# Mathematics and Computer Science

The Department of Mathematics and Computer Science offers undergraduate majors in mathematics and in computer science. We also participate in the Informatics and Modeling Certificate Program. The department's graduate programs include a PhD in mathematics and MA programs in mathematics and in computer science.

Each student's course of study is designed to provide an introduction to the basic areas of mathematics or computer science and to provide the technical tools that will be useful later in the student's career. The course of study is planned in consultation with the student's faculty advisor and the department's advisory committees, DADCOM for mathematics and CADCOM for computer science.

The department's graduate programs include a PhD program in mathematics and MA programs in mathematics and in computer science. The research emphasis at Wesleyan at the doctoral level is in pure mathematics and theoretical computer science. One of the distinctive features of our department is the close interaction between the computer science faculty and the mathematics faculty, particularly those in logic and discrete mathematics.

Graduate students at Wesleyan enjoy small classes and close interactions with faculty and fellow graduate students. Graduate students normally register for three classes a semester and are expected to attend departmental colloquia and at least one regular seminar. The number of graduate students ranges from 17 to 21, with an entering class of three to six each year. There have always been both male and female students, graduates of small colleges and large universities, and U.S. and international students, including, in recent years, students from Bulgaria, Chile, China, Germany, India, Iran, and Sri Lanka. All of the department's recent PhD recipients have obtained faculty positions. Some have subsequently moved to mathematical careers in industry and government.

For additional information, please visitÂ wesleyan.edu/mathcs/graduate/.

## Faculty

**Ilesanmi Adeboye**

PHD, University of Michigan

Assistant Professor of Mathematics

**Wai Kiu Chan**

BS, University of Hong Kong; MPHIL, University of Hong Kong; PHD, The Ohio State University

Professor of Mathematics

**Karen L. Collins**

BA, Smith College; PHD, Massachusetts Institute of Technology

Edward Burr Van Vleck Professor of Mathematics; Professor of Mathematics; Professor, Integrative Sciences

**David Constantine**

BS, Eastern Nazarene College; PHD, University of Michigan

Assistant Professor of Mathematics

**Norman Danner**

BA, University of California, Berkeley; PHD, Indiana University Bloomington

Associate Professor of Computer Science; Vice-Chair, Mathematics and Computer Science

**Adam Fieldsteel**

BA, Brown University; MAA, Wesleyan University; PHD, University of California, Berkeley

Professor of Mathematics; Chair, Mathematics and Computer Science

**Cameron Donnay Hill**

BA, Yale University; PHD, University of California, Berkeley

Assistant Professor of Mathematics; Assistant Professor, Integrative Sciences

**Mark A. Hovey**

BS, Ohio State University; PHD, Massachusetts Institute of Technology

Associate Provost; Professor of Mathematics; Professor, Integrative Sciences

**Sara Kalisnik Verovsek**

PHD, Stanford University

Assistant Professor of Mathematics

**Alex Kavvos**

DPHIL, Oxford University; MSC, Oxford University

Postdoctoral Research Associate; Visiting Assistant Professor of Computer Science

**Daniel Krizanc**

BS, University of Toronto; PHD, Harvard University

Professor of Computer Science; Professor, Integrative Sciences; Professor, Environmental Studies; Co-Coordinator, Informatics and Modeling

**Alex Kruckman**

PHD, University of California, Berkeley; SB, Brown University

Assistant Professor of Mathematics

**Constance Leidy**

BS, Tulane University; PHD, Rice University

Associate Professor of Mathematics

**Han Li**

BS, Nankai University; PHD, Yale University

Assistant Professor of Mathematics

**Dan Licata**

BS, Brown University; PHD, Carnegie Mellon University

Assistant Professor of Computer Science

**James Lipton**

BS, U Nebraska Lincoln; MSC, Cornell University; PHD, Cornell University

Professor of Computer Science; Professor, Integrative Sciences

**Victoria Ursula Manfredi**

BA, Smith College; MS, University of Massachusetts Amherst; PHD, University of Massachusetts Amherst

Assistant Professor of Computer Science

**David Pollack**

MA, Harvard University; PHD, Harvard University; SB, University of Chicago

Associate Professor of Mathematics

**Felipe A. RamÃrez**

BS, Colorado St University; PHD, University of Michigan

Assistant Professor of Mathematics

**Christopher Rasmussen**

BA, University of Virginia; MS, University of Virginia; PHD, University of Arizona

Associate Professor of Mathematics

**Saray Shai**

BS, Israel Institute of Technology; PHD, University of St Andrews

Assistant Professor of Computer Science

**Sebastian Zimmeck**

LLM, University of California, Berkeley; MS, Columbia University; PHD, University of Kiel; PHD, Columbia University

Assistant Professor of Computer Science

## Affiliated Faculty

**Tsampikos Kottos**

BA, University of Crete; MS, University of Crete; PHD, University of Crete

Professor of Physics; Professor, Integrative Sciences; Professor, Mathematics

## Visiting Faculty

**Daniel Christopher Alvey**

BS, US Military Academy

Graduate Student, MATH-PHD; Visiting Instructor in Mathematics

**Justin Alexander Bryant**

BS, Seattle University

Graduate Student, MATH-PHD; Visiting Instructor in Mathematics

**Alyson Hildum**

BA, Colorado School Mines; PHD, Brandeis University

Visiting Assistant Professor of Mathematics

**Peter R. Merkx**

BS, Duke University; MS, University of Oregon; PHD, University of California, Santa Barbara

