Computer Science | Mathematics

## Computer Science

### COMP 110 - Data and Computing Fundamentals

An introduction to the handling, analysis, and interpretation of "big data," the massive datasets now routinely collected in science, commerce, and government. The course is designed to be accessible to all students, regardless of background. Students will become proficient with R, a leading data and statistics computer environment. R skills are in high demand in research, commercial, NGO, and government areas. The course aligns with techniques being used in several courses in the sciences, statistics, and mathematics.

### COMP 120 - Computing and Society

Topics course that introduces students to the field of computing by way of a central theme. Topics vary; offerings include Digital Humanities, Green Computing, and Social Media. Full description given in advance of registration. This course is suitable for students with little or no experience with computing, but it can serve as a starting point for the Computer Science major.

Frequency: Typically offered in the fall as a first-year course.

### COMP 123 - Core Concepts in Computer Science

**This course introduces the field of computer science, including central concepts such as the design and implementation of algorithms and programs, testing and analyzing programs, the representation of information within the computer, and the role of abstraction and metaphor in computer science. The exploration of these central ideas will draw examples from a range of application areas including multimedia processing, turtle graphics, and text processing. Course work will use the Python programming language.**

Frequency: Every semester.

### COMP 124 - Object-Oriented Programming and Data Structures

This course introduces the principles of software design and development using the object-oriented paradigm (OOP) and the Java programming language. Students will learn to use data structures such as lists, trees and hash tables and they will compare the efficiency of these data structures for a particular application. Students will learn to decompose a project using OOP principles. They will work with integrated development environments (IDEs) and version control systems. Students will practice their skills by creating applications in areas such as graphics, games, simulations, and natural language processing. There is a required 1.5 hour laboratory section associated with this course.

Frequency: Every semester.

### COMP 154 - Ethics and the Internet

This course looks at ethical questions connected with the internet as we know it today: an online environment where content is generated and shared through user activities such as blogging, media sharing, social networking, tagging, tweeting, virtual world gaming, wiki developing, and the like. We will start by considering debates over freedom of speech, privacy, surveillance, and intellectual property: issues that pre-exist the development of the Internet, but which because of it have taken on new dimensions. From here we will go on to take up some ethical questions arising from four different domains of activity on the social web: gaming, social networking, blog/wiki developing, and "hacktivism." In the third part of the course, we will consider broad questions connected to the integration of the Internet with devices other than the personal computer and mobile phone and which open the prospect of a world of integrated networked systems. What are some of the impacts of such integration on our everyday ethical relations with others and on the overall quality of our lives? How does being networked affect the meaning of being human?

Frequency: Offered alternate years.

**Cross-Listed as**

### COMP 194 - Topics Course

Varies by semester. Consult the department or class schedule for current listing.

### COMP 221 - Algorithm Design and Analysis

An in-depth introduction to the design and analysis of algorithms. Topics may include algorithmic paradigms and structures, including recursion, divide and conquer, dynamic programming, greedy methods, branch and bound, randomized, probabilistic, and parallel algorithms, non-determinism and NP completeness. Applications to searching and sorting, graphs and optimization, geometric algorithms, and transforms.

Frequency: Every fall.

### COMP 225 - Software Design and Development

This course builds upon the software design foundation started in COMP 124. Students will design and implement medium-sized software projects using modern software design principles such as design patterns, refactoring, fault tolerance, stream-based programming, and exception handling. The concept of a distributed computing system will be introduced, and students will develop multithreaded and networked applications using currently available software libraries. Advanced graphical user interface methods will be studied with an emphasis on appropriate human-computer interaction techniques. Students will use operating systems services and be introduced to methods of evaluating the performance of their software.

Frequency: Every spring.

**Prerequisite(s)**

COMP 124 or permission of instructor.

