| Lower Division Courses | Math 100 | Math 101 | Math 102 | Math 104 |
| Math 113 | Math 121 | Math 127 | Math 128 | |
| Math 128H | Math 131 | Math 132 | Math 132H | |
| Math 233 | Math 233H | Math 235 | Math 300 | |
| Math 370 | Math 397A | Stat 111 | Stat 240 |
| Upper Division Courses | Math 331 | Math 411 | Math 412 | Math 421 |
| Math 425 | Math 441 | Math 455 | Math 456 | |
| Math 462 | Math 534H | Math 545 | Math 552 | |
| Math 563H | Stat 491A | Stat 501 | Stat 506 | |
| Stat 515 | Stat 516 |
| Graduate Courses | Math 612 | Math 621 | Math 624 | Math 652 |
| Math 691Y | Math 697LA | Math 697U | Math 704 | |
| Math 797AT | Stat 605 | Stat 608 | Stat 691P | |
| Stat 697L | Stat 706 |
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 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 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 300: Fundamental Concepts of Mathematics
Weimin Chen MWF 10:10-11:00
Arunas Rudvalis MWF 1:25-2:15
Prerequisites: Math 132
Text: Introduction to Mathematical Thinking: Algebra and Number Systems (paperback) by Will J. Gilbert, Scott A. Vanstone, Prentice Hall, ISBN 0131848682
Description: The goal of this course is to help students learn the language of rigorous mathematics, as structured by definitions, axioms and theorems. Students will be trained in how to read, understand, devise and communicate proofs of mathematical statements. A number of proof techniques (contrapositive, contradiction, and expecially induction) will be emphasized. We will discuss 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, quatifiers), and Number Theory (divisibility, Euclidean algorithm, congruences). Other possible topics from vector spaces, point set topology, groups and rings 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 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.)
Math 370: Writing in Mathematics
William Meeks MWF 12:20-1:10
Prerequisites: Math 300 and completion of College Writing (CW) requirement)
Text: TBA
Description: This course will focus on the structure, format, and execution of writing in, about, and with mathematics. Students will learn and use LaTeX. Part of the semester will also focus on building a solid resume and the job applications process.
Math 397A: Math. Found. of Act. Sci.
Thurlow Cook TuTh 2:30-3:45
Prerequisites: Math 233, 235 and Stat 515
Text: None
Description: This is a preparation course for the first actuarial exam in probability with applications to insurance. The student should have finished Calculus III (233), Linear Algebra (235) and Probability - Statistics (S515). Attendance is absolutely required - non attendance will result in a lowered grade. There is no new text required; course materials come from the SOA Web page. There will be weekly quizzes of questions from the past exams and some take-home exams. Your attendance and these exams will determine your grade.
Math 411: Introduction to Abstract Algebra I
Siman Wong MWF 10:10-11:00
Prerequisites: Math 235 or 236; Math 300 or permission of the instructor.
Text: Papantonopoulou, Algebra: Pure and Applied
Description: This course is an introduction to group theory, which is one of the oldest branches of modern algebra. It was invented in 1830 by a 19-year-old, Evariste Galois, with a goal of proving that there is no algebraic formula expressing the roots of every equation of degree 5 in terms of its coefficients. Since then, group theory has become the crucial tool in uncovering hidden symmetries of the world. The emphasis of this class will be on using concrete examples to develop problem-solving and proof-writing skills as we explore the abstract theory of groups. We will discuss permutations, cyclic and Abelian groups, cosets and Lagrange's theorem, quotient groups, group actions and Burnside's theorem.
Math 412: Introduction to Abstract Algebra II
Ivan Mirkovic TuTh 2:30-3:45
Prerequisites: Math 411
Text: Algebra: Pure and Applied Panpantonopoulou, Prentice Hall
Description: This course will be an introduction to ring and field theory. A ring is an algebraic system with two operations (addition and multiplication) satisfying various axioms, eg., the integers. We will see that many properties of the integers are shared by other broad classes of rings (for example polynomial rings with coefficients over a field). In particular we will explore the general notion of unique factorization and formulate conditions under which a ring has this property. Later in the course we will apply some of the results of ring theory to construct and study field extension. If time permits we will outline the main results of Galois theory which studies the structure of the extension generated by the roots of a polynomials in terms of an associated group.
