# Courses

Courses offered in the past four years.

▲ *indicates offered in the current term*

▹ *indicates offered in the upcoming term[s]*

##### MATH 0100 - A World of Mathematics ▲

**A World of Mathematics**

How long will oil last? What is the fairest voting system? How can we harvest food and other resources sustainably? To explore such real-world questions we will study a variety of mathematical ideas and methods, including modeling, logical analysis, discrete dynamical systems, and elementary statistics. This is an alternative first mathematics course for students not pursuing the calculus sequence in their first semester. The only prerequisite is an interest in exploring contemporary issues using the mathematics that lies within those issues. (Approval required; This course is not open to students who have had a prior course in calculus or statistics.) 3 hrs lect./disc. **DED**

Fall 2017, Fall 2018, Fall 2019, Fall 2020

##### MATH 0116 - Intro to Statistical Science ▲ ▹

**Introduction to Statistical Science**

A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0210 or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab. **DED**

Fall 2016, Spring 2017, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021

##### MATH 0121 - Calculus I ▲ ▹

**Calculus I**

Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. **DED**

Fall 2016, Spring 2017, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021

##### MATH 0122 - Calculus II ▲ ▹

**Calculus II**

A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. **DED**

Fall 2016, Spring 2017, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021

##### MATH 0190 - Math Proof: Art and Argument

**Mathematical Proof: Art and Argument**

Mathematical proof is the language of mathematics. As preparation for upper-level coursework, this course will give students an opportunity to build a strong foundation in reading, writing, and analyzing mathematical argument. Course topics will include an introduction to mathematical logic, standard proof structures and methods, set theory, and elementary number theory. Additional topics will preview ideas and methods from more advanced courses. We will also explore important historical examples of proofs, both ancient and modern. The driving force behind this course will be mathematical expression with a primary focus on argumentation and the creative process. (MATH 0122 or MATH 0200) 3 hrs. lect. **CW DED**

Spring 2017

##### MATH 0200 - Linear Algebra ▲ ▹

**Linear Algebra**

Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. **DED**

##### MATH 0213 - Categorical Data Analysis

**Categorical Data Analysis**

In this course we will survey the statistical methods used for the analysis of categorical data including methods for analyzing binary, multinomial, and count response variables. Tests and confidence intervals for the difference in proportions, relative risks, odds ratios, matched pairs, and logistic regression will be discussed. Nominal and ordinal responses will be considered. Additional topics may include larger contingency tables and Poisson, and negative-binomial regression models. Applications include examples in biology, economics, medicine, agriculture, and industry. R statistical software will be used for data analysis. (MATH 0116 or PSYC 0201 or ECON 0210; or by waiver) 3 hrs. lect. **DED**

Spring 2019

##### MATH 0214 - Research Design and Analysis

**Research Design and Analysis**

This course will be a survey of statistical methods needed for scientific research, including planning data collection and data analyses that provide evidence about a research hypothesis. The course will include factorial, block, and split-plot/repeated-measures designs and analyses of variance, interactions, contrasts, multiple comparisons, and graphical methods for displaying data. Special attention will be given to analysis of data from student projects such as theses and independent studies. The R statistical software will be used for data analysis. (MATH 0116, PSYC 0201, ECON 0210 or by waiver) 3 hrs. lect. **DED**

Fall 2018

##### MATH 0216 - Introduction to Data Science ▲ ▹

**Introduction to Data Science**

In this course students will gain exposure to the entire data science pipeline: forming a statistical question, collecting and cleaning data sets, performing exploratory data analyses, identifying appropriate statistical techniques, and communicating the results, all the while leaning heavily on open source computational tools, in particular the R statistical software language. We will focus on analyzing real, messy, and large data sets, requiring the use of advanced data manipulation/wrangling and data visualization packages. Students will be required to bring their own laptops as many lectures will involve in-class computational activities. 3 hrs lect./disc. **DED**