### COMP 240 - Computer Systems Organization

This course familiarizes the student with the internal design and organization of computers. Topics include number systems, internal data representations, microarchitectures, the functional units of a computer system, memory, processor, and input/output structures, instruction sets and assembly language, addressing techniques, system software, and concurrency and parallelism.

Frequency: Every fall.

**Prerequisite(s)**

COMP 124 , or permission of instructor.

### COMP 261 - Theory of Computation

A discussion of the basic theoretical foundations of computation as embodied in formal models and descriptions. The course will cover finite state automata, regular expressions, formal languages, Turing machines, computability and unsolvability, and the theory of computational complexity.

Frequency: Every spring.

**Cross-Listed as**

### COMP 294 - Topics Course

Varies by semester. Consult the department or class schedule for current listing.

### COMP 302 - Introduction to Database Management Systems

This course will introduce students to the design, implementation, and analysis of databases stored in database management systems (DBMS). Topics include implementation-neutral data modeling, database design, database implementation, and data analysis using relational algebra and SQL. Students will generate data models based on real-world problems, and implement a database in a state-of-the-art DBMS. Students will master complex data analysis by learning to first design database queries and then implement them in a database query language such as SQL. Advanced topics include objects in databases, indexing for improved performance, distributed databases, and data warehouses.

Frequency: Offered every spring semester.

### COMP 320 - Computational Biology

This course will examine selected topics in computational biology, including basic bioinformatics, algorithms used in genomics an genome analysis, computational techniques for systems biology, and synthetic biology. This is an interdisciplinary course that will often be cross-listed with a course in Biology.

Frequency: Offered occasionally.

**Prerequisite(s)**

Students with either Biology or Computer Science or Math coursework may register for this interdisciplinary course.

### COMP 340 - Digital Electronics

A survey of fundamental ideas and methods used in the design and construction of digital electronic circuits such as computers. Emphasis will be on applying the theoretical aspects of digital design to the actual construction of circuits in the laboratory. Topics to be covered include basic circuit theory, transistor physics, logic families (TTL, CMOS), Boolean logic principles, combinatorial design techniques, sequential logic techniques, memory circuits and timing, and applications to microprocessor and computer design. Three lectures and one three-hour laboratory per week.

Frequency: Offered alternate spring semesters.

**Prerequisite(s)**

MATH 137 or permission of instructor.

**Cross-Listed as**

### COMP 342 - Operating Systems and Computer Architecture

This course introduces the basic design and architecture of operating systems. Concepts to be discussed include sequential and concurrent processes, synchronization and mutual exclusion, processor scheduling, time-sharing, multitasking, parallel processing, memory management, file system design, and security. Students will learn concepts through lectures, readings, and low-level programming using the C programming language.

Frequency: Offered odd-numbered spring semesters.

**Prerequisite(s)**

COMP 240 or permission of instructor.

### COMP 346 - Internet Computing

This course introduces technologies for building dynamic web applications. It will look at all stages in the web application design process, including: 1) the basic protocols and technologies underlying the web (e.g. HTTP, REST), 2) front-end web technologies, such as HTML, CSS, and Javascript, 3) and application servers that manage requests for information, update data, etc. The course will be programming-intensive, with students using web frameworks to design and implement Internet applications. The format of the course will be mainly laboratory-based sessions, where students learn components of a web application, supported by lectures and discussions. Students will research particular topics and present their findings during these discussion sessions. The course will also investigate the usability of designs from a human factors standpoint and discuss privacy and other social consequences of this technology.

Frequency: Offered even-numbered fall semesters.

**Prerequisite(s)**

COMP 225 or permission of instructor.

### COMP 365 - Computational Linear Algebra

This course covers a central point of contact between mathematics and computer science. Many of the computational techniques important in science, commerce, and statistics are based on concepts from linear algebra: subspaces, projection, matrix decompositions, etc. The course reviews these concepts, adopts them to large scales, and applies them in the core techniques of scientific computing; solving systems of linear and nonlinear equations, approximation and statistical function estimation, optimization, interpolation, Monte Carlo techniques. Applications throughout the sciences and statistics.