Math 421: Complex Variables
Peter Dalakov MWF 11:15-12:05
Prerequisites: Math 233
Text: Churchill and Brown, Complex Variables and Applications, 8th Edition, McGraw-Hill 2009
Description: Introduction to complex variables. Topics: complex numbers, complex-valued functions of complex argument, differentiability. Cauchy-Riemann equations and harmonic functions. Integrals. Cauchy's integral formula and applications: Liouville's theorem, fundamental theorem of algebra, maximum modulus principle.
Sequences and series. Taylor and Laurent series. Isolated singular points. Residues. The residue theorem and evaluation of improper integrals. Conformal mappings.
Math 425: Advanced Multivariate Calculus
Peter Norman TuTh 2:30-3:45
Prerequisites: Math 233 and 235, or equivalent, knowledge of linear algebra and calculus of several variables
Text: Vector Calculus, 5th edition, by J.E. Marsden and A. J. Tromba
Description: This course treats the differential and integral calculus of several variables from an advanced perspective. Students are expected to be familiar with the fundamentals of multivariate calculus from Math 233. The course considers functions and mappings on n-dimensional space and develops the general notions of derivative and integrals. Some applications from geometry and optimization will motivate the theory. Also vector analysis in 3-space is fully developed, and its applications in physical science will be presented in enough detail to supply intuition about these concepts and formulas.
Math 425: Advanced Multivariate Calculus
HongKun Zhang TuTh 9:30-10:45
Prerequisites: Calculus I, II, III and linear algebra (Math 235). That is, a basic knowledge and understanding of differential and integral calculus in one, two and three real variables; multiplication of matrices and matrix of a linear transformation;
Text: Jerrold E. Marsden and Anthony J. Tromba, Vector Calculus, Fifth Edition, 2003, W.H. Freeman, ISBN: 0-7167-4992-0 (ISBN-13: 978-0-716-74992-9).
Description: This course treats the differential and integral calculus of functions of several variables from an advanced perspective. It considers mappings on n-dimensional space and develops the general notions of derivative and integral there. Some applications from geometry and optimization are used to motivate the theory. Specifics of vector analysis in 3-space are developed. The main goals are to understand, and to be able to do computations involving, the Implicit Function Theorem, the Change of Variables Theorem for integrals, and the classical theorems of Green, Gauss, and Stokes about line integrals, surface integrals, and volume integrals.
Math 441: Introduction to Mathematics of Finance
Eric Sommers MWF 10:10-11:00
Prerequisites: Math 131 and 132 or equivalent; knowledge of partial derivatives (Math 233) and probability (Stat 240 or higher)
Text: Notes by professor.
Recommend Text: Options, Futures, and other Derivatives 6th edition, by John C. Hull.
Description: This course is an introduction to the mathematical models used in finance with particular emphasis on models for pricing derivative instruments such as options and futures. The goal is to understand how the models derive from basic principles of economics, and to provide the necessary mathematical tools for their analysis. MATLAB will be used for some computational work.
Math 455: Introduction to Discrete Structures
Weimin Chen MWF 1:25-2:15
Prerequisites: Math 132, Math 235 or CMPSCI 250
Text: Discrete Mathematics with Applications, 3rd Edition; S. Epp
Description: This is an introduction to some topics of mathematics fundamental for computer science and engineering: combinatorics (systematic counting), elementary number theory, discrete probability, logic, graph theory, and, time permitting, cryptography. There will be weekly homework assignments, two mid-term exams, and a final exam.
Math 456: Mathematical Modeling
Bruce Turkington TuTh 9:30-10:45
Prerequisites: Calculus (Math 131, 132, 233), required: Linear Algebra (Math 235) and Differential Equations (Math 331), preferred.
