# Course Descriptions

## Lower Division Courses

### 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.

Note:

Students cannot receive credit for MATH 101 if they have already received credit for any MATH or STATISTC course numbered 127 or higher.

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 114: Math for Elementary Teachers II

See Preregistration guide for instructors and times

Prerequisites:

MATH 113

Description:

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

### MATH 121: Linear Methods and Probability for Business

See Preregistration guide for instructors and times

Prerequisites:

Working knowledge of high school algebra and plane geometry.

Description:

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

### MATH 127: Calculus for Life and Social Sciences I

See Preregistration guide for instructors and times

Prerequisites:

Proficiency in high school algebra, including word problems.

Description:

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

### MATH 128: Calculus for Life and Social Sciences II

See Preregistration guide for instructors and times

Prerequisites:

Math 127

Description:

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

### MATH 131: Calculus I

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

### MATH 132: Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

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

### MATH 233: Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

Techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals. Theorems of Green, Stokes and Gauss. Honors section available. (Gen.Ed. R2)

### 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; corequisite: Math 233

Text:

TBA

Description:

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

### STAT 111: Elementary Statistics

See Preregistration guide for instructors and times

Prerequisites:

High school algebra.

Description:

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

### STAT 190F: Foundations of Data Science

See SPIRE for instructors and times

Prerequisites:

Completion of the R1 General Education Requirement (or a score of 20 or higher on the Math Placement Exam, Part A) or one of the following courses: Math 101 & 102, Math 104, 127, 128, 131, or 132.

Note:

CS, INFORMATICS, AND MATH & STATS MAJORS ARE NOT ELIGIBLE. STUDENTS WILL NEED TO BRING A LAPTOP WITH A REASONABLY UP-TO-DATE WEB BROWSER.

Description:

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

### STAT 240: Introduction to Statistics

See Preregistration guide for instructors and times

Description:

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

### STAT 297F: ST - Fundamental Concepts/Stats

Krista J Gile TuTh 11:30-12:45

Prerequisites:

Math 132.

Text:

Statistical Inference via Data Science, Chester Ismay and Albert Y. Kim, 2020. Online edition freely available: \url{https://moderndive.com/}

Note:

Open to Math majors only.

Description:

This course is an introduction to the fundamental principles of statistical science. It does not rely on detailed derivations of mathematical concepts, but does require mathematical sophistication and reasoning. It is an introduction to statistical thinking/reasoning, data management, statistical analysis, and statistical computation. Concepts in this course will be developed in greater mathematical rigor later in the statistical curriculum, including in STAT 515, 516, 525, and 535. It is intended to be the first course in statistics taken by math majors interested in statistics. Concepts covered include point estimation, interval estimation, prediction, testing, and regression, with focus on sampling distributions and the properties of statistical procedures. The course will be taught in a hands-on manner, introducing powerful statistical software used in practical settings and including methods for descriptive statistics, visualization, and data management.

## Upper Division Courses

### MATH 300.1: Fundamental Concepts of Mathematics

Weimin Chen TuTh 1:00-2:15

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

How to Prove It, by Daniel J. Velleman, 2nd edition, Cambridge University Press.

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

Kuan-Wen Lai MWF 10:10-11:00

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

Description:

Math 300 is an introduction to rigorous, abstract mathematics. In lower-level courses like calculus, the emphasis is on applying theorems and formulas to solve specific, often numerical, problems. More advanced math classes are concerned with developing the theorems and formulas and solving general classes of problems. In particular, it's important to know why those theorems and formulas are true. In mathematics, the way we know a statement is true is by giving a proof of it, and this course is about learning what proof is, how to read, create, and present proofs, and how to tell a correct proof from an incorrect one. In many ways, this is like learning a language. We need to learn the grammar (logical deduction) and vocabulary (sets, functions, and other basic structures), but it also helps to have something to say. So we will also study some important and beautiful mathematics along the way. Starting with explicit axioms and precisely stated definitions, we will systematically develop basic propositions about integers and modular arithmetic, induction and recursion, equivalence classes and rational numbers, and such other topics as time allows.