Frequency: Every spring.

**Cross-Listed as**

### COMP 380 - Bodies/Minds: AI Robotics

This course examines two distinct aspects of work in robotics: the physical construction of the robot's "body" and the creation of robot control programs that form the robot's "mind." It will study the strengths and weaknesses of a variety of robot sensors, including sonar, infrared, touch, GPS, and computer vision. It will also examine both reactive and deliberative approaches to robot control programs. The course will include hands-on work with multiple robots, and a semester-long course project in robotics.

Frequency: Offered even-numbered spring semesters.

**Prerequisite(s)**

COMP 221 or permission of instructor.

### COMP 394 - Topics Course

Varies by semester. Consult the department or class schedule for current listing.

### COMP 440 - Collective Intelligence

This course introduces the theory and practice of data science applied to online communities such as Wikipedia, Facebook, and Twitter. Students will read and discuss recent academic research papers that analyze behavior on these websites and use computational simulation, machine learning, and data-mining techniques to analyze massive behavioral datasets in areas such as recommender systems, natural language processing, and tagging systems.

Frequency: Offered odd-numbered fall semesters.

### COMP 445 - Parallel and Distributed Processing

Many current computational challenges, such as Internet search, protein folding, and data mining require the use of multiple processes running in parallel, whether on a single multiprocessor machine (parallel processing) or on multiple machines connected together on a network (distributed processing). The type of processing required to solve such problems in adequate amounts of time involves dividing the program and/or problem space into parts that can run simultaneously on many processors. In this course we will explore the various computer architectures used for this purpose and the issues involved with programming parallel solutions in such environments. Students will examine several types of problems that can benefit from parallel or distributed solutions and develop their own solutions for them.

Frequency: Offered odd-numbered fall semesters.

### COMP 479 - Network Science

Topics in applied mathematics chosen from: cryptography; complexity theory and algorithms; integer programming; combinatorial optimization; computational number theory; applications of geometry to tilings, packings, and crystallography; applied algebra. This course counts towards the capstone requirement.

Frequency: Offered even-numbered fall semesters.

**Cross-Listed as**

### COMP 484 - Introduction to Artificial Intelligence

An introduction to the basic principles and techniques of artificial intelligence. Topics will include specific AI techniques, a range of application areas, and connections between AI and other areas of study (i.e., philosophy, psychology). Techniques may include heuristic search, automated reasoning, machine learning, deliberative planning and behavior-based agent control. Application areas include robotics, games, knowledge representation, and natural language processing.

Frequency: Offered even-numbered fall semesters.

**Prerequisite(s)**

COMP 221, or permission of instructor.

**Cross-Listed as**

### COMP 494 - Topics Course

Varies by semester. Consult the department or class schedule for current listing.

### COMP 601 - Tutorial

Closely supervised individual (or very small group) study with a faculty member in which a student may explore, by way of readings, short writings, etc., an area of computer science not available through the regular offerings.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### COMP 602 - Tutorial

Closely supervised individual (or very small group) study with a faculty member in which a student may explore, by way of readings, short writings, etc., an area of computer science not available through the regular offerings.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### COMP 603 - Tutorial

Closely supervised individual (or very small group) study with a faculty member in which a student may explore, by way of readings, short writings, etc., an area of computer science not available through the regular offerings.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### COMP 604 - Tutorial

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### COMP 611 - Independent Project

Individual project including library research, conferences with instructor, oral and written reports on independent work in computer science. Subject matter may complement but not duplicate material covered in regular courses.

Frequency: Every semester.

**Prerequisite(s)**

Arrangements must be made with a department member prior to registration and permission of instructor.

### COMP 612 - Independent Project

Individual project including library research, conferences with instructor, oral and written reports on independent work in computer science. Subject matter may complement but not duplicate material covered in regular courses.

