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

See Preregistration guide for instructors and times.

Prerequisites:

Math 127

Description:

Honors section of Math 128.

### MATH 131: Calculus I

See Preregistration guide for instructors and times

Prerequisites:

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

Description:

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

### MATH 132: Calculus II

See Preregistration guide for instructors and times

Prerequisites:

Math 131 or equivalent.

Description:

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

### MATH 233: Multivariate Calculus

See Preregistration guide for instructors and times

Prerequisites:

Math 132.

Description:

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

## Upper Division Courses

### MATH 300.1: Fundamental Concepts of Mathematics

Prerequisites:

Math 132 with a grade of 'C' or better

Text:

Title: How to Prove it: A structured Approach, 2nd edition
Author: Daniel J. Velleman, by Cambridge Univ. 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). 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

Prerequisites:

Math 132 with a grade of 'C' or better

Description:

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

### MATH 300.3: Fundamental Concepts of Mathematics

Prerequisites:

Math 132 with a grade of C or better

Description:

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

### MATH 370.1: Writing in Mathematics

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 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 370.2: Writing in Mathematics

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 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

Prerequisites:

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

Description:

Satisfies Junior Year Writing requirement. Develops research and writing skills in mathematics through peer review and revision. Students write on mathematical subject areas, prominent mathematicians, and famous mathematical problems.

### MATH 411.1: Introduction to Abstract Algebra I

Prerequisites:

Math 235; Math 300 or CS 250

Description:

Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning.

### MATH 411.2: Introduction to Abstract Algebra I

Prerequisites:

Math 235; Math 300 or CS 250

Description:

Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning.

### MATH 411.3: Introduction to Abstract Algebra I

Prerequisites:

Math 235; Math 300 or CS 250

Description:

Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning.

### MATH 412: Introduction to Abstract Algebra II

Prerequisites:

Math 411

Text:

A First Course in Abstract Algebra by John Fraleigh

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. Basic 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. In addition to learning theoretical tools, we will also experiment with rings and fields using the computer algebra system MAGMA.

### MATH 421: Complex Variables

Prerequisites:

Math 233

Text:

Complex Variables and Applications, 8-th 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. Evaluation of Improper integrals via residues. Conformal mappings.

### MATH 455: Introduction to Discrete Structures

Prerequisites:

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

Text:

Combinatorics and Graph Theory, by Harris, Hirst, and Mossinghoff, Second edition, Springer-Verlag.

Note:

A pdf of this book can be downloaded free from the University Library. An ebook version or a print-on-demand softcover is also available.

Description:

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

### MATH 456.1: Mathematical Modeling

Prerequisites:

Math 233 and Math 235. Some familiarity with a programming language is desirable (R studio, Python, etc.). Some familiarity with statistics and probability is desirable.

Recommended Text:

I will post my lecture notes, you do not need to buy a textbook, but if you want, then you may buy the following book online,

Statistics for risk modeling, 2ed or later by Abraham Weishaus. You can buy it online at http://www.studymanuals.com/Product/Show/453142456

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

Prerequisites:

Math 233 and Math 235. Some familiarity with a programming language is desirable (R studio, Python, etc.). Some familiarity with statistics and probability is desirable.

Recommended Text:

I will post my lecture notes, you do not need to buy a textbook, but if you want, then you may buy the following book online,

Statistics for risk modeling, 2ed or later by Abraham Weishaus. You can buy it online at http://www.studymanuals.com/Product/Show/453142456

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 456.3: Mathematical Modeling

Prerequisites:

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

Description:

Mathematics is usually termed as “the language of nature”. Complex physical phenomenon can be described by mathematical models with sufficient accuracy. In this course, students learn how to formulate and analyze some real-world problems by utilizing concepts, methods and theories from mathematics, thus coming to understand the interplay between mathematical theory and practice. Since mathematical models can be very broad and can appear in every discipline, this course will mainly focus on problems rising from data science. The goal is to discuss how to build and learn mathematical models in data-driven applications. Students will form several groups to investigate a modeling problem and each group will report their findings in a final presentation. Prerequisites of the course include Calculus (Math 131, 132, 233), Linear Algebra (Math 235) and Differential Equations (Math 331). Some familiarity with a programming language is desirable (Matlab, Python, etc.)

### MATH 471: Theory of Numbers

Prerequisites:

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

Text:

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

Recommended Text:

The Higher Arithmetic: An Introduction to the Theory of Numbers, by Harold Davenport.

Description:

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

### MATH 475: History of Mathematics

Prerequisites:

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

Description:

This course is an introduction to the history of mathematics, touching on aspects from ancient civilizations to present day. Students will explore several major mathematical discoveries in their cultural, historical, and scientific contexts, and so it offers them an opportunity to integrate their knowledge of mathematics with other kinds of intellectual and human endeavor. This course will involve presentations, group projects, class discussions, and a final paper. It satisfies the Integrative Experience requirement for BA-MATH and BS-MATH majors.