Text: TBA
Description: We will 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. In the first half of the semester, we will introduce some classic models from different branches of science that serve as prototypes for all models. In the second half, each student will investigate a modeling problem individually and will report to the class in a final presentation. The choice of modeling topics will be partially determined by the interests and background of the enrolled students, and the mathematical methods applied will draw upon whatever the students have already learned.
Math 462: Geometry II
Paul Hacking MWF 11:15-12:05
Prerequisites: Math 461: Geometry I
Text: Geometry and Topology, by Miles Reid and Balazs Szendroi, Cambridge. We will also use the Math 461 text Modern Geometries, by Michael Henle.
Description: This course is a continuation of Math 461: Geometry I.
We study euclidean, spherical, hyperbolic, affine, and projective geometries, with particular emphasis on the group of symmetries in each case.
Math 534H: Introduction to Partial Differential Equations
Panos Kevrekidis TuTh 11:15-12:30
Prerequisites: Math 233, 235, 331
Text: Partial Differential Equations: An Introduction by W. Strauss
Description: The course will cover the following topics: Introduction to and classification of second-order partial differential equations, wave equation, heat equation and Laplace equation, D'Alembert solution to the wave equation, solution of the heat equation, maximum principle, energy methods, separation of variables, Fourier series, Fourier transform methods and operator eigenvalue problems. Time-permitting, we will briefly examine numerical methods for partial differential equations, as well as some select examples of nonlinear partial differential equations. The final grade will be determined on the basis of homework, an in-class midterm and a final exam.
Math 545: Linear Algebra for Applied Mathematics
Robin Young TuTh 1:00-2:15
Qian-Yong Chen MWF 11:15-12:05
Note: Expect to use a computer linear algebra package such as Matlab or GNU Octave (a free clone), or something of your choice.
Prerequisites: Math 233, 235 and 300 or equivalents, or consent of the instructor.
Text: Linear Algebra and Its Applications, 4th ed., By Gilbert Strang
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, time permitting, numerical issues and/or basic linear programming. There will be elements of proof and computation in the course.
Math 552: Applications of Scientific Computing
Hans Johnston TuTh 2:30-3:45
Prerequisites: Math 551 or equivalent
Text: Elementary Numerical Analysis (3rd edtion),, Atkinson & Han, (Wiley)
Description: This course is the second half of a sequence in scientific computing, the first being Math 551, which is a prerequisite for this course. We will cover the following topics: Advanced Topics in Numerical Linear Algebra; Numerical Methods for Differential Equations; Finite Difference Methods for PDEs.
Grading Policy: Homework (30%), midterm exam (35%) and final exam (35%).
Homework assignments will be given out every week or so. While you may work on the homework in groups, they must be individually submitted. Problems should appear in the order they were assigned, graphs attached when required, and everything stapled together. Homework is due at the beginning of class on the given date. The midterm and final exam scores together with homework scores will determine your course grade, and the homework scores will be used to push the course grade up or down in borderline cases. Late homework will not be accepted.
Math 563H: Differential Geometry
Rob Kusner TuTh 11:15-12:30
Prerequisites: Math 233 (or 425), 235 (or 545) and preferably 461 or 462 (especially the Geometry and the Imagination version taught last spring by Rob Kusner)
Text: Curves and Surfaces by Sebastian Montiel and Antonio Ros and possibly Elementary Differential Geometry by Barrett O'Neill ISBN 0-12-526743-2
Description: This course will treat the differential geometry of curves and surfaces, emphasizing global and variational aspects of the subject. Examples and exercises, some drawn from research of UMass students and faculty, will help in learning the material. We will also develop more sophisticated tools, such as the calculus of differential forms and the basic topology of surfaces, than are usually found in the standard texts on the topic. In particular, we will treat the Gauss-Bonnet theorem connecting total curvature of a surface to its Euler Characteristic. We will also cover special topics including the global geometry of curves (periodic space curves and the four vertex theorem for plane curves that are necessarily convex) and special surfaces (Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature, for example) as time and tastes permit.