Frequency: Every semester.

**Prerequisite(s)**

Arrangements must be made with a department member prior to registration and permission of instructor.

### COMP 613 - Independent Project

Individual project including library research, conferences with instructor, oral and written reports on independent work in computer science. Subject matter may complement but not duplicate material covered in regular courses.

Frequency: Every semester.

**Prerequisite(s)**

Arrangements must be made with a department member prior to registration and permission of instructor.

### COMP 614 - Independent Project

Frequency: Every semester.

**Prerequisite(s)**

### COMP 621 - Internship

Internships are offered only as S/D/NC grading option.

Frequency: Every semester.

**Prerequisite(s)**

Available to junior and senior students with declared majors in computer science. Arrangements must be made prior to registration. Permission of instructor. Work with Internship Office.

### COMP 622 - Internship

Internships are offered only as S/D/NC grading option.

Frequency: Every semester.

**Prerequisite(s)**

Available to junior and senior students with declared majors in computer science. Arrangements must be made prior to registration. Permission of instructor. Work with Internship Office.

### COMP 623 - Internship

Internships are offered only as S/D/NC grading option.

Frequency: Every semester.

**Prerequisite(s)**

Available to junior and senior students with declared majors in computer science. Arrangements must be made prior to registration. Permission of instructor. Work with Internship Office.

### COMP 624 - Internship

Internships are offered only as S/D/NC grading option.

Frequency: Every semester.

**Prerequisite(s)**

### COMP 631 - Preceptorship

Work in assisting faculty in the planning and teaching of a course.

Frequency: Every semester.

**Prerequisite(s)**

Permission of the instructor. Work with Academic Programs Office to complete a Preceptor Learning Contract Form.

### COMP 632 - Preceptorship

Work in assisting faculty in the planning and teaching of a course.

Frequency: Every semester.

**Prerequisite(s)**

Permission of the instructor. Work with Academic Programs Office to complete a Preceptor Learning Contract Form.

### COMP 633 - Preceptorship

Work in assisting faculty in the planning and teaching of a course.

Frequency: Every semester.

**Prerequisite(s)**

Permission of the instructor. Work with Academic Programs Office to complete a Preceptor Learning Contract Form.

### COMP 634 - Preceptorship

Work in assisting faculty in the planning and teaching of a course.

Frequency: Every semester.

**Prerequisite(s)**

### COMP 641 - Honors Independent

Independent research, writing, or other preparation leading to the culmination of the senior honors project.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### COMP 642 - Honors Independent

Independent research, writing, or other preparation leading to the culmination of the senior honors project.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### COMP 643 - Honors Independent

Independent research, writing, or other preparation leading to the culmination of the senior honors project.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### COMP 644 - Honors Independent

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

## Mathematics

### MATH 125 - Epidemiology

Epidemiology is the study of the distribution and determinants of disease and health in human populations and the application of this understanding to the solution of public health problems. Topics include measurement of disease and health, the outbreak and spread of disease, reasoning about cause and effect, analysis of risk, detection and classification, and the evaluation of trade-offs. The course is designed to fulfill and extend the professional community's consensus definition of undergraduate epidemiology. In addition to the techniques of modern epidemiology, the course emphasizes the historical evolution of ideas of causation, treatment, and prevention of disease. The course is a required component of the concentration in Community and Global Health.

Frequency: Every semester.

### MATH 135 - Applied Multivariable Calculus I

**This course focuses on calculus useful for applied work in the natural and social sciences. There is a strong emphasis on developing scientific computing and mathematical modeling skills. The topics include functions as models of data, differential calculus of functions of one and several variables, integration, differential equations, and estimation techniques. Case studies are drawn from varied areas, including biology, chemistry, economics, and physics. **

Frequency: Every semester.

**Prerequisite(s)**

None.