Visiting Assistant Professor of Mathematics

**Mitchell Vern Riley**

MSC, University Wstrn Ontario; BS, University Of Queensland

Graduate Student, MATH-PHD; Visiting Instructor in Mathematics

**Phillip Wesolek**

BS, University of Wisconsin at Madison; MS, University of Illinois at Chicago; PHD, University of Illinois at Chicago

Visiting Assistant Professor of Mathematics; Visiting Scholar in Mathematics

## Emeriti

**Ethan M. Coven**

BA, University of Rochester; MA, Yale University; MAA, Wesleyan University; PHD, Yale University

Professor of Mathematics, Emeritus

**Anthony W. Hager**

BS, Pennsylvania State University; PHD, Pennsylvania State University

Professor of Mathematics, Emeritus

**Michael S. Keane**

BA, University of Texas Austin; MS, University of Gottingen; PHD, University of Erlangen-Nurnber

Professor of Mathematics, Emeritus

**Michael D. Rice**

BS, Western Mich University; MS, Western Mich University; PHD, Wesleyan University

Professor of Computer Science, Emeritus

**Philip H. Scowcroft**

BA, Harvard University; MA, Cornell University; PHD, Cornell University

Edward Burr Van Vleck Professor of Mathematics, Emeritus

**Carol S. Wood**

AB, Randolph Macon W College; MAA, Wesleyan University; PHD, Yale University

Edward Burr Van Vleck Professor of Mathematics, Emerita

## Departmental Undergraduate Advising Experts

DADCOM provides advice and transfer credit approval for students in mathematics. CADCOM provides advice and transfer credit approval for students in computer science.

## Computer Science

**COMP112 Introduction to Programming**

The course will provide an introduction to a modern, high-level programming language including a discussion of input/output, basic control structures, types, functions, and classes. The lectures will also discuss a variety of algorithms as well as program design issues.

The second meeting time for each section is a computer lab.

Offering: **Host**

Grading: **OPT**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**COMP113 Bioinformatics Programming**

This course is an introduction to bioinformatics and programming for students with interest in the life sciences. It introduces problem areas and conceptual frameworks in bioinformatics. The course assumes little or no prior programming experience and will introduce the fundamental concepts and mechanisms of computer programs and examples (e.g., sequence matching and manipulation, database access, output parsing, dynamic programming) frequently encountered in the field of bioinformatics.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-BIOL**

Identical With: **BIOL265, MB&B265, CIS265**

Prereq: **[MB&B181 or BIOL181]**

**COMP114 How to Talk to Machines**

How do we tell robots and computers how to do what they do? Getting a handle on this question is the goal of this course. Since telling a device how to do something depends a lot on what that device can do, along the way we will learn a bit about what is "in the box." We will start with the kind of programming one might use to instruct a robot how to interact with the world around it. That will lead us to the Turing machine, a beautiful mathematical model of a computer. We will adapt that model to something that is closer to how most computer systems today are designed. We will end with an introduction to high-level programming, learning the fundamentals of programming in a language such as Python or Java.

The goal of the course is to understand not just programming, but how computers are designed, and how those designs are reflected in the way we program them. After passing this course, students will have a basic knowledge of programming and how a computer works. COMP 114 can be used to satisfy the COMP 211 prerequisite and also the mathematics major "elementary knowledge of algorithms and computer programming" requirement.

Offering: **Host**

Grading: **OPT**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**COMP115 How to Design Programs**

In this course, students will learn to systematically design programs, going from a problem statement to a well-organized solution in a step-by-step fashion. We will apply these program design skills to many applications within computer science and in other disciplines. Students will develop their mathematical skills, because we will use a symbolic view of computation that explains the process of running a program as simple manipulations of its text. Students will also develop their technical reading and writing skills, such as understanding complex problem descriptions and precisely articulating the design of solutions. No prior experience with programming or computer science is expected.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**COMP211 Computer Science I**

This is the first course in a two-course sequence (COMP211-212) that is the gateway to the computer science major. It is intended for prospective computer science majors and others who want an in-depth understanding of programming and computer science. Topics to be covered in COMP211-212 include an introduction to the fundamental ideas of programming in imperative and functional languages, correctness and cost specifications, and proof techniques for verifying specifications.

Specifics such as choice of programming language, which topics are covered in which semesters, etc., will vary according to the tastes of the faculty offering the courses.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP112 OR COMP113 OR COMP114 OR COMP115**

**COMP212 Computer Science II**

This is the second course in a two-course sequence (COMP211-212) that is the gateway to the computer science major. It is intended for prospective computer science majors and others who want an in-depth understanding of programming and computer science. Topics to be covered in COMP211-212 include an introduction to the fundamental ideas of programming in imperative and functional languages, correctness and cost specifications, and proof techniques for verifying specifications.

