Explores the ways and means by which we communicate with numbers; the everyday math we encounter on a regular basis. The fundamental quantitative skill set is covered in depth providing a firm foundation for further coursework in mathematics and the sciences. Topics include ratios, rates, percentages, units, descriptive statistics, linear and exponential modeling, correlation, logic, and probability. A project-based course using Microsoft Excel, emphasizing conceptual understanding and application. Reading of current newspaper articles and exercises involving personal finance are incorporated to place the mathematics in real-world context.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Fall Semester

The purpose of this course is to provide a comprehensive introduction to data analysis and data visualization. Students will use spreadsheet applications to analyze and interpret data before progressing to the more powerful tools of R and Tableau. Students will come to appreciate the ease and utility of spreadsheets, but also learn that for many projects, other software platforms provide more power, flexibility, and convenience, and produce better results. A main goal of the course is to transition students to a coding environment, overcoming the conceptual and practical hurdles involved in that transition. The course is organized around a set of case studies. For each data set, we set out to create the same graphics using each of three tools: Excel, Tableau, and R. Students will learn how to wrangle their data into a tidy form suitable for analysis and visualization. We will engage in all aspects of the data science process.

Terms offered: 2025 Spring Semester

An introduction to statistical methods used across the social and natural sciences with an emphasis on computational techniques. Covers conceptual understanding and includes topics from exploratory data analysis, the experimental design, probability, and statistical inference. Computational skills form a core element of the course, used throughout the semester both to explore data and to execute statistical tests. Not open to students who have credit for Economics 2557 or Psychology 2520 or who have credit for or are concurrently enrolled in Mathematics 1400.

Terms offered: 2021 Fall Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

Functions, including the trigonometric, exponential, and logarithmic functions; the derivative and the rules for differentiation; the anti-derivative; applications of the derivative and the anti-derivative. Four to five hours of class meetings and computer laboratory sessions per week, on average. Open to students who have taken at least three years of mathematics in secondary school.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

Supplemental problem-solving workshop for differential calculus students. Concurrent enrollment in Math 1600 required. Enrollment by permission of instructor. One-half credit. Grading is Credit/D/Fail.

Terms offered: 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester

The definite integral; the Fundamental theorems; improper integrals; applications of the definite integral; differential equations; and approximations including Taylor polynomials and Fourier series. An average of four to five hours of class meetings and computer laboratory sessions per week.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

Supplemental problem-solving workshop for integral calculus students. Concurrent enrollment in Math 1700 required. Enrollment by permission of instructor. One-half credit. Grading is Credit/D/Fail.

Terms offered: 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester

A review of the exponential and logarithmic functions, techniques of integration, and numerical integration. Improper integrals. Approximations using Taylor polynomials and infinite series. Emphasis on differential equation models and their solutions. An average of four to five hours of class meetings and computer laboratory sessions per week. Open to students whose backgrounds include the equivalent of Mathematics 1600 and the first half of Mathematics 1700. Designed for first-year students who have completed an AB Advanced Placement calculus course in their secondary schools.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

An introduction to data science through computer programming. Emphasis on the use of computational methods to explore, visualize, and contextualize data using a variety of statistical and probability models. Readings from scientific literature are paired with techniques to interpret data in a variety of contexts. Topics include computer programming, data organization, exploratory data analysis, probability, random variables, statistical tests, regression, the use (and misuse) of p-values, and scientific argumentation. No previous programming experience is assumed. Not open to students who have credit for Economics 2557.

Terms offered: 2024 Fall Semester

A study of mathematical modeling in biology, with a focus on translating back and forth between biological questions and their mathematical representation. Biological questions are drawn from a broad range of topics, including disease, ecology, genetics, population dynamics, and neurobiology. Mathematical methods include discrete and continuous (ODE) models and simulation, box models, linearization, stability analysis, attractors, oscillations, limiting behavior, feedback, and multiple time-scales. Within the biology major, this course may count as the mathematics credit or as biology credit, but not both. Students are expected to have taken a year of high school or college biology prior to this course. This course originates in Mathematics and is crosslisted with: Biology. (Same as: BIOL 1175)

Terms offered: 2025 Spring Semester

Multivariate calculus in two and three dimensions. Vectors and curves in two and three dimensions; partial and directional derivatives; the gradient; the chain rule in higher dimensions; double and triple integration; polar, cylindrical, and spherical coordinates; line integration; conservative vector fields; and Green’s theorem. An average of four to five hours of class meetings and computer laboratory sessions per week.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