### MATH 137 - Applied Multivariable Calculus II

**This course focuses on calculus useful for both theoretical and applied work in the mathematical, natural, and social sciences. Topics include: partial derivatives, gradients, contour plots, constrained and unconstrained optimization, Taylor polynomials, and differential equations, interpretations of integrals via finite sums, the fundamental theorem of calculus, double integrals over a rectangle. Attention is given to both symbolic and numerical computing.**

Frequency: Every semester.

**Prerequisite(s)**

**MATH 135 or a year of high school calculus at the level of AP calculus with an AB score of 4 or higher. **

### MATH 155 - Introduction to Statistical Modeling

An introductory statistics course with an emphasis on multivariate modeling. Topics include descriptive statistics, experiment and study design, probability, hypothesis testing, multivariate regression, single and multi-way analysis of variance, logistic regression.

Frequency: Every semester.

### MATH 194 - Topics Course

Varies by semester. Consult the department or class schedule for current listing.

### MATH 212 - Philosophy of Mathematics

Why does 2 + 2 equal four? Can a diagram prove a mathematical truth? Is mathematics a social construction or do mathematical facts exist independently of our knowing them? Philosophy of mathematics considers these sorts of questions in an effort to understand the logical and philosophical foundations of mathematics. Topics include mathematical truth, mathematical reality, and mathematical justifications (knowledge). Typically we focus on the history of mathematics of the past 200 years, highlighting the way philosophical debates arise in mathematics itself and shape its future.

Frequency: Alternate years.

**Cross-Listed as**

### MATH 236 - Linear Algebra

Linear algebra is one of the pillars of mathematics, both pure and applied. Linear relations can be used to model phenomena from numerous disciplines in the mathematical sciences, physical sciences, social sciences, engineering, and computer science. This introduction to linear algebra blends mathematical computation, theory, abstraction, and application. It starts with systems of linear equations and grows into the study of matrices, vector spaces, linear independence, dimension, linear transformations, orthogonality and projections, eigenvectors, and their applications. The resulting linear algebraic framework is a flexible and powerful way to approach multidimensional problems.

Frequency: Offered every semester.

### MATH 237 - Multivariable Calculus

This course focuses on calculus useful for the mathematical and physical sciences. Topics include: scalar and vector-valued functions and derivatives; parameterization and integration over regions, curves, and surfaces; the divergence theorem; and Taylor series. Attention is given to both symbolic and numerical computing. Applications drawn from the natural sciences, probability, and other areas of mathematics.** **

Frequency: Every semester.

**Prerequisite(s)**

** **MATH 137 or a strong high school calculus at the level of AP calculus with a BC score of 4 or higher.

### MATH 253 - Statistical Computing and Machine Learning

**Statistics as applied to "big data," including large numbers of variables. The linear and logistic modeling techniques from Math 155 will be augmented with computer-based methods of data exploration, visualization, data mining, supervised and unsupervised clustering, and other techniques central to machine learning. The course also deals with methods of combining and organizing data from diverse sources and the high-level statistical computer programming needed to carry out sophisticated data analysis and graphical presentation. **

Frequency: Every semester

### MATH 279 - Discrete Mathematics

An introduction to the basic techniques and methods used in combinatorial problem-solving. Includes basic counting principles, induction, logic, recurrence relations, and graph theory.

Frequency: Every semester.

### MATH 294 - Topics Course

Varies by semester. Consult the department or class schedule for current listing.

### MATH 312 - Differential Equations

Introduction to the theory and application of differential equations. Solving linear and first-order systems using algebra, linear algebra, and complex numbers. Using computers to solve equations both symbolically and numerically and to visualize the solutions. Qualitative methods for nonlinear dynamical systems. Applications to diverse areas of modeling.

Frequency: Every semester.

### MATH 313 - Advanced Symbolic Logic

A second course in symbolic logic which extends the methods of logic. A main purpose of this course is to study logic itself-to prove things about the system of logic learned in the introductory course. This course is thus largely logic about logic. Topics include second order logic and basic set theory; soundness, consistency and completeness of first order logic; incompleteness of arithmetic; Turing computability; modal logic; and intuitionistic logic.