Specifics such as choice of programming language, which topics are covered in which semesters, etc., will vary according to the tastes of the faculty offering the courses.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP211**

**COMP260 Special Topics in Computer Science**

This course is designed for nonmajors who wish to pursue some topic in computer science beyond introduction to programming. Topics will vary according to the instructor.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **QAC260**

Prereq: **COMP112**

**COMP266 Bioinformatics**

This course is an introduction to bioinformatics for students with interest in the life sciences. The course is similar to BIOL265 but only meets in the second half of the semester (with BIOL265) and is designed for students with programming background, ideally in Python. The course introduces problem areas and conceptual frameworks in bioinformatics and discusses programming approaches used in bioinformatics such as sequence matching and manipulation algorithms using dynamic programming, clustering analysis of gene expression data, analysis of genetic nets using Object Oriented Programming, and sequence analysis using Hidden Markov Models, Regular Expressions, and information theory.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **0.50**

Gen Ed Area: **NSM-BIOL**

Identical With: **BIOL266, MB&B266, CIS266**

Prereq: **[MB&B181 OR BIOL181]**

**COMP301 Automata Theory and Formal Languages**

This course is an introduction to formalisms studied in computer science and mathematical models of computing machines. The language formalisms discussed will include regular, context-free, recursive, and recursively enumerable languages. The machine models discussed include finite-state automata, pushdown automata, and Turing machines.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP500**

Prereq: **COMP211 AND COMP212 AND MATH228**

**COMP312 Algorithms and Complexity**

The course will cover the design and analysis of efficient algorithms. Basic topics will include greedy algorithms, divide-and-conquer algorithms, dynamic programming, and graph algorithms. Some advanced topics in algorithms may be selected from other areas of computer science.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP510**

Prereq: **COMP212 AND MATH228**

**COMP321 Design of Programming Languages**

This course is an introduction to concepts in programming languages. Topics include parameter passing, type checking and inference, control mechanisms, data abstraction, module systems, and concurrency. Basic ideas in functional, object-oriented, and logic programming languages will be discussed.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP521**

Prereq: **COMP212 AND MATH228**

**COMP323 Programming Language Implementation**

This course is an introduction to the implementation of programming languages.

Students will learn how to formally describe and implement major components of the implementation pipeline. Topics may include lexical analysis and parsing (checking whether source code is well-formed and converting it to an internal programmatic representation), type-checking and -inference (static program analysis for safety features), interpretation (direct execution of a high-level language program), and compilation (translation to a low-level language such as assembly or bytecode).

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP523**

Prereq: **COMP212 AND MATH228**

**COMP327 Evolutionary and Ecological Bioinformatics**

Bioinformatic analysis of gene sequences and gene expression patterns has added enormously to our understanding of ecology and evolution. For example, through bioinformatic analysis of gene sequences, we can now reconstruct the evolutionary history of physiology, even though no traces of physiology exist in the fossil record. We can determine the adaptive history of one gene and all the gene's descendants. We can now construct the evolutionary tree of all of life. Bioinformatics is particularly promising for analysis of the ecology and biodiversity of microbial communities, since well over 99 percent of microorganisms cannot be cultured; our only knowledge of these organisms is through analysis of their gene sequences and gene expression patterns. For example, even when we cannot culture most of a microbial community, we can determine which metabolic pathways are of greatest significance through analysis of community-level gene expression. All these research programs are made accessible not only by breakthroughs in molecular technology but also by innovation in the design of computer algorithms. This course, team-taught by an evolutionary biologist and a computer scientist, will present how bioinformatics is revolutionizing evolutionary and ecological investigation and will present the design and construction of bioinformatic computer algorithms underlying the revolution in biology. Students will learn algorithms for reconstructing phylogeny, for sequence alignment, and for analysis of genomes, and students will have an opportunity to create their own algorithms.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-BIOL**

Identical With: **BIOL327, BIOL527, COMP527, CIS327**

Prereq: **[BIOL182 or MB&B182] OR [BIOL196 or MBB196] OR COMP112 OR COMP211**

**COMP331 Computer Structure and Organization**

The purpose of the course is to introduce and discuss the structure and operation of digital computers. Topics will include the logic of circuits, microarchitectures, microprogramming, conventional machine architectures, and an introduction to software/hardware interface issues. Assembly language programming will be used to demonstrate some of the basic concepts.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP531**

Prereq: **COMP212**

**COMP332 Computer Networks**

This course will provide an introduction to the fundamentals of computer networks. Computer networks have become embedded in our everyday lives, from the Internet to cellular phones to cloud networking, enabling applications such as email, texting, web browsing, on-demand video, video conferencing, peer-to-peer file sharing, social networking, cloud computing, and more. This course will delve into the infrastructure and protocols that have allowed computer networks to achieve their current ubiquity. While the primary focus of the course will be on the Internet's architecture, protocols, and applications, we will also touch on other types of computer networks. Programming assignments will be done using Python; prior knowledge of Python is not required.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP212 and MATH228**

**COMP342 Software Engineering**

This course provides an introduction to the processes and tools of software engineering: the design, development, testing, and maintenance of large software systems. The course is based on the Berkeley MOOC "Software Engineering as a Service" and uses on-line material from the MOOC to provide some of the course content.

The first part of the course will cover developing software in teams as well as learning the languages and tools used in the course, including Ruby, Rails, Cucumber, RSpec, Pivotal Tracker, and gitHub.

The second part of the course will continue to present software engineering concepts but will also focus on developing a team service-learning software development project for an external customer.