### MATH 300.3: Fundamental Concepts of Mathematics

Kuan-Wen Lai MWF 9:05-9:55

Prerequisites:

Math 132 with a grade of C or better

Text:

Description:

Math 300 is an introduction to rigorous, abstract mathematics. In lower-level courses like calculus, the emphasis is on applying theorems and formulas to solve specific, often numerical, problems. More advanced math classes are concerned with developing the theorems and formulas and solving general classes of problems. In particular, it's important to know why those theorems and formulas are true. In mathematics, the way we know a statement is true is by giving a proof of it, and this course is about learning what proof is, how to read, create, and present proofs, and how to tell a correct proof from an incorrect one. In many ways, this is like learning a language. We need to learn the grammar (logical deduction) and vocabulary (sets, functions, and other basic structures), but it also helps to have something to say. So we will also study some important and beautiful mathematics along the way. Starting with explicit axioms and precisely stated definitions, we will systematically develop basic propositions about integers and modular arithmetic, induction and recursion, equivalence classes and rational numbers, and such other topics as time allows.

### MATH 370.1: Writing in Mathematics

Alejandro Morales TuTh 11:30-12:45

Prerequisites:

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

Description:

This course will introduce students to writing in mathematics, both technical and otherwise. Writing assignments will include proofs, instructional handouts, resumes, cover letters, presentations, and a final paper. All assignments will be completed using LaTeX using offline and online editors. By the end of the semester, students should be able to clearly convey mathematical ideas through their writing, and to tailor that writing for a particular audience. Students will also learn about LaTeX offline and online editors, file sharing and version control (GitHub).

### MATH 370.2: Writing in Mathematics

Andrew Havens MWF 10:10-11:00

Prerequisites:

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

Description:

While the mathematicians of the pre-internet age often spread their mathematical ideas within the community via written letters prior to publication, modern mathematical correspondence and exposition is rapidly facilitated by a variety of digital tools. Of great importance to the publishing process in mathematical sciences is the LaTeX markup language, used to typeset virtually all modern mathematical publications, even at the pre-print stage. In this course we will develop facility with LaTeX, and develop a variety of writing practices important to participation in the mathematical community. There will be regular written assignments completed in LaTeX, as well as collaborative writing assignments, owing to the importance of collaborative writing in mathematical research. Writing topics may include proofs, assignment creation, pre-professional writing (resumes/cover letters, research and teaching statements), expository writing for a general audience, recreational mathematics, and the history of mathematics. Short writing assignments on such topics will be assigned in response to regular assigned readings from a variety of accessible/provided sources. Towards the end of the semester groups will complete a research paper of an expository nature and craft a seminar style presentation. This course meets the junior year writing requirement.

### MATH 370.3: Writing in Mathematics

Andrew Havens MWF 12:20-1:10

Prerequisites:

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

Description:

While the mathematicians of the pre-internet age often spread their mathematical ideas within the community via written letters prior to publication, modern mathematical correspondence and exposition is rapidly facilitated by a variety of digital tools. Of great importance to the publishing process in mathematical sciences is the LaTeX markup language, used to typeset virtually all modern mathematical publications, even at the pre-print stage. In this course we will develop facility with LaTeX, and develop a variety of writing practices important to participation in the mathematical community. There will be regular written assignments completed in LaTeX, as well as collaborative writing assignments, owing to the importance of collaborative writing in mathematical research. Writing topics may include proofs, assignment creation, pre-professional writing (resumes/cover letters, research and teaching statements), expository writing for a general audience, recreational mathematics, and the history of mathematics. Short writing assignments on such topics will be assigned in response to regular assigned readings from a variety of accessible/provided sources. Towards the end of the semester groups will complete a research paper of an expository nature and craft a seminar style presentation. This course meets the junior year writing requirement.

### MATH 411.1: Introduction to Abstract Algebra I

Jenia Tevelev TuTh 1:00-2:15

Prerequisites:

Math 235; Math 300 or CS 250

Text:

Audrey Terras, Abstract Algebra with Applications (Cambridge Mathematical Textbooks), 1st Edition

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 counting with groups.