Frequency: Alternate years.

**Cross-Listed as**

### MATH 354 - Probability

An introduction to probability theory and application. Fundamental probability concepts include: sample spaces, combinatorics, conditional probability, independence, random variables, probability distributions, expectation, variance, moment-generating functions, and limit theorems. Special course topics vary and may include: computer simulation, stochastic processes, and statistical inference.

Frequency: Every semester.

### MATH 361 - Theory of Computation

A discussion of the basic theoretical foundations of computation as embodied in formal models and descriptions. The course will cover finite state automata, regular expressions, formal languages, Turing machines, computability and unsolvability, and the theory of computational complexity. Introduction to alternate models of computation and recursive function theory.

Frequency: Every spring.

**Cross-Listed as**

### MATH 365 - Computational Linear Algebra

A mix of applied linear algebra and numerical analysis, this course covers a central point of contact between mathematics and computer science. Many of the computational techniques important in science, commerce, and statistics are based on concepts from linear algebra, such as subspaces, projections, and matrix decompositions. The course reviews these concepts, adopts them to large scales, and applies them in the core techniques of scientific computing. These include solving systems of linear and nonlinear equations, approximation and statistical function estimation, optimization, interpolation, eigenvalue and singular value decompositions, and compression. Applications throughout the natural sciences, social sciences, statistics, and computer science

Frequency: Every spring.

**Cross-Listed as**

### MATH 376 - Algebraic Structures

Introduction to algebraic structures, including groups, rings, fields, and vector spaces. Other topics may include geometric constructions, symmetry groups, algebraic coding theory, Burnside's counting theorem, Galois theory.

Frequency: Every spring.

### MATH 377 - Real Analysis

Basic theory for the real numbers and the notions of limit, continuity, differentiation, integration, convergence, uniform convergence, and infinite series. Additional topics may include metric and normed linear spaces, point set topology, analytic number theory, Fourier series.

Frequency: Every fall.

**Prerequisite(s)**

### MATH 378 - Complex Analysis

A course in the study of functions of complex numbers, a topic which touches fields as varied as number theory, applied mathematics, physics, engineering, algebraic geometry, and more. We cover: geometry and algebra of complex numbers; complex functions; differentiation and integration, including the CauchyRiemann equations, Cauchy's theorem, and the Cauchy integral formula; Taylor series, Laurent series, and the Residue Theorem. Throughout, we emphasize complex functions as transformations of the plane, and also make a strong

connection to applications. This course is appropriate both for students with an interest and background in theoretical mathematics and proof, and students whose primary interest is the application of mathematics to other fields.

Frequency: Even numbered spring semesters.

### MATH 379 - Combinatorics

A second course in discrete mathematics that develops more advanced counting techniques. Combinatorics is the study of arrangements, patterns and configurations. Generally speaking, we fix a set of objects and then arrange those objects into patterns satisfying special rules. Once we identify an interesting family of objects, we ask: how many are there? what are their structural properties? how can we find the "best" one(s)? Topics are drawn from graph theory, enumerative combinatorics, graph algorithms, and generating functions.

Frequency: Offered odd-numbered fall semesters.

### MATH 394 - Topics Course

Varies by semester. Consult the department or class schedule for current listing.

### MATH 432 - Mathematical Modeling

Draws on the student's general background in mathematics to construct models for problems arising from such diverse areas as the physical sciences, life sciences, political science, economics, and computing. Emphasis will be on the design, analysis, accuracy, and appropriateness of a model for a given problem. Case studies will be used extensively. Specific mathematical techniques will vary with the instructor and student interest. This course counts towards the capstone requirement.

Frequency: Odd numbered fall semesters.