Fall 2016, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021

##### MATH 0218 - Statistical Learning ▹

**Statistical Learning**

This course is an introduction to modern statistical, machine learning, and computational methods to analyze large and complex data sets that arise in a variety of fields, from biology to economics to astrophysics. The theoretical underpinnings of the most important modeling and predictive methods will be covered, including regression, classification, clustering, resampling, and tree-based methods. Student work will involve implementation of these concepts using open-source computational tools. (MATH 0216) 3 hrs. lect./disc. **DED**

Spring 2017, Spring 2020, Spring 2021

##### MATH 0223 - Multivariable Calculus ▲ ▹

**Multivariable Calculus**

The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

##### MATH 0225 - Topics in Linear Alg & Diff Eq ▲ ▹

**Topics in Linear Algebra and Differential Equations**

Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021

##### MATH 0228 - Intro to Numerical Analysis

**Introduction to Numerical Analysis**

We will study the development, analysis, and implementation of numerical methods for approximating solutions to mathematical problems. We will begin with applications of Taylor polynomials, computer representation of numbers, and types of errors. Other topics will include polynomial and spline interpolation, numerical integration and differentiation, rootfinding, and numerical solutions of differential equations. Accuracy will be quantified by the concept of numerical error. Additionally, we will study the stability, efficiency, and implementation of algorithms. We will utilize the software MATLAB throughout to demonstrate concepts, as well as to complete assignments and projects. (MATH 0200) **DED**

Fall 2017

##### MATH 0230 - Euc and Non-Euc Geometries

**Euclidean and Non-Euclidean Geometries**

In roughly 300 BCE, Euclid set down his axioms of geometry which subsequently became the standard by which people understood the mathematics of the world around them. In the first half of the 19th century, mathematicians realized, however, that they could remove one of Euclid’s axioms, the one known as the “parallel postulate,” and still produce logically consistent examples of geometries. These new geometries displayed behaviors that were wildly different from Euclidean geometry. In this course we will study examples of these revolutionary non-Euclidean geometries, with a focus on Klein's Erlangen Program, which is a modern way of understanding them. (MATH 0200 or by waiver) 3 hrs. lect. **DED**

Spring 2019

##### MATH 0241 - Elementary Number Theory

**Elementary Number Theory**

Divisibility and prime factorization. Congruences; the theorems of Lagrange, Fermat, Wilson, and Euler; residue theory; quadratic reciprocity. Diophantine equations. Arithmetic functions and Mobius inversion. Representation as a sum of squares. (MATH 0122 or by waiver) **DED**

Fall 2016, Fall 2018, Spring 2020

##### MATH 0247 - Graph Theory ▹

**Graph Theory**

A graph (or network) is a useful mathematical model when studying a set of discrete objects and the relationships among them. We often represent an object with a vertex (node) and a relation between a pair with an edge (line). With the graph in hand, we then ask questions, such as: Is it connected? Can one traverse each edge precisely once and return to a starting vertex? For a fixed *k/, is it possible to “color” the vertices using /k* colors so that no two vertices that share an edge receive the same color? More formally, we study the following topics: trees, distance, degree sequences, matchings, connectivity, coloring, and planarity. Proof writing is emphasized. (MATH 0122 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2017, Fall 2019, Spring 2021

##### MATH 0261 - History of Mathematics ▲

**History of Mathematics**

This course studies the history of mathematics chronologically beginning with its ancient origins in Babylonian arithmetic and Egyptian geometry. The works of Euclid, Apollonius, and Archimedes and the development of ancient Greek deductive mathematics is covered. The mathematics from China, India, and the Arab world is analyzed and compared. Special emphasis is given to the role of mathematics in the growth and development of science, especially astronomy. European mathematics from the Renaissance through the 19th Century is studied in detail including the development of analytic geometry, calculus, probability, number theory, and modern algebra and analysis. (MATH 0122 or waiver) **CMP DED**