Offering: **Host**

Grading: **A-F**

Credits: **1.50**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP211 AND COMP212**

**COMP350 Computational Media: Videogame Development**

This course examines the interplay of art and science in the development of contemporary video games using "game tool" applications to achieve a variety of purposes. It combines a detailed understanding of computational media, including legal and commercial aspects, with hands-on experience in the creative process. There will be discussions with invited industry leaders in various subject areas. Students will have the opportunity to work as part of development teams and create working prototypes to understand the challenges and rewards of producing video games in a professional context.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **2.00**

Gen Ed Area: **NSM-IDEA**

Identical With: **IDEA350, FILM250**

Prereq: **None**

**COMP360 Special Topics in Computer Science: Information Security and Privacy**

This course explores principles and practical applications of computer security and privacy. Some of the topics covered include static and dynamic code analysis, secure authentication, privacy enhancing technologies, usable privacy and security, and web tracking. We will also touch upon theoretical areas, such as basic cryptographic concepts as well as differential privacy. The course has the objective to provide students with the conceptual knowledge and technical skills to identify and resolve privacy and security issues in the design, development, and evaluation of information systems.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP212 AND MATH228**

**COMP360A Special Topics in Computer Science**

This course covers special topics in computer science. Topics will vary according to the instructor.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP212 AND MATH228**

**COMP360B Special Topics in Computer Science**

This course covers special topics in computer science. Topics will vary according to the instructor.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP212 AND MATH228**

**COMP360C Special Topics in Computer Science: Network Science**

Network science is an emerging field that focuses on the analysis of real-world complex systems arising in the social, biological, and physical sciences by abstracting them into networks (or graphs). The size and complexity of real networks has produced a deep change in the way that graphs are approached, and led to the development of new mathematical and computational tools.

This course provides an introduction to network science by walking through modern techniques for modeling, analyzing, and simulating the structures and dynamics of complex networks. Specific topics to be discussed will include: network models and measures, graph algorithms, visualization and simulation, models of dynamic/adaptive networks, network modularity and community detection, and some applications. Python and NetworkX will be used for modeling and analysis of networks, in addition to other computational tools. Students should have a reasonable amount of experience in Python programming or willingness to learn "on the go."

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP212 AND MATH228**

**COMP360D Special Topics in Computer Science**

TBD

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP212 AND MATH228**

**COMP361 Advanced Topics in Computer Science**

This course covers advanced topics in Computer Science. The precise topics will vary with the offering, but will typically have prerequisites beyond COMP 211-212. This course may be repeated for credit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **COMP321**

**COMP401 Individual Tutorial, Undergraduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP402 Individual Tutorial, Undergraduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP403 Department/Program Project or Essay**

Project to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **A-F**

**COMP404 Department/Program Project or Essay**

Project to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **A-F**

**COMP407 Senior Tutorial (downgraded thesis)**

Downgraded Senior Thesis Tutorial - Project to be arranged in consultation with the tutor. Only enrolled in through the Honors Coordinator.

Offering: **Host**

Grading: **A-F**

**COMP408 Senior Tutorial (downgraded thesis)**

Downgraded Senior Thesis Tutorial - Project to be arranged in consultation with the tutor. Only enrolled in through the Honors Coordinator.

Offering: **Host**

Grading: **A-F**

**COMP409 Senior Thesis Tutorial**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP410 Senior Thesis Tutorial**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP411 Group Tutorial, Undergraduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP412 Group Tutorial, Undergraduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP419 Student Forum**

Student-run group tutorial, sponsored by a faculty member and approved by the chair of a department or program.

Offering: **Host**

Grading: **Cr/U**

**COMP420 Student Forum**

Student-run group tutorial, sponsored by a faculty member and approved by the chair of a department or program.

Offering: **Host**

Grading: **Cr/U**

**COMP421 Undergraduate Research, Sciences**

Individual research projects for undergraduate students supervised by faculty members.

Offering: **Host**

Grading: **A-F**

**COMP422 Undergraduate Research, Sciences**

Individual research projects for undergraduate students supervised by faculty members.

Offering: **Host**

Grading: **OPT**

**COMP423 Advanced Research Seminar, Undergraduate**

Advanced research tutorial; project to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP424 Advanced Research Seminar, Undergraduate**

Advanced research tutorial; project to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP469 Education in the Field, Undergraduate**

Students must consult with the department and class dean in advance of undertaking education in the field for approval of the nature of the responsibilities and method of evaluation.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**COMP491 Teaching Apprentice Tutorial**

The teaching apprentice program offers undergraduate students the opportunity to assist in teaching a faculty member's course for academic credit.

Offering: **Host**

Grading: **OPT**

**COMP492 Teaching Apprentice Tutorial**

The teaching apprentice program offers undergraduate students the opportunity to assist in teaching a faculty member's course for academic credit.

Offering: **Host**

Grading: **OPT**

**COMP500 Automata Theory and Formal Languages**

This course is an introduction to formalisms studied in computer science and mathematical models of computing machines. The language formalisms discussed will include regular, context-free, recursive, and recursively enumerable languages. The machine models discussed include finite-state automata, pushdown automata, and Turing machines.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP301**

Prereq: **COMP211 AND COMP212 AND MATH228**

**COMP501 Individual Tutorial, Graduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP502 Individual Tutorial, Graduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP503 Selected Topics, Graduate Sciences**

Topic to be arranged in consultation with the tutor. A seminar primarily concerned with papers taken from current research publications designed for, and required of, graduate students.

Offering: **Host**

Grading: **A-F**

**COMP504 Selected Topics, Graduate Sciences**

Topic to be arranged in consultation with the tutor. A seminar primarily concerned with papers taken from current research publications designed for, and required of, graduate students.

Offering: **Host**

Grading: **A-F**

**COMP510 Algorithms and Complexity**

The course will cover the design and analysis of efficient algorithms. Basic topics will include greedy algorithms, divide-and-conquer algorithms, dynamic programming, and graph algorithms. Some advanced topics in algorithms may be selected from other areas of computer science.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP312**

Prereq: **COMP212 AND MATH228**

**COMP511 Group Tutorial, Graduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP512 Group Tutorial, Graduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP521 Design of Programming Languages**

This course is an introduction to concepts in programming languages. Topics include parameter passing, type checking and inference, control mechanisms, data abstraction, module systems, and concurrency. Basic ideas in functional, object-oriented, and logic programming languages will be discussed.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP321**

Prereq: **COMP212 AND MATH228**

**COMP523 Programming Language Implementation**

This course is an introduction to the implementation of programming languages.