### MATH 411.2: Introduction to Abstract Algebra I

Jenia Tevelev TuTh 2:30-3:45

Prerequisites:

Math 235; Math 300 or CS 250

Text:

Audrey Terras, Abstract Algebra with Applications (Cambridge Mathematical Textbooks), 1st Edition

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 counting with groups.

### MATH 412: Introduction to Abstract Algebra II

Eric Sommers TuTh 1:00-2:15

Prerequisites:

Math 411

Text:

"Abstract Algebra" by Saracino, Dan. 2nd Edition. ISBN: 9781577665366

Description:

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

### MATH 421: Complex Variables

Laura Colmenarejo TuTh 10:00-11:15

Prerequisites:

Math 233

Text:

Complex Variables and Applications, 8th Edition, by James Ward Brown and Ruel V. Churchill, McGraw-Hill.

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 Laurent series. Classification of isolated singularities. The Argument Principle and Rouche's Theorem. Evaluation of Improper integrals via residues. Conformal mappings.

### MATH 425.2: Advanced Multivariate Calculus

Mohammed Zuhair Mullath MWF 10:10-11:00

Prerequisites:

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

Description:

Calculus of several variables, Jacobians, implicit functions, inverse functions; multiple integrals, line and surface integrals, divergence theorem, Stokes' theorem.

### MATH 425.3: Advanced Multivariate Calculus

Mohammed Zuhair Mullath MWF 11:15-12:05

Prerequisites:

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

Description:

Calculus of several variables, Jacobians, implicit functions, inverse functions; multiple integrals, line and surface integrals, divergence theorem, Stokes' theorem.

### MATH 455: Introduction to Discrete Structures

Paul Gunnells TuTh 8:30-9:45

Prerequisites:

Calculus (MATH 131, 132, 233), Linear Algebra (MATH 235), and Math 300 or CS 250.

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, enumeration, and generating functions. As part of the course, student groups will be assigned and a final project will be presented. This course satisfies the university's Integrative Experience (IE) requirement for math majors.

### MATH 456.1: Mathematical Modeling

Jinguo Lian MWF 9:05-9:55

Prerequisites:

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

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 456.2: Mathematical Modeling

Qian-Yong Chen TuTh 10:00-11:15

Prerequisites:

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

Text:

Textbook: Not following any particular book.

General mathematical references:

Topics in Mathematical Modeling, by K. K. Tung, Princeton University Press, 2007;

Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. American Mathematical Society.

Game theory by James N. Webb. Springer Undergraduate Series.

Description:

Math 456 is an introduction to mathematical modeling, and is one of the Integrated Experience courses approved by the General Education Council. The main goal of the class is to learn how to translate problems from "real-life" into a mathematical model and how to use mathematics to solve the problem. We will learn how to build, use and critique mathematical models. In the beginning, we'll focus on differential equation based models. For the second half, we will study a number of topics from games and gambling, economics, social sciences, for which we will use elementary tools from probability, game theory, information theory, and optimization.

In addition, each student will join a group of 3 students, and the group will investigate a modeling problem. Each group will give a final presentation at the end of the semester. Each student will write an individual report on the group project at the end of the course. After discussion/consultation with the instructor, the choice of modeling topics will be 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 456.3: Mathematical Modeling

Yao Li MWF 12:20-1:10

Prerequisites:

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

Note:

Not following any particular book. General mathematical references:

Topics in Mathematical Modeling, by K. K. Tung, Princeton University Press, 2007;

Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. American Mathematical Society.

Game theory by James N. Webb. Springer Undergraduate Series.

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. In the beginning, we'll focus on differential equation based models. For the second half, we will study a number of topics from games and gambling, economics, social sciences, for which we will use elementary tools from probability, game theory, information theory, and optimization. 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 471: Theory of Numbers

Vefa Goksel MWF 1:25-2:15

Prerequisites:

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

Text:

Elementary Number Theory, 7th edition, by David Burton.

Description:

Basic properties of the positive integers including congruence arithmetic, the theory of prime numbers, quadratic reciprocity, and continued fractions. Some additional topics may be discussed as time permits. To help learn these materials, students will be assigned computational projects using computer algebra software.

### MATH 475: History of Mathematics

Franz Pedit MW 2:30-3:45

Prerequisites:

Math 131, 132, 233 and Math 300 or CS 250.