### MATH 513: Combinatorics

Prerequisites:

COMPSCI 250 or MATH 455 with a grade of 'B' or better. Math 411 recommended but not required. Mathematical maturity.

Text:

T. Kyle Petersen, Inquiry-Based Enumerative Combinatorics, Undergraduate Texts Mathematics, Springer, 2019.

Description:

This course is a basic introduction to enumerative combinatorics and graph theory for advanced undergraduates in computer science, mathematics, engineering and science. Topics covered include: permutations, recurrences generating functions, counting trees, counting Eulerian circuits, matchings, Catalan numbers, random partitions, plane partitions, and Mobius inversion.

### MATH 523H: Introduction to Modern Analysis I

Prerequisites:

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

Description:

This course is an introduction to mathematical analysis. A rigorous treatment of the topics covered in calculus will be presented with a particular emphasis on proofs. Topics include: properties of real numbers, sequences and series, continuity, Riemann integral, differentiability, sequences of functions and uniform convergence.

### MATH 524: Introduction to Modern Analysis II

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

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.

Description:

The course will start with the study of transport equations, and an introduction to and classification of second-order partial differential equations and their applications. Subsequently, we will proceed to examine in more detail the wave equation, heat equation and Laplace equation. For instance, we will touch upon the D'Alembert solution to the wave equation, the solution of the heat equation, the maximum principle, energy methods, separation of variables, Fourier series and Fourier transform methods, as well as operator eigenvalue problems.

Time-permitting, we will briefly examine numerical methods for partial differential equations and relevant implementation thereof, e.g., in Matlab, as well as some select examples of nonlinear partial differential equations and the traveling or standing wave solutions possible therein.

The final grade will be determined on the basis of attendance/in class participation, homework, an in-class midterm and a final exam.

### MATH 536: Actuarial Probability

Prerequisites:

Math 233 and Stat 515

Recommended Text:

ASM Study Manual for Exam P by Weishaus , 4th 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

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

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 545.2: 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. 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

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

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.

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

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.

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

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.

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

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.

Description:

Introduction to the application of computational methods to models arising in science and engineering, concentrating mainly on the solution of partial differential equations. Topics include finite differences, finite elements, boundary value problems, fast Fourier transforms.

### MATH 557: Linear Optimization and Polytopes

Prerequisites:

Math 235, Math 300 or CS 250

Description:

This proof-based course covers the fundamentals of linear optimization and polytopes and the relationship between them. The course will give a rigorous treatment of the algorithms used in linear optimization. The topics covered in linear optimization are graphical methods to find optimal solutions in two and three dimensions, the simplex algorithm, duality and Farkas’ lemma, variation of cost functions, an introduction to integer programming and Chvátal-Gomory cuts. The topics covered simultaneously in polytopes are polytopes in two and three dimensions, f-vectors, equivalence of the vertex and hyperplane descriptions of polytopes, the Hirsch conjecture, the secondary polytope, and an introduction to counting lattice points of polytopes.

### MATH 571: Intro Mathematical Cryptography

Prerequisites:

CompSci 250/Math 300 and Math 471 or permission of the instructor

Text:

An Introduction to Mathematical Cryptography (Second Edition), Hoffstein, Pipher, Silverman, Springer 2014.

Description:

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

### MATH 597F: ST - Fourier Methods

Prerequisites:

MATH 235, 300, and 331

Description:

The course introduces and uses Fourier series and Fourier transform as a tool to understand varies important problems in applied mathematics: linear ODE & PDE, time series, signal processing, etc. We'll treat convergence issues in a non-rigorous way, discussing the different types of convergence without technical proofs. Topics: complex numbers, sin & cosine series, orthogonality, Gibbs phenomenon, FFT, applications, including say linear PDE, signal processing, time series, etc; maybe ending with (continuous) Fourier transform.

### STAT 310: Fundamental Concepts of Statistics

Prerequisites:

Math 132

Note:

Previously numbered Stat 297F

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.

### STAT 501: Methods of Applied Statistics

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 (R)

### STAT 515.1: 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 515.2: 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

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

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

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

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

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

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 516.3: Statistics II

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

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 525.1: Regression Analysis

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

Prerequisites:

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

Text:

Applied Linear Regression Models by Kutner, Nachsteim and Neter (4th edition) or, Applied Linear Statistical Models by Kutner, Nachtsteim, Neter and Li (5th edition). Both published by McGraw-Hill/Irwin.