Students will learn how to formally describe and implement major components of the implementation pipeline. Topics may include lexical analysis and parsing (checking whether source code is well-formed and converting it to an internal programmatic representation), type-checking and -inference (static program analysis for safety features), interpretation (direct execution of a high-level language program), and compilation (translation to a low-level language such as assembly or bytecode).

Offering: **Crosslisting**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP323**

Prereq: **COMP212 AND MATH228**

**COMP527 Evolutionary and Ecological Bioinformatics**

Bioinformatic analysis of gene sequences and gene expression patterns has added enormously to our understanding of ecology and evolution. For example, through bioinformatic analysis of gene sequences, we can now reconstruct the evolutionary history of physiology, even though no traces of physiology exist in the fossil record. We can determine the adaptive history of one gene and all the gene's descendants. We can now construct the evolutionary tree of all of life. Bioinformatics is particularly promising for analysis of the ecology and biodiversity of microbial communities, since well over 99 percent of microorganisms cannot be cultured; our only knowledge of these organisms is through analysis of their gene sequences and gene expression patterns. For example, even when we cannot culture most of a microbial community, we can determine which metabolic pathways are of greatest significance through analysis of community-level gene expression. All these research programs are made accessible not only by breakthroughs in molecular technology but also by innovation in the design of computer algorithms. This course, team-taught by an evolutionary biologist and a computer scientist, will present how bioinformatics is revolutionizing evolutionary and ecological investigation and will present the design and construction of bioinformatic computer algorithms underlying the revolution in biology. Students will learn algorithms for reconstructing phylogeny, for sequence alignment, and for analysis of genomes, and students will have an opportunity to create their own algorithms.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-BIOL**

Identical With: **BIOL327, COMP327, BIOL527, CIS327**

Prereq: **[BIOL182 or MB&B182] OR [BIOL196 or MBB196] OR COMP112 OR COMP211**

**COMP531 Computer Structure and Organization**

The purpose of the course is to introduce and discuss the structure and operation of digital computers. Topics will include the logic of circuits, microarchitectures, microprogramming, conventional machine architectures, and an introduction to software/hardware interface issues. Assembly language programming will be used to demonstrate some of the basic concepts.

Offering: **Crosslisting**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Identical With: **COMP331**

Prereq: **COMP212**

**COMP549 Advanced Research Seminar, Graduate**

Advanced research tutorial; project to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**COMP550 Advanced Research Seminar, Graduate**

Offering: **Host**

Grading: **OPT**

**COMP571 Special Topics in Computer Science**

Supervised reading course of varying length. This course may be repeated for credit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**COMP572 Special Topics in Computer Science**

Supervised reading course of varying length. This course may be repeated for credit.

Offering: **Host**

Grading: **OPT**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

## Mathematics

**MATH117 Introductory Calculus**

This course is designed to introduce basic ideas and techniques of differential calculus. Students should enter with sound precalculus skills but with very limited or no prior study of calculus. Topics to be considered include differential calculus of algebraic, exponential, and logarithmic functions. (Integral calculus will be introduced in MATH118.)

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH118 Introductory Calculus II: Integration and Its Applications**

This course continues MATH117 and is designed to introduce basic ideas and techniques of calculus. Students should enter MATH118 with sound precalculus skills and with very limited or no prior study of integral calculus. Topics to be considered include differential and integral calculus of algebraic, exponential, and logarithmic functions.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH119 Elements of Calculus, Part I**

This course is the first half of a two-semester calculus sequence (MATH119, MATH120). This sequence is designed for students who have not previously studied calculus. The course, together with MATH120, will cover limits, derivatives, and integrals. Exponential, logarithmic, and trigonometric functions will be introduced and their calculus will be studied. Applications of calculus to biology, economics, physics, and/or other fields will be emphasized.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH120 Elements of Calculus, Part II**

This course is the second half of a two-semester calculus sequence. This sequence is designed for students who have not previously studied calculus. The course, together with MATH119, will cover limits, derivatives, and integrals. Exponential, logarithmic, and trigonometric functions will be introduced and their calculus will be studied. Applications of calculus to biology, economics, physics, and/or other fields will be emphasized.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH119**

**MATH121 Calculus I, Part I**

MATH121 is designed for students who have completed a high school calculus course and who might pursue study in an area for which calculus is an essential tool but who are not prepared to place out of calculus. This course is a deeper and broader study of calculus than MATH117; theoretical aspects are not the main focus but will not be avoided. The course will, together with MATH122, treat limits, derivatives, and integrals; the calculus of exponential, logarithmic, trigonometric, and inverse trigonometric functions; techniques of integration; plane analytic geometry; various applications of calculus; and sequences and series, including power series and intervals of convergence.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH122 Calculus I, Part II**

The continuation of MATH121. Topics covered include techniques and applications of integration and an introduction to sequences and series.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH132 Elementary Statistics**

Topics included in this course are organizing data, central measures, measures of variation, distributions, sampling, estimation, conditional probability (Bayes' theorem), hypothesis testing, simple regression and correlation, and analysis of variation.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH211 Problem Solving for the Putnam**

This course will explore the problems and problem-solving techniques of the annual William Lowell Putnam mathematical competition. Particular emphasis will be placed on learning to write clear and complete solutions to problems. The competition is open to all undergraduate students.