Recommended Text:

Mathematics and its History, by John Stillwell. Springer Undergraduate Texts.
History of Mathematics, by Craig Smorynski, Springer.
A Concise History of Mathematics, by Dirk Struik, Dover Publications.
And any book with History of Mathematics'' in the title.

Note:

No text book purchases necessary.

Description:

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

### MATH 523H: Int. Mod. Analysis I

Franz Pedit MW 4:00-5:15

Prerequisites:

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

Recommended Text:

Elementary Analysis: The Theory of Calculus, by Kenneth Ross. Springer
Introduction to Real Analysis, by William Trench https://digitalcommons.trinity.edu/mono/7/
Fundamental Ideas of Analysis, by Michael Reed. John Wiley & Sons.
Analysis by its History, by Hairer and Wanner. Springer.
Any text book which covers Analysis in one variable.

Note:

Text book purchase not necessary.

Description:

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

### MATH 524: Introduction to Modern Analysis II

Zahra Sinaei MWF 11:15-12:05

Prerequisites:

MATH 523H

Description:

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

### MATH 534H: Introduction to Partial Differential Equations

Wei Zhu MWF 12:20-1:10

Prerequisites:

Math 233, 235, and 331.

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

Text:

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

Recommended Text:

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

Description:

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

### MATH 536: Actuarial Probability

Eric Knyt TuTh 8:30-9:45

Prerequisites:

Math 233 and Stat 515

Text:

ASM Study Manual for Exam P by Weishaus , 3nd edition with StudyPlus+ - DIGITAL

Description:

This course is based on the first examination of the Society of Actuaries. Its content is largely dependent on that examination. Presently, it covers: calculus of a single variable (integration, differentiation, infinite series, Taylor's series etc.); calculus of several variables (Jacobians, Lagrange multipliers, double and triple integrals, etc.); probability Theory (discrete and continuous distributions, conditional probability and expectations, Bayes' rule, joint distributions, moment generating functions, the central limit theorem, etc.) The problems are drawn from old SOA examinations and most will have an insurance industry emphasis. Much of the material is a review of several courses, but this review is extensive and probably exceeds most interested students' backgrounds.

### MATH 537: Intro. to Math of Finance

HongKun Zhang TuTh 11:30-12:45

Prerequisites:

Math 233 and either Stat 515 or MIE 273

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

Eric Sarfo Amponsah TuTh 1:00-2:15

Prerequisites:

Math 233 and 235, both with grade of 'C' or better, Math 300 or CS 250

Text:

Linear Algebra and Its Applications, 4th ed., By Gilbert Strang

Recommended Text:

Linear Algebra and Its Applications, 4th ed., By Gilbert Strang

Description:

Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications.

### MATH 545.2: Linear Algebra for Applied Mathematics

Siman Wong MWF 12:20-1:10

Prerequisites:

Math 233 and 235, both with grade of 'C' or better, Math 300 or CS 250

Description:

Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications. Homeworks include programming projects.

### MATH 545.3: Linear Algebra for Applied Mathematics

Prerequisites:

Math 233 and 235, both with grade of 'C' or better, Math 300 or CS 250

Description:

Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications.

### MATH 545.4: Linear Algebra for Applied Mathematics

Eric Sarfo Amponsah TuTh 4:00-5:15

Text:

Linear Algebra and Its Applications, 4th ed., By Gilbert Strang

Recommended Text:

Linear Algebra and Its Applications, 4th ed., By Gilbert Strang

Description:

Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications.

### MATH 551.1: Intr. Scientific Computing

Hans Johnston TuTh 11:30-12:45

Prerequisites:

MATH 233 & 235 and either COMPSCI 121, E&C-ENG 122, PHYSICS 281, or E&C-ENG 242

Knowledge of a scientific programming language, e.g. MATLAB, Fortran, C, C++, Python, Java.

Text:

A First Course in Numerical Methods, by Ascher & Greif (SIAM) SBN-13: 978-0898719970

Note:

You may purchase the book (suggested), or access the full text for FREE via the UMass Library:

Description:

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis.