### MATH 437 - Topics in Applied Mathematics

Topics in applied mathematics chosen from: Fourier analysis; partial differential equations; wavelets; signal processing; time-frequency analysis; stochastic processes; optimization; computational geometry; and more. Topics are examined in theoretical and applied contexts, and from analytical and computational viewpoints. This course counts toward the capstone requirement.

Frequency: Odd numbered spring semesters.

### MATH 453 - Survival Analysis

Survival analysis refers to a set of methods used for modeling "time-to-event" or "duration" data. In many studies, the outcome of interest is the time between between events (e.g. onset of Alzheimer's until death, time unlit default on a loan, unemployment duration, marriage duration, removal-to-recurrence of a tumor, emergency room length of stay). Survival analysis evolved from a practical reality: the precise values of data are often unknown. We will introduce the concepts of censoring and truncation, and discuss the Kaplan-Meier curve, parametric regression models, Cox's proportional hazards model, and time-varying covariates. The course will have an applied focus. Examples may be drawn from a variety of fields including, but not restricted to, medicine, economics, sociology, and political science. The course will count toward completion of the concentration in Community and Global Health. This course counts toward the capstone requirement.

Frequency: Even fall and even spring semesters.

### MATH 454 - Bayesian Statistics

Bayesian statistics, an alternative to the traditional frequentist approach taken in our other statistics courses, is playing an increasingly integral role in modern statistics. Highlighted by Nate Silver of fivethirtyeight.com and Baseball Prospectus fame, Bayesian statistics has even reached a popular audience. This course explores the Bayesian philosophy, the Bayesian approach to statistical analysis, Bayesian computing, as well as both sides of the frequentist versus Bayesian debate. Topics include Bayes' Theorem, prior and posterior probability distributions, Bayesian regression, Bayesian hierarchical models, and an introduction to Markov chain Monte Carlo techniques.

Frequency: Odd fall and odd spring semesters.

### MATH 455 - Mathematical Statistics

An important course for students considering graduate work in statistics or biostatistics, this course explores the mathematics underlying modern statistical applications. Topics include: classical techniques for parameter estimation and evaluation of estimator properties, hypothesis testing, confidence intervals, and linear regression. Special topics vary and may include: tests of independence, resampling techniques, introductory Bayesian concepts, and nonparametric methods. Though not the focus of this course, concepts will be highlighted

through applications in a variety of settings.

Frequency: Even numbered spring semesters.

**Prerequisite(s)**

### MATH 471 - Topology

A course in both theoretical and computational mathematics. It covers fundamental ideas from point set topology-continuity, convergence, and connectedness-as well as selected topics from algebraic topology the fundamental group, elementary homotopy theory, and homology. This theoretical framework provides a backbone to understand new advances in computational topology via persistent homology. Applications are chosen from diverse fields such as biological aggregations, medicine, image processing, signal processing, and sensor networks. This course counts towards the capstone requirement.

Frequency: Odd spring semesters.

### MATH 476 - Representation Theory

A course in matrix representations of groups, a topic which unites the powers of group theory and linear algebra. Topics include: symmetry in linear spaces, modules, group actions, characters, tensor products, and Fourier analysis on groups. Applications are chosen from: ranked data, molecular vibrations, quantum mechanics, random walks, number theory, and combinatorics. Important ideas from linear algebra are revisited from a more sophisticated point of view. These include: linear transformations, abstract vector spaces, change of basis, subspaces, direct sums, projections, and eigenvalues and eigenvectors.

Frequency: Odd numbered fall semesters.

**Prerequisite(s)**

### MATH 477 - Projects in Analysis

Students will work on semester projects that build on the material of MATH 377 or MATH 378. These projects are designed to serve as Capstone projects and will be open-ended exploratory projects on topics chosen from real, complex, or functional analysis.

Frequency: Even numbered spring semesters.

