large deviations and its insights in providing better sampling algorithms for rare events. Finally, will also discuss recent progress on the uncertainty quantification and sensitivity analysis of rare events, that allow us to assess their impact on the predictions of statistical models.

MATH 797U: Lie Algebra

Ivan Mirkovic TuTh 2:30-3:45

Prerequisites:

Algebra 611. Also, the second algebra course 612 is recommended.

Text:

Book: James E. Humphreys, Introduction to Lie algebras and representation theory (Springer).

Recommended Text:

Notes: The book is not strictly necessary as we will also use a number of notes on Lie algebras are available online and there will be online class notes.

Description:

Lie algebras are linear algebra devices of great usefulness in mathematics and physics as an efficient tool for study of symmetries of objects.
The topics to be covered in this course include:
I) Notions of Lie algebras. Groups GL(n) and SL(n) and their Lie algebras.
Representations of Lie algebras,. Gauge Lie algebras.

II) Nilpotent and solvable Lie algebras: theorem’s of Engel, Lie and Cartan.

III) Semisimple Lie algebras: Killing form, root systems, classification.

IV) Representations of semisimple Lie algebras: enveloping algebras, classification of finite dimensional representations, Weyl and Kostant formulas; canonical bases and geometric constructions of representations.
Representations of Lie algebras, loop Lie algebras.

II) Nilpotent and solvable Lie algebras: theorem’s of Engel, Lie and Cartan.

III) Semisimple Lie algebras: Killing form, root systems, classification.

IV) Representations of semisimple Lie algebras. Enveloping algebras,. Classification of finite dimensional representations, Weyl and Kostant character formulas. Canonical bases and geometric constructions of representations.

STAT 605: Probability Theory I

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

Prerequisites:

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

Text:

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

Recommended Text:

Probability Essentials by Jean Jacod and Philip Protter, Universitext, Springer; 2nd edition (October 4, 2013) ISBN-10: 3540438718 ISBN-13: 978-3540438717

Probability: Theory and Examples by Rick Durrett, Cambridge Series in Statistical and Probabilistic Mathematics Cambridge University Press; 4 edition (August 30, 2010) ISBN-10: 0521765390 ISBN-13: 978-0521765398

Description:

Math 605: In this course we will build up the tools and foundations of probability theory needed for understanding and using statistical theories, stochastic simulation, and stochastic processes. Topics covered in this class are measure and integration (construction of probability spaces), distribution functions, random variables and their simulation, convergence of random variables, laws of large numbers and Monte-Carlo methods, concentration inequalities, central limit theorem, information theory, random walks.

A class in real analysis (integration theory, Math 623) is not required for this class as we will review, as needed, the basic constructions of probability spaces. It can be beneficial to take these two classes concurrently for the student who wants and in-depth understanding of the mathematical foundations of probability.

The primary goal of the class is to understand and master the basic probability tools and concepts needed in modern applications such as in stochastic simulation, data science and machine learning, engineering, and economics. Motivated students with various backgrounds are welcome.

The class is the first part of the sequence Math605/606 and Math 606 will cover the theory of stochastic processes and stochastic simulation: Martingale theory, Poisson processes, Markov chains in discrete and continuous time, Markov chain Monte-carlo, Brownian motion.

STAT 607: Mathematical Statistics I

Daeyoung Kim TuTh 10:00-11:15

Prerequisites:

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

Text:

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

Description:

The first part of a two-semester graduate level sequence in probability and statistics, this course develops probability theory at an intermediate level
(i.e., non measure-theoretic - Stat 605 is a course in measure-theoretic probability) and introduces the basic concepts of statistics.
Topics include: general probability concepts; discrete probability; random variables (including special discrete and continuous distributions) and random vectors;
independence; laws of large numbers; central limit theorem; statistical models and sampling distributions; and an introduction to point estimation,
confidence intervals, and hypothesis testing.
Statistical inference will be developed more fully in Stat 608.
This course is also suitable for graduate students in a wide variety of disciplines and will give strong preparation for further courses in statistics, econometrics, and
stochastic processes, time series, decision theory, operations research, etc.
You will be expected to read sections of the text book in parallel with topics covered in lectures, since important part of graduate study is to learn how to study independently.