### MATH 551.2: Intr. Scientific Computing

Hans Johnston TuTh 10:00-11:15

Prerequisites:

MATH 233 & 235 and either COMPSCI 121, E&C-ENG 122, PHYSICS 281, or E&C-ENG 242

Knowledge of a scientific programming language, e.g. MATLAB, Fortran, C, C++, Python, Java.

Text:

A First Course in Numerical Methods, by Ascher & Greif (SIAM) SBN-13: 978-0898719970

Recommended Text:

You may purchase the book (suggested), or access the full text for FREE via the UMass Library:

Description:

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis.

### MATH 551.3: Intr. Scientific Computing

Maria Correia TuTh 3:20-3:45

Prerequisites:

MATH 233 & 235 and either COMPSCI 121, E&C-ENG 122, PHYSICS 281, or E&C-ENG 242

Knowledge of a scientific programming language, e.g. MATLAB, Fortran, C, C++, Python, Java.

Text:

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

Description:

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis.

### MATH 552: Applications of Scientific Computing

Matthew Dobson MWF 9:05-9:55

Prerequisites:

Math 233, Math 235, Math 331 or permission of instructor, Math 551 (or equivalent) or permission of instructor.

Knowledge of scientific programming language is required.

Text:

Timothy Sauer, Numerical Analysis

Description:

Introduction to the application of computational methods to models arising in science and engineering. Topics include finite differences, finite elements, boundary value problems, Monte-Carlo simulation, Brownian motion, stochastic differential equations, finding eigenvalues, and finding singular values.

### MATH 563H: Differential Geometry

Rob Kusner MW 2:30-3:45

Prerequisites:

Very good understanding of Advanced Multivariable Calculus and Linear Algebra (Math 425, 233 and 235). Math 331 highly recommended.

Text:

Curves and Surfaces: Second Edition
Sebastián Montiel and Antonio Ros
Publication Year: 2009
ISBN-10: 0-8218-4763-5
ISBN-13: 978-0-8218-4763-3
Graduate Studies in Mathematics, vol. 69.R

Recommended Text:

• O'Neill
• doCarmo
• Rob's notes (links here http://www.gang.umass.edu/~kusner/class/classes.html being updated)

Note:

This is a homework- and project-based course. All students will complete a challenging expository-research project and will make a final oral presentation, which (at least during the COVID19 pandemic) may be via YouTube (and possibly also Zoom)

Description:

This course is an introduction to differential geometry, where we apply theory and computational techniques from linear algebra, multivariable calculus and differential equations to study the geometry of curves, surfaces and (as time permits) higher dimensional objects; global and variational aspects of geometry will be a central theme of the course.

### STAT 501: Methods of Applied Statistics

Joanna Jeneralczuk TuTh 11:30-12:45

Prerequisites:

Knowledge of high school algebra, junior standing or higher

Description:

For graduate and upper-level undergraduate students, with focus on practical aspects of statistical methods.Topics include: data description and display, probability, random variables, random sampling, estimation and hypothesis testing, one and two sample problems, analysis of variance, simple and multiple linear regression, contingency tables. Includes data analysis using a computer package.

### STAT 515.1: Statistics I

Jiayu Zhai TuTh 11:30-12:45

Prerequisites:

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

Description:

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

### STAT 515.2: Statistics I

Prerequisites:

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

Description:

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

### STAT 515.3: Statistics I

Prerequisites:

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

Description:

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

### STAT 515.4: Statistics I

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

Prerequisites:

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

Description:

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

### STAT 515.5: Statistics I

Jiayu Zhai TuTh 2:30-3:45

Prerequisites:

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

Description:

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

### STAT 515.6: Statistics I

Faith Zhang MWF 1:25-2:15

Prerequisites:

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

Description:

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

### STAT 515.7: Statistics I

Faith Zhang MWF 12:20-1:10

Prerequisites:

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

Description:

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

### STAT 516.1: Statistics II

Zheni Utic MWF 9:05-9:55

Prerequisites:

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

Description:

Continuation of Stat 515. The overall objective of the course is the development of basic theory and methods for statistical inference from a mathematical and probabilistic perspective. Topics include: sampling distributions; point estimators and their properties; method of moments; maximum likelihood estimation; Rao-Blackwell Theorem; confidence intervals, hypothesis testing; contingency tables; and non-parametric methods (time permitting).