Math 612: Algebra II
Jenia Tevelev MWF 10:10-11:00
Prerequisites: Math 611 (Algebra I) or consent of instructor
Text: Basic Algebra (Knapp)
Recommend Text: Algebra (Lang), Galois Theory(Cox), Introduction to Commutative Algebra (Atiyah, Macdonald), Representation theory: a first course (Fulton, Harris)
Description: This is a second half of the standard graduate algebra sequence. We will concentrate on Galois theory and on basic representation theory.
Math 621: Complex Analysis
Tom Weston MWF 9:05-9:55
Prerequisites: Advanced Calculus. Students are expected to have a working knowledge of complex numbers and functions at the level of M421 for example.
Text: Complex Analysis, by Stein and Shakarchi, Princeton, 2003.
Description: We will cover the basic theory of functions of one complex variable, at a pace that will allow for the inclusion of some non-elementary topics at the end. Basic Theory: Holomorphic functions, conformal mappings, Cauchy's Theorem and consequences, Taylor and Laurent series, singularities, residues, elliptic functions, other topics as time permits.
Math 624: Real Analysis II
Robert Gardner TuTh 9:30-10:45
Prerequisites: Math 523 and 623, or equivalent
Text: Real Analysis, 2nd ed., Folland
Description: This course is a continuation of Math 623, and will cover the following topics: differentiation of functions of bounded variation and the fundamental theorem of calculus for Lebegue-integrable functions, theory of Lp spaces, introduction to functional analysis and operator theory in Banach and Hilbert space, distributional derivatives and Sobolev space, Fourier series representation of L2 functions and applications to elementary partial differential equations.
Math 652: Numerical Solution of PDE's
Nathaniel Whitaker TuTh 2:30-3:45
Prerequisites: Math 651 or permission of instructor.
Text: Numerical Solution of Partial Differential Equations, K. W. Morton and D. F. Mayers, Cambridge University Press, ISBN 0-521-42922-6 or latest edition.
Description: The following is a brief outline: Boundary and initial value problems in ordinary differential equations (finite difference and shooting methods), Finite difference methods for partial differential equations (consistency, stability and convergence), Finite Element Methods and Spectral Methods. Applications to various contexts from physics, chemistry, and biology will be discussed. Homework and programming will be assigned.
Math 691Y: Applied Mathematics Project Seminar
Qian-Yong Chen F 2:30-3:45
Text: TBA
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 an applied science problem, 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. The particular topic to be investigated will be announced at the first class meeting.
Math 697LA: Introduction to Lie Algebras
Eric Sommers MWF 11:15-12:05
Prerequisites: Math 411-412 and a good background in linear algebra. It is advisable to have completed 611.
Text: Humphreys, J.E., Introduction to Lie algebras and representation theory, Springer, 1994.
Description: An introduction to the classification of semisimple Lie algebras and their representation theory. Topics covered include root systems and the Weyl group; survey of the classical Lie algebras; structure theory and classification; and highest weight theory.
Math 697U: Stochastic Processes
Luc Rey-Bellet MWF 10:10-11:00
Prerequisites: Stat 515 or Stat 607 or equivalent.
Text: Introduction to Stochastic Processes, Second Edition 2006, Chapman & Hall/CRC by Gregory Lawler
Description: This class is an introduction to stochastic processes and Monte-Carlo methods. One of the goal of this class is to develop the mathematical tools to analyze the short-time and long-time behavior of systems subject to random forces. In particular we consider Markov chains on countable state space and discuss the concepts of ineducibility, aperiodicity, recurrence as well as law of large numbers (ergodicidy) and its refinements (central-limit theorom and large deviations). We illustrate the theory with various examples such as random walks, birth and death processes, queueing and branching processes, stochastic Ising models and so on. We will also discuss Monte-Carlo methods which are efficient stochastic algorithms designed to simulate a given probability distribution. If time permits we will discuss Brownian motion and martingales.