**Prerequisite(s)**

### MATH 479 - Network Science

The modern Information Age has produced a wealth of data about the complex networks that tie us together. In response, the field of Network Science has arisen, bringing together mathematics, computer science, sociology, biology, economics and other fields. This course will explore the fundamental questions and the mathematical tools of Network Science. This includes: the structure of complex networks, including connectedness, centrality and "long tails"; community detection; random/strategic models for network formation; diffusion/contagion and "tipping points" on networks; and algorithms for analyzing complex networks.

Frequency: Even numbered fall semesters.

**Cross-Listed as**

### MATH 494 - Topics Course

Varies by semester. Consult the department or class schedule for current listing.

### MATH 601 - Tutorial

Closely supervised individual (or very small group) study with a faculty member in which a student may explore, by way of readings, short writings, etc., an area of mathematics not available through the regular offerings.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### MATH 602 - Tutorial

Closely supervised individual (or very small group) study with a faculty member in which a student may explore, by way of readings, short writings, etc., an area of mathematics not available through the regular offerings.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### MATH 603 - Tutorial

Closely supervised individual (or very small group) study with a faculty member in which a student may explore, by way of readings, short writings, etc., an area of mathematics not available through the regular offerings.

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### MATH 604 - Tutorial

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### MATH 611 - Independent Project

Individual project including library research, conferences with instructor, oral and written reports on independent work in mathematics. Subject matter may complement but not duplicate material covered in regular courses.

**Prerequisite(s)**

Arrangement with faculty prior to registration, departmental approval, and permission of instructor.

### MATH 612 - Independent Project

Individual project including library research, conferences with instructor, oral and written reports on independent work in mathematics. Subject matter may complement but not duplicate material covered in regular courses.

**Prerequisite(s)**

Arrangement with faculty prior to registration, departmental approval, and permission of instructor.

### MATH 613 - Independent Project

Individual project including library research, conferences with instructor, oral and written reports on independent work in mathematics. Subject matter may complement but not duplicate material covered in regular courses.

**Prerequisite(s)**

Arrangement with faculty prior to registration, departmental approval, and permission of instructor.

### MATH 614 - Independent Project

**Prerequisite(s)**

Arrangement with faculty prior to registration, departmental approval, and permission of instructor.

### MATH 621 - Internship

Internships are offered only as S/D/NC grading option.

Frequency: Every semester.

**Prerequisite(s)**

Junior and Senior standing. Arrangements must be made prior to registration. Departmental approval and permission of instructor required. Work with Internship Office.

### MATH 622 - Internship

Internships are offered only as S/D/NC grading option.

Frequency: Every semester.

**Prerequisite(s)**

Junior and Senior standing. Arrangements must be made prior to registration. Departmental approval and permission of instructor required. Work with Internship Office.

### MATH 623 - Internship

Internships are offered only as S/D/NC grading option.

Frequency: Every semester.

**Prerequisite(s)**

Junior and Senior standing. Arrangements must be made prior to registration. Departmental approval and permission of instructor required. Work with Internship Office.

### MATH 624 - Internship

Internships are offered only as S/D/NC grading option.

Frequency: Every semester.

**Prerequisite(s)**

### MATH 631 - Preceptorship

Work in assisting faculty in the planning and teaching of a course.

Frequency: Every semester.

**Prerequisite(s)**

### MATH 632 - Preceptorship

Work in assisting faculty in the planning and teaching of a course.

Frequency: Every semester.

**Prerequisite(s)**

### MATH 633 - Preceptorship

Work in assisting faculty in the planning and teaching of a course.

Frequency: Every semester.

**Prerequisite(s)**

### MATH 634 - Preceptorship

Work in assisting faculty in the planning and teaching of a course.

Frequency: Every semester.

**Prerequisite(s)**

### MATH 641 - Honors Independent

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### MATH 642 - Honors Independent

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### MATH 643 - Honors Independent

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.

### MATH 644 - Honors Independent

Frequency: Every semester.

**Prerequisite(s)**

Permission of instructor.