Offering: **Host**

Grading: **Cr/U**

Credits: **0.25**

Gen Ed Area: **None**

Prereq: **None**

**MATH221 Vectors and Matrices**

This is a course in the algebra of matrices and Euclidean spaces that emphasize the concrete and geometric. Topics to be developed include solving systems of linear equations; matrix addition, scalar multiplication, and multiplication; properties of invertible matrices; determinants; elements of the theory of abstract finite dimensional real vector spaces; dimension of vector spaces; and the rank of a matrix. These ideas are used to develop basic ideas of Euclidean geometry and to illustrate the behavior of linear systems. We conclude with a discussion of eigenvalues and the diagonalization of matrices.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH222 Multivariable Calculus**

This course treats the basic aspects of differential and integral calculus of functions of several real variables, with emphasis on the development of calculational skills. The areas covered include scalar- and vector-valued functions of several variables, their derivatives, and their integrals; the nature of extremal values of such functions and methods for calculating these values; and the theorems of Green and Stokes.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH223 Linear Algebra**

An alternative to MATH221, this course will cover vector spaces, inner-product spaces, dimension theory, linear transformations and matrices, determinants, eigenvalues and eigenvectors, Hermitian and unitary transformations, and elementary spectral theory. It will present applications to analytic geometry, quadratic forms, and differential equations as time permits. The approach here is more abstract than that in MATH221, though many topics appear in both.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH225 Fundamentals of Analysis: An Introduction to Real Analysis**

In this rigorous treatment of calculus, topics will include, but are not limited to, real numbers, limits, sequences and series, continuity and uniform continuity, differentiation, the Riemann integral, sequences and series of functions, pointwise and uniform convergence of functions, and interchange of limiting processes. MATH228 or comparable experience in writing mathematical proofs is strongly recommended for success in this course.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **(MATH222 AND MATH221) OR (MATH222 AND MATH223)**

**MATH226 Complex Analysis**

This course will present the basic properties of complex analytic functions. We begin with the complex numbers themselves and elementary functions and their mapping properties, then discuss Cauchy's integral theorem and Cauchy's integral formula and applications, Taylor and Laurent series, zeros and poles and residue theorems, the argument principle, and Rouche's theorem. In addition to a rigorous introduction to complex analysis, students will gain experience in communicating mathematical ideas and proofs effectively.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **(MATH222 AND MATH221) OR (MATH222 AND MATH223)**

**MATH228 Discrete Mathematics**

This course is a survey of discrete mathematical processes. Students will be introduced to the process of writing formal mathematical proofs, including mathematical induction. Topics may include set theory, logic, number theory, finite fields, permutations, elementary combinatorics, or graph theory.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH229 Differential Equations**

This course is an introduction to the theory of ordinary differential equations. Many aspects of mathematics and computer science are important in this discipline, and a broad view will be presented, in agreement with modern theory and practice. The only prerequisite for the course is multivariable calculus; all other necessary tools will be developed as the course proceeds.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH222**

**MATH231 An Introduction to Probability**

This course teaches the basic theory of probability. Although the notions are simple and the mathematics involved require only a basic knowledge of the ideas of differential and integral calculus, a certain degree of mathematical maturity is necessary. The fundamental concepts to be studied are probability spaces and random variables, the most important ideas being conditional probability and independence. The main theorems we will study are the law of large numbers and the central limit theorem.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH222 AND MATH228**

**MATH232 Mathematical Statistics**

This course covers the basic notions of estimation, hypothesis testing, regression, analysis of variance, experimental design, and other topics in statistics from a rigorous mathematical perspective. This material will be supplemented by various case studies.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH231**

**MATH241 Set Theory**

This course covers ordinal and cardinal numbers, cardinal arithmetic, theorems of Cantor and Schroeder-Bernstein, introduction to Zermelo-Fraenkel set theory, Axiom of Choice, and some infinitary combinatorics.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH243 Mathematical Logic**

This course is an introduction to mathematical logic, including first-order logic and model theory, axiomatic set theory, and, as time permits, Goedel's incompleteness theorem.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH241 OR MATH261 OR MATH228**

**MATH244 Topology: Point Set**

This is an introduction to general topology, the study of topological spaces. We will begin with the most natural examples, metric spaces, and then move on to more general spaces. This subject, fundamental to mathematics, enables us to discuss notions of continuity and approximation in their broadest sense. We will illustrate topology's power by seeing important applications to other areas of mathematics.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **None**

**MATH246 Applied Topology**

This course teaches the main concepts in Applied Topology. Students will learn to apply nonlinear methods to analyze the shape of data sets. These approaches are drawn from classical topology and focus on the shape in one of two ways: they either 'measure' it, that is count the occurrences of patterns within the data set; or build combinatorial representations of the data set. As an example of the former, we will look at persistent homology, whereas the latter will be represented by mapper. The topics covered include: basic notions from topology, simplicial complexes (Cech complexes, Vietoris-Rips complexes, etc.), homology, persistent homology and applications, mapper.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH223**

**MATH252 Differential Forms**

This class will be an introduction to differential forms, a central tool in modern topology, geometry, and physics. The course begins where MATH222 ends, with Green's theorem, the divergence theorem, and Stokes' theorem. All of these theorems are special cases of one theorem, known as the general Stokes' theorem, about integration of differential forms. The objective of the first part of the course will be to understand and prove this theorem. We will then discuss manifolds and what can be learned about them using differential forms, concentrating on de Rham cohomology.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **(MATH221 AND MATH222) OR (MATH222 AND MATH223)**