Math 704: Theory of Manifolds II
Eduardo Cattani MW 2:30-3:45
Prerequisites: Math 703
Text: No textbook required.
Recommend Text: Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry; Lee: Introduction to Smooth Manifolds and Riemannian Manifolds: an Introduction to Curvature ; Spivak: Differential Geometry, vol. I and II.
Description: This course is the continuation of Math 703. In the first half of the semester we will discuss differential forms, integration of manifolds and deRham cohomology. The second half will be an introduction to Riemannian geometry.
After discussing the classical theory of surfaces we will study basic notions such as connections, curvature, and geodesics in arbitrary Riemannian manifolds. Additional topics, if time permits.
Math 797AT: Algebraic Topology
Tom Braden TuTh 1:00-2:15
Prerequisites: Math 671 and Math 611.
Text: Allen Hatcher, Algebraic Topology, Cambridge University Press. Also available for download from the author's website.
Description: An introduction to the basic tools of algebraic topology, which studies topological spaces and continuous maps by producing associated algebraic structures (groups, vector spaces, rings, and homomorphism between them). Emphasis will be placed on being able to compute these invariants, not just on their definitions and associated theorems.
Topics will include: Homotopy, fundamental group and covering spaces, simplical and cell complexes, singular and simplicial homology, long exact sequences and excision, cohomology, Künneth formulas, Poincaré duality.
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
Stat 491A: Statistics Cross-Disciplinary Research
Michael Lavine TUTH 9:30-10:45
Prerequisites: Permission of the instructor.
Text: None
Recommend Text: None
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 will 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. That way, all students will learn about several areas of application and about 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. Each team will make an oral presentation to the department's faculty at the end of the semester.
Stat 501: Methods of Applied Statistics
Joanna Jeneralczuk TuTh 11:15-12:30
Prerequisites: Knowledge of high school algebra, junior standing or higher
Text: Introduction to Probability , Mendenhall, Beaver and Beaver, 13th ed.
Description: An applied statistics course for graduate students and upper level undergraduates with no previous background in statistics who will need statistics in their further studies in 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, contingency tables. The course has a large data-analytic component using a statistical computing package.
Stat 506: Design of Experiments
John Staudenmayer MWF 9:05-9:55
Prerequisites: Previous coursework in Statistics including knowledge of estimation, hypothesis testing and confidence intervals (Stat 516 or S501)
Text: Applied Linear Statistical Models by Kutner, et.al. (5th ed.)
Description: An applied statistics course on the analysis design and interpretation of experiments of various types. Coverage includes factorial designs, randomized blocks, Latin squares, incomplete block designs, nested, and crossover designs, random effects and mixed models. Data analysis using R (no prior experience assumed).
Stat 515: Statistics I
Daeyoung Kim TuTh 9:30-10:45
H. K. Hsieh MW 2:30-3:45
Prerequisites: Two semeseters of single variable calculus (Math 131-132 or equivalent).
Text: Mathematical Statistics with Applications(7th Edition) : D. D. Wackerly, W. Mendenhall and R. L. Schaeffer
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 Stat 516). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, the central limit theorem, and sampling distributions.
Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.
We will cover much of chapters 2-7 in the text (with some omissions) and probably some portions of chapter 8.
Stat 516: Introduction to Probability and Statistics II
Daeyoung Kim TuTh 1:00-2:15
Prerequisites: Stat 515 or equivalent
Text: Mathematical Statistics with Applications, 7th edition by Wackerly, Mendenhall, Schaeffer.
Description: Basic theory of point and interval estimation and hypothesis testing; development in one and two sample problems, simple linear regression, and some topics out of the one-way analysis of variance; discrete data and nonparametric methods.