Note:

The first 14 chapters of Applied Linear Statistical Models (ALSM) are EXACTLY equivalent to the 14 chapters that make up Applied Linear Regression Models, 4th ed., with the same pagination. The second half of ALSM covers experimental design and the analysis of variance, and is used in our STAT 526. If you are going to take STAT 526, you should buy the Applied Linear Statistical Models (but it is a large book).

Description:

Regression 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

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 526: Design Of Experiments

Prerequisites:

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

Text:

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

Note:

This course will be delivered in a multi-modal format. Students have the option to take the course remotely via Zoom or in-person at Mount Ida

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 programming software SAS (no prior SAS experience assumed).

### STAT 535: Statistical Computing

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)

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

Prerequisites:

Math 611 (or consent of the instructor).

Text:

(required) Abstract Algebra, 3rd edition by Dummit and Foote

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.

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.

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 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

Prerequisites:

Advanced Calculus. Students are expected to have a working knowledge of complex numbers and functions at the level of Math 421 for example.

Text:

Complex Analysis by Stein & Shakarchi

Description:

We will cover the basic theory of functions of one complex variable, at a pace that will allow for the inclusion of some non-elementary topics at the end. Basic Theory: Holomorphic functions, conformal mappings, Cauchy's Theorem and consequences, Taylor and Laurent series, singularities, residues; other topics as time permits.

### MATH 624: Real Analysis II

Prerequisites:

Math 523H, Math 524 and Math 623.

Description:

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

### MATH 646: Applied Math and Math Modeling

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

Prerequisites:

Math 651 or permission of the instructor

Recommended Text:

Finite Difference Methods for Ordinary and Partial Differential Equations,
Randall J LeVeque. SIAM. ISBN 978-0-898716-29-0

Numerical Methods for Conservation Laws, Randall J LeVeque. Springer 1992. ISBN 978-3-0348-8629-1

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic
Conservation Laws, Chi-Wang Shu, NASA/CR-97-206253. ICASE Report No. 97-65

Spectral Methods for Time-dependent problems,
Jan S. Hesthaven, Sigal Gottlieb, David Gottlieb,
Cambridge Monographs on Applied and Computational Mathematics, Series Number 21

K.W. Morton and D.F. Mayers, Numerical Solution of Partial Differential Equations, 2nd
edition, Cambridge

Description:

The first topic to cover is the finite difference methods for both boundary value problems and
initial value problems. The focus is on building an understanding of
the development, analysis and practical use of finite difference methods for parabolic, elliptic equations
and hyperbolic conservation laws. The concept of consistency, stability, and convergence will be reviewed.
The second topic is the spectral methods. Basic theoretical framework will be covered. It will be applied to solve
1D and 2D non-linear Schrodinger equation.

Regular homework and programming projects will be assigned every one or two
weeks. Allowed programming languages include: Matlab, Fortran, C, C++, Python, Julia.
Grades will be based on homework and programming projects.

### MATH 672: Algebraic Topology

Prerequisites:

Math 671, Math 611 or equivalent.

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.

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

Prerequisites:

Graduate Student in Applied Math MS Program

Description:

Continuation of Project.

### MATH 697AC: ST - Analytic Combinatorics

Prerequisites:

(a good background in discrete math (e.g.Math 455 or Compsci575/Math513) OR analysis (e.g. Math 421 or Math 523) ) AND (willingness to learn substantial specific techniques from various other areas of mathematics)

Description:

Large recursively defined discrete structures such as trees, strings, permutations and compositions can be precisely analysed by encoding them using the generating function (GF), a formal algebraic encoding of the relevant information. In most cases we can interpret the GF as a complex function and derive a lot of information from studying its singularities. This powerful and beautiful theory (a discrete analog of the way differential equations are solved via using Laplace or Fourier transforms) has many applications to probability theory, statistical physics, computational biology, information theory, and analysis of algorithms in computer science. There are strong connections with computer algebra, special functions, and asymptotic expansions of integrals.

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

Prerequisites:

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

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 705: Symplectic Topology

Prerequisites:

A solid understanding of Math 703. Basic elements of Riemannian geometry, Kahler geometry, and characteristic classes are preferable, but not absolutely required.

Text:

Instructor will provide lecture notes.

Description:

This course aims to introduce the basic notions and techniques of symplectic topology. The core materials can be grouped into 3 units as follows.

Part 1. Foundational Materials
1. Basic notions and examples.
2. Linear symplectic geometry.
3. Moser's argument.
4. Symplectic group actions.

Part 2. Fundamental constructions
1. Symplectic cutting and symplectic blowing-up.
2. Symplectic fiber bundles.
3. Symplectic normal connected sum.
4. Symplectic handlebodies and Weinstein manifolds.

Part 3. Aspect of contact geometry
1. Basic notions and examples.
2. Stability and neighborhood theorems.