STAT 625: Regression Modeling

Krista J Gile TuTh 2:30-3:45

Prerequisites:

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

Text:

Applied Linear Regression Models, by Kutner, Nachshem and Neter (4th edition) or Applied Linear Statistical Models by Kutner, Nachtshem, Neter and Li (5th edition). Both published by McGraw-Hill/Irwin. The first 14 chapters of Applied Linear Statistical Models (ALSM) are EXACTLY equivalent to the 14 chapters that make up Applied Linear Regression Models, 4th ed., with the same pagination. The second half of ALSM covers experimental design and the analysis of variance and is used in our ST526 course. (A) Students planning to take STAT 526 should buy the ALSM textbook.

Description:

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

STAT 697B: ST - Bayesian Statistics

Erin Conlon MW 2:30-3:45

Prerequisites:

Graduate students only. A one-year graduate level calculus-based statistical theory course such as STAT 607-608 or the equivalent is required, experience with regression at the level of STAT 525/STAT 697R is required, knowledge of matrix algebra, and prior experience with R including coding and data analysis (for example, at the level of STAT 535 [previously STAT 597A]). Stat 515-516 is not a sufficient prerequisite for this course.

Text:

Bayesian Methods for Data Analysis, 3rd Edition, by Carlin and Louis (2008), Taylor and Francis/CRC Press. ISBN-13: 978-1584886976.

Description:

This course will introduce students to Bayesian data analysis, including modeling and computation. We will begin with a description of the components of a Bayesian model and analysis (including the likelihood, prior, posterior, conjugacy and credible intervals), and illustrate these objects in simple models. We will then develop Bayesian approaches to more complex models such as regression models and hierarchical models. The course will introduce Markov chain Monte Carlo methods, and the R statistical language will be used throughout the course. Students will also have the opportunity to learn to use the JAGS and WinBUGS open source statistical packages for computation.

STAT 697ML: ST-Machine Learning

Patrick Flaherty TuTh 11:30-12:45

Prerequisites:

Students should have taken Stat515 as a prerequisite or Stat607 as a co-requisite. Students must have an understanding of linear algebra at the level of Math 235. Students must be comfortable with a high-level programming language such as MATLAB, R or python.

Text:

Pattern Recognition and Machine Learning by Bishop

Description:

This course is intended to provide a foundation in statistical machine learning with emphasis on statistical methodology as it applies to large-scale data applications using the graphical model framework. At the end of this course, students will be able to build and test a latent variable statistical model with companion inference algorithm to solve real problems in a domain of their interest including genomics, recommendation systems, topic modeling, and other high-dimensional data problems. Course topics include: exponential families, sufficiency and conjugacy, graphical model framework and approximate inference methods such as expectation-maximization, variational inference, and sampling-based methods. Additional topics may include: nonparametric Bayesian methods, cross-validation, bootstrap, empirical Bayes, and deep learning networks.

STAT 705: Linear Models I

John Staudenmayer MWF 10:10-11:00

Prerequisites:

Calculus based Probablity and Mathematical Statistics (preferably Stat 607-608 or rough equivalent), matrix theory and linear algebra.

Text:

TBA

Description:

Linear models are at the heart of many statistics techniques (linear regression and design of experiments), are closely related to many other important areas (multivariate analysis, time series, econometrics, etc.) and form the basis for many more modern techniques dealing with mixed and hierarchical models, both linear and nonlinear. Stat 705 is the first of two semester sequence covering the theory of linear models and related topics, but can also be taken as a stand-alone course. Coverage includes i) a brief review of important definitions and results from linear and matrix algebra and then what is assumed to be some new topics (idempotency, generalized inverses, etc.) in linear algebra; ii) Random vectors, multivariate distribution, the multivariate normal, linear and quadratic forms including an introduction to non-central t, chi-square and F distributions; iii) development of basic theory for inferences (estimation, confidence intervals, hypothesis testing, power) for the general linear model with "application" to both full rank regression and correlation models as well as some treatment of less than full rank models arising in the analysis of variance (one and some two-factor models). The applied part of the course is not directed towards extensive data analysis (which is available in many other applied courses). Instead, the emphasis with applications is on understanding and using the models and on some computational aspects, including understanding the documentation and methods used in some of the computing packages. [Stat 706 will pick up some additional regression topics, do more on experimental designs settings and then address mixed models of various forms including estimating variance components, modelling and analyzing linear mixed models broadly, and repeated measures/hierarchical regression models more specifically, and cover generalized linear and nonlinear mixed models.]