Stat 605: Probability Theory
HongKun Zhang TuTh 1:00-2:15
Prerequisites: Math 623 (Real Analysis) or permission of instructor
Text: A. N. Shiryaev, Probability, (2nd Edition), Springer-Verlag, New York, 1996
Recommend Text: Leo Breiman, Probability,(Addison-Wesley Publishing Co., London, 1968.
Description: The subject matter of probability theory is the mathematical analysis of random events, which are empirical phenomena having some statistical regularity but not deterministic regularity. The theory combines aesthetic beauty, deep results, and the ability to model and to predict the behavior of a wide range of physical systems as well as systems arising in technological applications. In order to properly handle applications involving continuous state spaces, a measure-theoretic treatment of probability is required. The purpose of this course is to present such a treatment, which is based on Kolmogorov’s axiomatic approach. Topics to be covered include the following: a) random variables, expectation, independence, laws of large numbers, weak convergence, central limit theorems, and large deviations; b) the concepts of conditional probability and conditional expectation; c) basic properties of certain classes of random processes such as Markov chains and random walks.
Stat 608: Mathematical Statistics II
Michael Lavine MWF 11:15-12:05
Prerequisites: Stat 607 or permission of instructor
Text: Introduction to Statistical Thought. Lavine. Available for free download at
www.math.umass.edu/~lavine//Book/book.html
Recommend Text: Statistical Inference. Casella and Berger. This is one of the most widely used texts for similar courses around the world. You may want to have it as a reference or for its different presentation of the material.
Description: This is the second part of a two semester sequence on probability and mathematical statistics. Stat 607 covered basic probability and basic statistical modelling and inference. Stat 608 covers more advanced probability and statistics topics. As with Stat 607 this is primarily a theory course emphasizing fundamental concepts and techniques, including computing in the R statistical environment
Stat 691P: Project Seminar
Michael Lavine TuTh 9:30-10:45
Prerequisites: Permission of the instructor.
Text: None
Recommend Text: None
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 will 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. That way, all students will learn about several areas of application and about 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. Each team will make an oral presentation to the department's faculty at the end of the semester.
Stat 697L: Categ. Data Anal
Anna Liu TuTh 11:15-12:30
Prerequisites: Pevious course work in probabliity and mathematical statistics including knowledge of distribution theory, estimation, confidence intervals, hypothesis testing and multiple linear regression; e.g. Stat 516 and Stat 505 (or equivalent).
Text: Categorical data analysis by Alan Agresti, Wiley. 2nd edition.
Description: Distribution and inference for binomial and multinomial
variables with contingency tables, generalized linear models, logistic
regression for binary responses, logit models for multiple response
categories, loglinear models, inference for matched-pairs and correlated
clustered data. Textbook chapters 1-12 are to be covered.
Stat 706: Linear Models II
H. K. Hsieh MWF 12:20-1:10
Prerequisites: Linear models I, and SAS codes or any other computing skill (e.g. R)
Text: First part of the lecture (about 1/4) will be based on N. Ravishanker and D.K. Dey's A First Course in Linear Model Theory and the rest will be based on Generalized Linear and Mixed Models, 2nd ed. , McCulloch, Scale and Neuhaus, Wiley
Description: 1. Review of major theorems proved in S705. 2) Two-factor fixed effects models: Complete designs and incomplete designs; main effects and interactions; testing for interactions, and interpretations of mail effects if interactions are significant; computation of expected mean squares; power of the F-test and estimation of sample sizes. 3) One and two factor with random effects: Estimation of variance components; best linear unbiased predictors (BLUP); justification for some sums of squares to have chi-square distributions; construction of F-tests; BIB and nested designs. 4) Some Large sample results: Asymptotic LR test, information matrix, Wald tests, score tests. 5) Linear mixed models: Model formulation; estimation techniques - ML, REML, EM, Bayesian, etc;; growth curves analysis. 6) Generalized linear models: Discrete response models (e.g., binary regression); link function, estimation and asymtotic confidence intervals and tests of hypotheses. 7) Multivariate techniques: Principal components, structure models, discrimination.
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