Spring 2018, Fall 2020

##### MATH 0302 - Abstract Algebra I ▲

**Abstract Algebra**

Groups, subgroups, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, rings and ideals, integral domains and fields, the field of quotients of a domain, the ring of polynomials over a domain, Euclidean domains, principal ideal domains, unique factorization, factorization in a polynomial ring. (MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2016, Spring 2017, Fall 2017, Fall 2018, Spring 2019, Fall 2019, Fall 2020

##### MATH 0310 - Probability ▲

**Probability**

An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications. (concurrent or prior MATH 0223 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2016, Fall 2017, Fall 2018, Fall 2019, Fall 2020

##### MATH 0311 - Statistics ▹

**Statistics**

An introduction to the mathematical methods and applications of statistical inference. Topics will include: survey sampling, parametric and nonparametric problems, estimation, efficiency and the Neyman-Pearsons lemma. Classical tests within the normal theory such as F-test, t-test, and chi-square test will also be considered. Methods of linear least squares are used for the study of analysis of variance and regression. There will be some emphasis on applications to other disciplines. (MATH 0310) 3 hrs. lect./disc. **DED**

Spring 2018, Spring 2020, Spring 2021

##### MATH 0315 - Mathematical Models ▹

**Mathematical Models in the Social and Life Sciences**

An introduction to the role of mathematics as a modeling tool and an examination of some mathematical models of proven usefulness in problems arising in the social and life sciences. Topics will be selected from the following: axiom systems as used in model building, optimization techniques, linear and integer programming, theory of games, systems of differential equations, computer simulation, stochastic process. Specific models in political science, ecology, sociology, anthropology, psychology, and economics will be explored. (MATH 0200 or waiver) 3 hrs. lect./disc. **DED**

Fall 2016, Fall 2018, Spring 2021

##### MATH 0318 - Operations Research

**Operations Research**

Operations research is the utilization of quantitative methods as an aid to managerial decisions. In the course, several of these methods will be introduced and studied in both a mathematical context and a physical context. Topics included will be selected from the following: classification of problems and the formulation of models, linear programming, network optimization, transportation problems, assignment problems, integer programming, nonlinear programming, inventory theory, and game theory. (MATH 0200 or waiver) **DED**

Fall 2017, Fall 2019

##### MATH 0323 - Real Analysis ▲

**Real Analysis**

An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc. **DED**

Fall 2016, Fall 2017, Spring 2018, Fall 2018, Fall 2019, Spring 2020, Fall 2020

##### MATH 0325 - Complex Analysis ▹

**Complex Analysis**

An introduction to functions of a complex variable. Mappings of the complex plane, analytic functions, Cauchy Integral Theorem and related topics. (MATH 0223 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2017, Spring 2019, Spring 2021

##### MATH 0328 - Numerical Linear Algebra ▲

**Numerical Linear Algebra**

Numerical linear algebra is the study of algorithms for solving problems such as finding solutions of linear systems and eigenvalues of matrices. Many real-life applications simplify to these scenarios and often involve millions of variables. We will analyze shortcomings of direct methods such as Gaussian Elimination, which theoretically produces the true solution but fails in practical applications. In contrast, iterative methods are often more practical and precise, and continually evolve with changing technology and our understanding of mathematics. Our study will include the First Order Richardson, Steepest Descent, and Conjugate Gradient algorithms for linear systems, and the power method for eigenvalue problems. (MATH 0200) 3 hrs. lect. **CW DED**

Spring 2017, Spring 2019, Fall 2020

##### MATH 0335 - Differential Geometry ▲

**Differential Geometry**

This course will be an introduction to the concepts of differential geometry. For curves in space, we will discuss arclength parameterizations, Frenet formulas, curvature, and torsion. On surfaces, we will explore the Gauss map, the shape operator, and various types of curvature. We will apply our knowledge to understand geodesics, metrics, and isometries of general geometric spaces. If time permits, we will consider topics such as minimal surfaces, constant curvature spaces, and the Gauss-Bonnet theorem. (MATH 0200 and MATH 0223) 3 hr. lect./disc. **DED**