### STAT 516.2: Statistics II

Haben Michael TuTh 2:30-3:45

Prerequisites:

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

Text:

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

Description:

Continuation of Stat 515. The overall objective of the course is the development of basic theory and methods for statistical inference from a mathematical and probabilistic perspective. Topics include: sampling distributions; point estimators and their properties; method of moments; maximum likelihood estimation; Rao-Blackwell Theorem; confidence intervals, hypothesis testing; contingency tables; and non-parametric methods (time permitting).

### STAT 516.3: Statistics II

Zheni Utic MWF 10:10-11:00

Prerequisites:

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

Description:

Continuation of Stat 515. The overall objective of the course is the development of basic theory and methods for statistical inference from a mathematical and probabilistic perspective. Topics include: sampling distributions; point estimators and their properties; method of moments; maximum likelihood estimation; Rao-Blackwell Theorem; confidence intervals, hypothesis testing; contingency tables; and non-parametric methods (time permitting).

### STAT 516.4: Statistics II

Haben Michael TuTh 4:00-5:15

Text:

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

Description:

Continuation of Stat 515. The overall objective of the course is the development of basic theory and methods for statistical inference from a mathematical and probabilistic perspective. Topics include: sampling distributions; point estimators and their properties; method of moments; maximum likelihood estimation; Rao-Blackwell Theorem; confidence intervals, hypothesis testing; contingency tables; and non-parametric methods (time permitting).

### STAT 525.1: Regression Analysis

Maryclare Griffin TuTh 8:30-9:45

Prerequisites:

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

Description:

Regression analysis is the most popularly used statistical technique with application in almost every imaginable field. The focus of this course is on a careful understanding and of regression models and associated methods of statistical inference, 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; expressing regression models and methods in matrix form; an introduction to weighted least squares, regression with correlated errors and nonlinear regression. Extensive data analysis using R or SAS (no previous computer experience assumed). Requires prior coursework in Statistics, preferably ST516, and basic matrix algebra. Satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

### STAT 525.2: Regression Analysis

Maryclare Griffin TuTh 10:00-11:15

Prerequisites:

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

Description:

Regression analysis is the most popularly used statistical technique with application in almost every imaginable field. The focus of this course is on a careful understanding and of regression models and associated methods of statistical inference, 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; expressing regression models and methods in matrix form; an introduction to weighted least squares, regression with correlated errors and nonlinear regression. Extensive data analysis using R or SAS (no previous computer experience assumed). Requires prior coursework in Statistics, preferably ST516, and basic matrix algebra. Satisfies the Integrative Experience requirement for BA-Math and BS-Math majors.

### STAT 525.3: Regression Analysis

Mike Sullivan TuTh 1:00-2:15

Prerequisites:

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

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 526: Design Of Experiments

Zijing Zhang Thursdays 6:00-8:30 PM

Prerequisites:

Stat 516 (previous coursework in statistics including knowledge of estimation, hypothesis testing and confidence intervals).

Text:

Required: Applied Linear Statistical Models, 5th Edition; Authors: Kutner, Nachtsheim, Neter, Li; Year Published: 2005; ISBN-13 Number 9780073108742.

Note:

Offered through the UMass Newton campus Stat M.S. program (fully remote in Spring 2021).

Description:

An applied statistics course on planning, statistical analysis and interpretation of experiments of various types. Coverage includes factorial designs, randomized blocks, incomplete block designs, nested and crossover designs. Computer analysis of data using the statistical package SAS (no prior SAS experience assumed).

### STAT 535: Statistical Computing

Patrick Flaherty MW 2:30-3:45

Prerequisites:

Stat 516 and CompSci 121

Description:

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

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

Anna Liu and Krista J Gile Fridays 12:20-1:10

Prerequisites:

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

Description:

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

### MATH 612: Algebra II

Tom Weston TuTh 10:00-11:15

Prerequisites:

Math 611 (or consent of the instructor).