**MATH255 Fundamentals of Analysis II**

Topics to be addressed include the topology of metric spaces (continuity, connectedness, and compactness), convergence of sequences and series of functions, spaces of functions and their topologies, the Lebesgue integral (on the line) and its basic convergence theorems, and Fourier series.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH225**

**MATH261 Abstract Algebra: Groups, Rings, and Fields**

This course is an introduction to abstract algebra, a core area of mathematics: the study of the basic properties of structures, with emphasis on fundamental results about groups and rings. MATH228, or comparable experience in writing proofs and in abstract reasoning, is strongly recommended.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **(MATH221 AND MATH228) OR (MATH223 AND MATH228)**

**MATH262 Abstract Algebra**

This continuation of MATH261 will discuss fields and Galois theory. Additional topics will be covered as time permits.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH261**

**MATH271 Error-Correcting Codes**

Nowadays messages are sent electronically through different kinds of communication channels. Most of these channels are not perfect and errors are created during the transmission. The object of an error-correcting code is to encode the data so that the message can be recovered if not too many errors have occurred. The goal of this course is to introduce the basic mathematical ideas behind the design of error-correcting codes. It makes use of algebraic techniques involving vector spaces, finite fields, and polynomial rings. These techniques will be developed in this course so that prior knowledge is not necessary.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH221 OR MATH223**

**MATH272 Elementary Number Theory**

This is a course in the elements of the theory of numbers. Topics covered include divisibility, congruences, quadratic reciprocity, Diophantine equations, and a brief introduction to algebraic numbers.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH228**

**MATH273 Combinatorics**

This course will present a broad, comprehensive survey of combinatorics. Topics may include partitions, the topic of inclusion-exclusion, generating functions, recurrence relations, partially ordered sets, trees, graphs, and min-max theorems.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH228**

**MATH274 Graph Theory**

A graph is a set V of elements called vertices and a set E of pairs of elements of V called edges. From this simple definition, many elegant models have been developed. Indeed, graph theory is essential to applications of computer science to network analysis and planar mapping. This course will be an introduction to graph theory with an emphasis on the connections between graph theory and linear algebra.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH221 OR MATH223**

**MATH275 Probabilistic Graphical Models**

Graphical models are used to represent complex, uncertain relationships among several, possibly very many, variables. They are fundamental in many domains of application, including medical diagnosis and prognosis, vision and image processing, robotics, and computational biology. This course will familiarize students with the graph theory and probability theory needed to discuss graphical models. After that, students will investigate exact and approximate statistical inference for graphical models, learning/inference of parameters, and possibly learning of graph structure.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **MATH222**

**MATH283 Differential Geometry**

This course is an introduction to the classical differential geometry of curves and surfaces in Euclidean 3-space. Topics from global differential geometry and extensions to higher dimensions will be considered as time and the background of the students permit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **NSM-MATH**

Prereq: **(MATH222 AND MATH221) OR (MATH222 AND MATH223)**

**MATH401 Individual Tutorial, Undergraduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH402 Individual Tutorial, Undergraduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH407 Senior Tutorial (downgraded thesis)**

Downgraded Senior Thesis Tutorial - Project to be arranged in consultation with the tutor. Only enrolled in through the Honors Coordinator.

Offering: **Host**

Grading: **A-F**

**MATH408 Senior Tutorial (downgraded thesis)**

Offering: **Host**

Grading: **A-F**

**MATH409 Senior Thesis Tutorial**

Topics to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH410 Senior Thesis Tutorial**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH411 Group Tutorial, Undergraduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH412 Group Tutorial, Undergraduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH419 Student Forum**

Student-run group tutorial, sponsored by a faculty member and approved by the chair of a department or program.

Offering: **Host**

Grading: **Cr/U**

**MATH421 Undergraduate Research, Science**

Individual research projects for undergraduate students supervised by faculty members.

Offering: **Host**

Grading: **OPT**

**MATH422 Undergraduate Research, Science**

Individual research projects for undergraduate students supervised by faculty members.

Offering: **Host**

Grading: **OPT**

**MATH423 Advanced Research Seminar, Undergraduate**

Offering: **Host**

Grading: **OPT**

**MATH424 Advanced Research Seminar, Undergraduate**

Offering: **Host**

Grading: **OPT**

**MATH465 Education in the Field, Undergraduate**

Students must consult with the department and class dean in advance of undertaking education in the field for approval of the nature of the responsibilities and method of evaluation.

Offering: **Host**

Grading: **OPT**

**MATH466 Education in the Field, Undergraduate**

Students must consult with the department and class dean in advance of undertaking education in the field for approval of the nature of the responsibilities and method of evaluation.

Offering: **Host**

Grading: **OPT**

**MATH469 Education in the Field, Undergraduate**

Students must consult with the department and class dean in advance of undertaking education in the field for approval of the nature of the responsibilities and method of evaluation.

Offering: **Host**

Grading: **OPT**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH470 Independent Study, Undergraduate**

Credit may be earned for an independent study during a summer or authorized leave of absence provided that (1) plans have been approved in advance, and (2) all specified requirements have been satisfied.

Offering: **Host**

Grading: **OPT**

Credits: **0.50**

Gen Ed Area: **None**

Prereq: **None**

**MATH491 Teaching Apprentice Tutorial**

The teaching apprentice program offers undergraduate students the opportunity to assist in teaching a faculty member's course for academic credit.