Fall 2020

##### MATH 0338 - Fundamental Algebraic Geometry

**Fundamentals of Algebraic Geometry**

Algebraic geometry is one of the oldest areas of mathematics, yet it is thoroughly modern and active. It is the study of geometric spaces locally defined by polynomial equations. The aim of this course is to introduce students to some basic notions and ideas in algebraic geometry. We will study affine and projective spaces, affine and projective curves, singularities, intersection theory, Hilbert’s Nullstellensatz, Bezout’s Theorem, and the arithmetic of elliptic curves. There will be an emphasis on examples and problem solving. (MATH 302) 3 hrs. lect. **DED**

Spring 2018, Spring 2020

##### MATH 0345 - Combinatorics

**Combinatorics**

Combinatorics is the “art of counting.” Given a finite set of objects and a set of rules placed upon these objects, we will ask two questions. Does there exist an arrangement of the objects satisfying the rules? If so, how many are there? These are the questions of existence and enumeration. As such, we will study the following combinatorial objects and counting techniques: permutations, combinations, the generalized pigeonhole principle, binomial coefficients, the principle of inclusion-exclusion, recurrence relations, and some basic combinatorial designs. (MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2018, Spring 2020

##### MATH 0410 - Stochastic Processes ▹

**Stochastic Processes**

Stochastic processes are mathematical models for random phenomena evolving in time or space. This course will introduce important examples of such models, including random walk, branching processes, the Poisson process and Brownian motion. The theory of Markov chains in discrete and continuous time will be developed as a unifying theme. Depending on time available and interests of the class, applications will be selected from the following areas: queuing systems, mathematical finance (Black-Scholes options pricing), probabilistic algorithms, and Monte Carlo simulation. (MATH 0310) 3 hrs. lect./disc. **DED**

Spring 2017, Spring 2019, Spring 2021

##### MATH 0432 - Elementary Topology

**Elementary Topology**

An introduction to the concepts of topology. Theory of sets, general topological spaces, topology of the real line, continuous functions and homomorphisms, compactness, connectedness, metric spaces, selected topics from the topology of Euclidean spaces including the Jordan curve theorem. (MATH 0122 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2019

##### MATH 0500 - Advanced Study ▲ ▹

**Advanced Study**

Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

Fall 2016, Winter 2017, Spring 2017, Fall 2017, Winter 2018, Spring 2018, Fall 2018, Winter 2019, Spring 2019, Fall 2019, Winter 2020, Spring 2020, Fall 2020, Winter 2021, Spring 2021

##### MATH 0701 - Galois Theory

**Galois Theory**

This course is a tutorial in Galois theory for students who have completed Abstract Algebra. Starting from the concept of a ring, we will develop the theory of polynomial rings over fields, and use this to carry out an in-depth investigation of field extensions. Our work together will culminate in proving the fundamental theorem of Galois theory. Working independently and in small groups, students will explore related areas of algebra and communicate their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0302) 3 hrs. sem. **DED**

Spring 2020

##### MATH 0702 - Adv Topics Algebra/Ellip Curve ▹

**Advanced Topics in Algebra: The Arithmetic of Elliptic Curves**

The study of elliptic curves has fascinated mathematicians for the last 120 years.

It is the meeting place of algebra, number theory, and analysis. There's something for everyone. It combines hands-on computational with deep theoretical implications. Elliptic curves played a central role in Wiles' proof of Fermat's Last Theorem. They are used in factoring algorithms and elliptic curve cryptosystems have become the backbone of credit card and internet transactions. If you want to become rich and famous The Clay Institute has put a $1 million bounty on the Birch and Swinnerton-Dyer Conjecture which connects the algebraic and analytic theory of elliptic curves. (MATH 0302; Approval required) 3 hrs. sem.