Description:

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

I. Group Theory and Representation Theory.

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

II. Linear Algebra and Commutative Algebra.

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

III. Field Theory and Galois Theory

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

### MATH 621: Complex Analysis

Sohrab Shahshahani MW 8:40-9:55

Description:

Complex number field, elementary functions, holomorphic functions, integration, power and Laurent series, harmonic functions, conformal mappings, applications.

### MATH 624: Real Analysis II

Robin Young MWF 11:15-12:05

Prerequisites:

Math 523H, Math 524 and Math 623.

Text: Recommended Text: Description:

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

### MATH 646: Applied Math and Math Modeling

Qian-Yong Chen TuTh 8:30-9:45

Description:

This course covers classical methods in applied mathematics and math modeling, including dimensional analysis, asymptotics, regular and singular perturbation theory for ordinary differential equations, random walks and the diffusion limit, and classical solution techniques for PDE. The techniques will be applied to models arising throughout the natural sciences.

### MATH 652: Int Numerical Analysis II

Brian Van Koten MW 2:30-3:45

Prerequisites:

Math 651

Description:

Presentation of the classical finite difference methods for the solution of the prototype linear partial differential equations of elliptic, hyperbolic, and parabolic type in one and two dimensions. Finite element methods developed for two dimensional elliptic equations. Major topics include consistency, convergence and stability, error bounds, and efficiency of algorithm.

### MATH 672: Algebraic Topology

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

Prerequisites:

Math 671, Math 611 or equivalent.

Description:

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

Grade will be based on regularly assigned homework, an in-class exam, and a final presentation.

### MATH 691Y: Applied Math Project Sem.

Matthew Dobson Fridays 2:30-3:45

Prerequisites:

Graduate Student in Applied Math MS Program

Description:

Continuation of Project

### MATH 697FA: ST - Math Foundations of Probabilistic Artificial Intelligence II

Luc Rey-Bellet and Markos Katsoulakis TuTh 11:30-12:45

Description:

This is the second semester of a 2-semester, year long, class on probabilistic artificial intelligence. The main emphasis of the course is on building and understanding the mathematical tools and conceptual foundations of AI, especially from a probabilistic point of view. Furthermore, group projects of the students will serve to explore applications and implementations.

### MATH 697U: ST-Stochastic Processes and Appl

Yao Li MWF 10:10-11:00

Prerequisites:

Stat 605 or Stat 607. A good working knowledge of linear algebra and analysis.

Text:

Pierre Brémaud, Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues.

Description:

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

### MATH 704: Topics in Geometry II

Weimin Chen TuTh 10:00-11:15

Prerequisites:

Math 671-2, Math 703.

Description:

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

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

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

### MATH 797RM: ST - Moduli Spaces/Reprsnt Theory

Owen Gwilliam MWF 12:20-1:10

Description:

This course will be a guided tour of moduli spaces that have played a central role in topology, differential geometry, and representation theory. The emphasis will be on explicit examples rather than theory. For more details, visit https://people.math.umass.edu/~celliott/Math797RM.html

### MATH 797W: ST - Algebraic Geometry

Eyal Markman TuTh 11:30-12:45

Description:

Algebraic geometry is the study of geometric spaces locally defined by polynomial equations. It is a central subject in mathematics with strong connections to differential geometry, number theory, and representation theory. This course will be a fast-paced introduction to the subject with a strong emphasis on examples.

In the algebraic approach to the subject, local data is studied via the commutative algebra of quotients of polynomial rings in several variables. Passing from local to global data is delicate (as in complex analysis) and is either accomplished by working in projective space (corresponding to a graded polynomial ring) or by using sheaves and their cohomology.

Topics will include projective varieties, singularities, differential forms, line bundles, and sheaf cohomology, including the Riemann--Roch theorem and Serre duality for algebraic curves. Examples will include projective space, the Grassmannian, the group law on an elliptic curve, blow-ups and resolutions of singularities, algebraic curves of low genus, and hypersurfaces in projective 3-space.

Prerequisites: Commutative algebra (rings and modules) as covered in 611-612. Some prior experience of manifolds would be useful (but not essential).

### STAT 608.1: Mathematical Statistics II

Daeyoung Kim TuTh 10:00-11:15

Prerequisites:

STAT 607 or permission of the instructor.