Depending on the students' preparations and interests, some pseudo-holomorphic curve theory or advanced topics from contact geometry could also be included. Final Grade is based on a few homework assignments, a final presentation, and in-class participation.

### MATH 708: Complex Algebraic Geometry

Prerequisites:

Holomorphic functions of one complex variable (at the level of Math 621).
Differentiable Manifolds and their de Rham cohomology (at the level of Math 703).

Recommended Text:

Principles of algebraic geometry, by Phillip Griffiths and Joseph Harris.
Complex geometry, an introduction, by Daniel Huybrechts.
Algebraic geometry I: Complex projective varieties, by David Mumford.
Hodge theory and complex algebraic geometry I and II, by Claire Voisin.

Description:

An introduction to the geometry of complex projective varieties, including topology, Hodge theory, singularities, and the study of curves and surfaces.

### MATH 725: Intro Functional Analysis I

Prerequisites:

A solid working knowledge in Analysis such as Math 623-624. In case of doubt, contact your instructor.

Text:

No official textbook, but many references will be provided.

Description:

Functional analysis deals with the structure of infinite dimensional vector spaces and (mostly) linear on such spaces. Many such spaces are spaces of functions, hence the name functional analysis, but we it covers also space of measures and much of the theory will developed for abstract spaces (spaces with a norm or a scale product).

We shall assume that the reader has taken Math 624 (or an equivalent course) and is familiar with the basic objects of functional analysis: Banach spaces and Hilbert spaces, linear functionals and duals, bounded linear operators. We will review these topics but at a rather brisk pace. Our main goal is to develop a series of tools instrumental in the applications of functional analysis to PDE's, probability, machine learning, ergodic theory, etc... Among the topics covered in this class are

• The fundamental theorems of functional analysis: Hahn-Banach theorem, Baire theorem, Inverse mapping and closed graph theorems.
• Spectral theory I: Compact operators, Fredholm operators and applications
• Positive operators
• Semigroups
• Spectral theory II: The spectral theorem
• Unbounded operators
• Banach algebras

### MATH 797LD: ST - Low Dimensional Topology

Prerequisites:

Point-set and algebraic topology (671-672), differentiable manifolds (703), or the consent of the instructor

Text:

Matsumoto, "An introduction to Morse theory"
Gompf and Stipsicz, "4-manifolds and Kirby calculus"

Recommended Text:

Saveliev, "Lectures on the topology of 3-manifolds"
Thurston, "Three dimensional geometry and topology"
Ozbagci and Stipsicz, "Contact and symplectic topology"
Barth, Peters and van de Ven, "Compact complex surfaces"

Note:

The course grade will be based on homework and final presentations

Description:

The goal of this course is to study knots, surfaces, 3- and 4-dimensional spaces using geometric, topological, and algebraic methods.

### STAT 608.1: Mathematical Statistics II

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

Prerequisites:

STAT 607 or equivalent, or permission of the instructor.

Note:

This class meets on the Newton Campus of UMass-Amherst. This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

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 610: Bayesian Statistics

Prerequisites:

Graduate students only. A one-year graduate level calculus-based statistical theory course such as STAT 607-608 or the equivalent is required, experience with regression at the level of STAT 625 is required, knowledge of matrix algebra, and prior experience with R including coding and data analysis (for example, at the level of STAT 535). Stat 515-516 is not a sufficient prerequisite for this course.

Text:

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

Note:

This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

This class meets on the Newton Campus of UMass-Amherst.

Description:

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

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

Prerequisites:

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

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.

Note:

This class meets on the Newton Campus of UMass-Amherst. This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

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

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.

Note:

This class meets on the Newton Campus of UMass-Amherst. This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

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 697TS: ST - Time Series Analysis and Appl

Prerequisites:

Open to Graduate Math and Statistics students only.
Prerequisites: STAT 607/608 for familiarity with maximum likelihood estimation. STAT 625 or 705 for familiarity with linear algebra, specifically in the context of regression, recommended but not required.

Description:

This course will cover several workhorse models for analysis of time series data. The course will begin with a thorough and careful review of linear and general linear regression models, with a focus on model selection and uncertainty quantification. Basic time series concepts will then be introduced. Having built a strong foundation to work from, we will delve into several foundational time series models: autoregressive and vector autoregressive models. We will then introduce the state-space modeling framework, which generalizes the foundational time series models and offers greater flexibility. Time series models are especially computationally challenging to work with - throughout the course we will explore and implement the specialized algorithms that make computation feasible in R and/or STAN. Weekly problem sets, two-to-three short exams, and a final project will be required.

### STAT 697V: ST - Data Visualization

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.

Note:

This class meets on the Newton Campus of UMass-Amherst. This course may be taken remotely. Please enroll and contact the instructor if you would like to take the course remotely.

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 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.