Offering: **Host**

Grading: **OPT**

**MATH492 Teaching Apprentice Tutorial**

Offering: **Host**

Grading: **OPT**

**MATH495 Research Apprentice, Undergraduate**

Project to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **Cr/U**

**MATH496 Research Apprentice, Undergraduate**

Project to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **Cr/U**

**MATH500 Graduate Pedagogy**

The elements of good teaching will be discussed and demonstrated through lectures, practice teaching sessions, and discussions of problems encountered in the actual teaching environment. The staff consists of faculty and experienced graduate students. An integral part of the course is a required one-day workshop BEFORE the first day of formal classes.

Training in pedagogy in the first semester of attendance is required for all incoming Wesleyan MA and PhD students who have not already fulfilled this requirement at Wesleyan. BA/MA students are not required to get training in pedagogy but may choose to do so.

Offering: **Crosslisting**

Grading: **Cr/U**

Credits: **0.50**

Gen Ed Area: **None**

Identical With: **E&ES500, CHEM500, BIOL500, ASTR500, MB&B500, MUSC500, PHYS500, PSYC500**

Prereq: **None**

**MATH501 Individual Tutorial, Graduate**

Topic to be arranged in consultation with tutor.

Offering: **Host**

Grading: **OPT**

**MATH502 Individual Tutorial, Graduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH503 Selected Topics, Graduate Sciences**

Topic to be arranged in consultation with the tutor. A seminar primarily concerned with papers taken from current research publications designed for, and required of, graduate students.

Offering: **Host**

Grading: **OPT**

**MATH504 Selected Topics, Graduate Sciences**

Topic to be arranged in consultation with the tutor. A seminar primarily concerned with papers taken from current research publications designed for, and required of, graduate students.

Offering: **Host**

Grading: **OPT**

**MATH507 Topics in Combinatorics**

Each year the topic will change.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH509 Model Theory**

This course will emphasize model theoretic algebra. We will consider the model theory of fields, including algebraically closed, real-closed, and p-adically closed fields; algebraically closed valued fields; and also general questions of definability in fields. As time permits, we will consider more recent applications of model theory in number theory and arithmetic geometry. Ideally, the student should understand what it means to be first-order definable and should have the equivalent of a year's study of abstract algebra. To study various applications, it will be necessary to assume certain results from the areas of application--that is, without proving them ab initio.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH511 Group Tutorial, Graduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH512 Group Tutorial, Graduate**

Topic to be arranged in consultation with the tutor.

Offering: **Host**

Grading: **OPT**

**MATH513 Analysis I**

MATH513 and MATH514 constitute the first-year graduate course in real and complex analysis. One semester will be devoted to real analysis, covering such topics as Lebesgue measure and integration on the line, abstract measure spaces and integrals, product measures, decomposition and differentiation of measures, and elementary functional analysis. One semester will be devoted to complex analysis, covering such topics as analytic functions, power series, Mobius transformations, Cauchy's integral theorem and formula in its general form, classification of singularities, residues, argument principle, maximum modulus principle, Schwarz's lemma, and the Riemann mapping theorem.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH514 Analysis I**

MATH513 and MATH514 constitute the first-year graduate course in real and complex analysis. One semester will be devoted to real analysis, covering such topics as Lebesgue measure and integration on the line, abstract measure spaces and integrals, product measures, decomposition and differentiation of measures, and elementary functional analysis. One semester will be devoted to complex analysis, covering such topics as analytic functions, power series, Mobius transformations, Cauchy's integral theorem and formula in its general form, classification of singularities, residues, argument principle, maximum modulus principle, Schwarz's lemma, and the Riemann mapping theorem.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH515 Analysis II**

This is a topics course in analysis and varies from year to year. It may be repeated for credit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH516 Analysis II**

This is a topics course in analysis and varies from year to year. It may be repeated for credit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **MATH513**

**MATH523 Topology I**

This course is an introduction to topological spaces and the fundamental group; topological spaces, continuous maps, metric spaces; product and quotient spaces; compactness, connectedness, and separation axioms; and introduction to homotopy and the fundamental group.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH524 Topology I**

A continuation of MATH523, this course will be an introduction to algebraic topology, concentrating on the fundamental group and homology.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH525 Topology II: Topics in Topology**

This is a topics course in topology that varies from year to year. This course may be repeated for credit. Recent topics have included knot theory, homotopy theory, Lie groups, and topological graph theory.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH526 Topology II**

This is a topics course in topology that varies from year to year. It may be repeated for credit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH543 Algebra I**

This course covers group theory including Sylow theorems, and basic ring and module theory, including structure of finitely generated modules over principal-ideal domains.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH544 Algebra I**

This course studies Galois theory, finitely generated modules over principal-ideal domains, and other topics as time permits.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH545 Algebra II: Topics in Algebra**

This is a topics course in algebra that varies from year to year. This course may be repeated for credit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH546 Algebra II**

This is a topics course in algebra that varies from year to year. It may be repeated for credit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**

**MATH549 Advanced Research Seminar, Graduate**

Offering: **Host**

Grading: **OPT**

**MATH550 Advanced Research Seminar, Graduate**

Offering: **Host**

Grading: **OPT**

**MATH572 Special Topics in Mathematics**

This is a supervised reading course on advanced topics in number theory. This course may be repeated for credit.

Offering: **Host**

Grading: **A-F**

Credits: **1.00**

Gen Ed Area: **None**

Prereq: **None**