Text:

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

Recommended Text:

All of Statistics: A Concise Course in Statistical Inference, by Larry Wasserman

Description:

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

### STAT 608.2: Mathematical Statistics II

Hyunsun Lee Mondays 6:00-8:30 PM

Prerequisites:

Statistc 607 or equivalent, or permission of the instructor.

Text:

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

Recommended Text:

All of Statistics: A Concise Course in Statistical Inference, by Larry Wasserman

Note:

Offered through the UMass Newton campus Stat M.S. program (fully remote in Spring 2021).

Description:

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

### STAT 697D: ST - Applied Statistics and Data Analysis

Anna Liu and Krista J Gile TuTh 2:30-3:45 and Fridays 12:20-1:10

Description:

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

### STAT 697DS: Statistical Methods for Data Science

Hyunsun Lee Tuesdays 6:00-8:30 PM

Prerequisites:

Probability and Statistics at a calculus-based level such as Stat 607 and Stat 608 (concurrent) or Stat 515 and Stat 516 (concurrent), and knowledge of regression at the level of Stat 525 or Stat 625. Students must have an understanding of linear algebra at the level of Math 235. Students must have prior experience with a statistical programming language such as R, Python or MATLAB.

Text:

Required: “An Introduction to Statistical Learning: with Applications in R” by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, 2013, Springer. ISBN-13: 978-1461471370.

Note:

Offered through the UMass Newton campus Stat M.S. program (fully remote in Spring 2021).

Description:

This course provides an introduction to the statistical techniques that are most applicable to data science. Topics include regression, classification, resampling, linear model selection and regularization, tree-based methods, support vector machines and unsupervised learning. The course includes a computing component using statistical software. Students must have prior experience with a statistical programming language such as R, Python or MATLAB.

### STAT 697MV: ST - Applied Multivariate Statistics

Shai Gorsky Mondays 6:00-8:30 PM

Prerequisites:

Open to Graduate Students only. Undergraduates may enroll with permission of instructor.

Prerequisites: Probability and Statistics at a calculus-based level such as Stat 607 and Stat 608 (concurrent) or Stat 515 and Stat 516 (concurrent). Students must have prior experience with a statistical programming language such as R, Python or MATLAB.

Text:

Required: “Applied Multivariate Statistical Analysis”, 6th edition, by R.A. Johnson and D.W. Wichern, Prentice Hall. ISBN-13: 978-0131877153.

Note:

Offered through the UMass Newton campus Stat M.S. program (fully remote in Spring 2021).

Description:

This course provides an introduction to the more commonly-used multivariate statistical methods. Topics include principal component analysis, factor analysis, clustering, discrimination and classification, multivariate analysis of variance (MANOVA), and repeated measures analysis. The course includes a computing component.

### STAT 697V: ST - Data Visualization

Shai Gorsky Wednesdays 6:00-8:30 PM

Prerequisites:

Open to Graduate Students only. Undergraduates may enroll with permission of instructor.

Prerequisites: Probability and Statistics at a calculus-based level such as Stat 607 and Stat 608 (concurrent) or Stat 515 and Stat 516 (concurrent). Students must have prior experience with a statistical programming language such as R, Python or MATLAB.

Text:

Required: “Graphical Data Analysis with R” by Antony Unwin, 2015, CRC Press. ISBN-13: 978-1498715232.

Recommended Text:

(Recommended): “Interactive Data Visualization for the Web”, 2nd edition, by Scott Murray, 2017, O’Reilly Media. ISBN-13: 978-1491921289.

Note:

Offered through the UMass Newton campus Stat M.S. program (fully remote in Spring 2021).

Description:

The increasing production of descriptive data sets and corresponding software packages has created a need for data visualization methods for many application areas. Data visualization allows for informing results and presenting findings in a structured way. This course provides an introduction to graphical data analysis and data visualization. Topics covered include exploratory data analysis, data cleaning, examining features of data structures, detecting unusual data patterns, and determining trends. The course will also introduce methods to choose specific types of graphics tools and understanding information provided by graphs. The statistical programming language R is used for the course.