Fall 2018, Spring 2021

##### MATH 0703 - Finite Fields Seminar

**Finite Fields Seminar**

This course is a tutorial in the theory and applications of finite fields, which lie in the intersection of algebra and number theory. Working in small groups, students will study the fundamental structure and properties of finite fields (also known as Galois fields). They will then work independently, exploring applications in cryptography, coding theory, or other areas. Students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0241 or MATH 0302; Approval required) 3 hrs. Sem

Fall 2017, Spring 2020

##### MATH 0704 - Senior Seminar

**Senior Seminar**

Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc.

Fall 2016, Spring 2017, Fall 2017

##### MATH 0710 - Advanced Probability Seminar

**Advanced Probability Seminar**

This course is a tutorial in Probability Theory for students who have completed work in Probability and Real Analysis. Starting from elementary results about random walks, we will explore the fundamental mathematical ideas underlying measure theoretic probability, martingales, the Weiner process, and the Itô stochastic calculus. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0310, MATH 0323, and by approval). 3 hrs. sem.

Spring 2019, Spring 2020

##### MATH 0715 - Advanced Math Modeling Seminar

**Advanced Mathematical Modeling Seminar**

A tutorial on advanced mathematical model building and analysis for students who have completed work in Differential Equations and Probability. We will study deterministic and stochastic models of interacting populations with a focus on mathematical ecology and epidemiology. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. (Approval Only) 3 hrs. Sem. **DED**

Spring 2018, Fall 2019

##### MATH 0723 - Topics in Analysis Seminar

**Topics in Analysis Seminar**

The foundation in analysis covered in MATH 0323 provides the tools necessary to engage a range of important and fascinating topics of both a pure and applied nature. In the first part of this seminar we will collectively work our way through the theory of Lebesgue measure and integration, studying the classical Banach spaces of integrable functions. After this common introduction, students will each choose a project from a range of options that includes topics in functional analysis (e.g., the open mapping theorem, the Hahn-Banach theorem) or more classical real analysis (e.g., Fourier series, orthogonal polynomials, the gamma function). Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0323 or by approval). 3 hrs. sem.

Spring 2019

##### MATH 0728 - Math Fluid Dynamics Seminar ▹

**Mathematical Methods in Fluid Dynamics**

This course is an introduction to the mathematical models and methods used in modern fluid dynamics. Students will derive and analyze fundamental equations of fluid flow, explore their applications, as well as examine theoretical and practical solution techniques. Equations of study will include the Poisson, diffusion, and Navier-Stokes equations. We will also introduce basic methods of computational fluid dynamics. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. 3 hrs. Lect./Lab (Approval Only) **DED**

Spring 2018, Spring 2021

##### MATH 0732 - Topology Seminar ▲

**Topology Seminar**

Topology is the rigorous mathematical study of shape at the most fundamental level—for example, the shapes of the letters I and U are topologically equivalent, but neither is equivalent to that of the letter O. In this senior seminar students will encounter topological objects such as manifolds, braids, and knots, studying them using tools ranging from combinatorial to geometric to algebraic. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0302) 3 hrs sem.

Fall 2020

##### MATH 0741 - Advanced Number Theory

**Advanced Number Theory**

A senior tutorial on some topics in advanced elementary number theory and an introduction to analytic number theory. In this course we will review key areas of elementary number theory and abstract algebra followed by the study of integer partitions, continued fractions, rational approximations of irrationals, primes and primality testing, the average order of magnitude of several number theoretic functions, the Basel problem, Bernoulli numbers, and the Riemann zeta function. (MATH 0241 or MATH 0302) 3 hrs. sem. **DED**

Fall 2019

##### MATH 0745 - Polynomial Method Seminar ▲

**The Polynomial Method**

A tutorial in the Polynomial Method for students who have completed work in Abstract Algebra and at least one of Combinatorics, Graph Theory, and Number Theory. We will study Noga Alon’s Combinatorial Nullstellensatz and related theorems, along with their applications to combinatorics, graph theory, number theory, and incidence geometry. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. (Approval required; MATH 0302 and one of the following: MATH 0241, MATH 0247, or MATH 0345).

Spring 2017, Fall 2018, Fall 2020