A study of mathematical modeling in biology, with a focus on translating back and forth between biological questions and their mathematical representation. Biological questions are drawn from a broad range of topics, including disease, ecology, genetics, population dynamics, and neurobiology. Mathematical methods include discrete and continuous (ODE) models and simulation, box models, linearization, stability analysis, attractors, oscillations, limiting behavior, feedback, and multiple time-scales. Within the biology major, this course may count as the mathematics credit or as biology credit, but not both. Students are expected to have taken a year of high school or college biology prior to this course. This course originates in Mathematics and is crosslisted with: Biology. (Same as: BIOL 1174)

Terms offered: 2022 Spring Semester; 2023 Spring Semester

A study of linear algebra in the context of Euclidean spaces and their subspaces, with selected examples drawn from more general vector spaces. Topics will include: vectors, linear independence and span, linear transformations, matrices and their inverses, bases, dimension and rank, determinants, eigenvalues and eigenvectors, diagonalization and change of basis, and orthogonality. Applications drawn from linear systems of equations, discrete dynamical systems, Markov chains, computer graphics, and least-squares approximation.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

An introduction to logical deductive reasoning and mathematical proof through diverse topics in higher mathematics. Specific topics include set and function theory, modular arithmetic, proof by induction, and the cardinality of infinite sets. May also consider additional topics such as graph theory, number theory, and finite state automata.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

This course introduces Fourier transforms through a combination of computational methods, theory, and practical applications. Topics covered include Fourier series, Fourier transforms of continuous and discrete signals, convergence in function spaces, convolutions, and the fast Fourier transform (FFT). The course will also explore applications in areas such as image compression, audio processing, and seismology.

A study of optimization problems arising in a variety of situations in the social and natural sciences. Analytic and numerical methods are used to study problems in mathematical programming, including linear models, but with an emphasis on modern nonlinear models. Issues of duality and sensitivity to data perturbations are covered, and there are extensive applications to real-world problems.

Terms offered: 2024 Fall Semester; 2025 Spring Semester

A study of the mathematical models used to formalize nondeterministic or “chance” phenomena. General topics include combinatorial models, probability spaces, conditional probability, discrete and continuous random variables, independence and expected values. Specific probability densities, such as the binomial, Poisson, exponential, and normal, are discussed in depth.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

A study of some of the ordinary differential equations that model a variety of systems in the physical, natural and social sciences. Classical methods for solving differential equations with an emphasis on modern, qualitative techniques for studying the behavior of solutions to differential equations. Applications to the analysis of a broad set of topics, including population dynamics, oscillators and economic markets. Computer software is used as an important tool, but no prior programming background is assumed.

Terms offered: 2021 Fall Semester; 2022 Spring Semester; 2022 Fall Semester; 2023 Spring Semester; 2023 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

An introduction to the theory and application of numerical analysis. Topics include approximation theory, numerical integration and differentiation, iterative methods for solving equations, and numerical analysis of differential equations.

Terms offered: 2022 Spring Semester; 2024 Spring Semester; 2025 Fall Semester

A continuation of Linear Algebra focused on the interplay of algebra and geometry as well as mathematical theory and its applications. Topics include matrix decompositions, eigenvalues and spectral theory, vector and Hilbert spaces, norms and low-rank approximations. Applications to biology, computer science, economics, and statistics, including artificial learning and pattern recognition, principal component analysis, and stochastic systems. Course and laboratory work balanced between theory and application.

Terms offered: 2022 Fall Semester

The differential and integral calculus of functions of a complex variable. Cauchy’s theorem and Cauchy’s integral formula, power series, singularities, Taylor’s theorem, Laurent’s theorem, the residue calculus, harmonic functions, and conformal mapping.

Terms offered: 2022 Spring Semester; 2024 Spring Semester

A survey of modern approaches to Euclidean geometry in two dimensions. Axiomatic foundations of metric geometry. Transformational geometry: isometries and similarities. Klein’s Erlanger Programm. Symmetric figures. Other topics may be chosen from three-dimensional geometry, ornamental groups, area, volume, fractional dimension, and fractals.

Terms offered: 2022 Spring Semester; 2023 Spring Semester; 2024 Spring Semester; 2025 Spring Semester

A survey of number theory from Euclid’s proof that there are infinitely many primes through Wiles’s proof of Fermat’s Last Theorem in 1994. Prime numbers, unique prime factorization, and results on counting primes. The structure of modular number systems. Continued fractions and “best” approximations to irrational numbers. Investigation of the Gaussian integers and other generalizations. Squares, sums of squares, and the law of quadratic reciprocity. Applications to modern methods of cryptography, including public key cryptography and RSA encryption.

Terms offered: 2023 Fall Semester

An introduction to combinatorics and graph theory. Topics to be covered may include enumeration, matching theory, generating functions, partially ordered sets, Latin squares, designs, and graph algorithms.

Terms offered: 2021 Fall Semester; 2023 Spring Semester; 2025 Fall Semester

An introduction to the theory of finite and infinite groups, with examples ranging from symmetry groups to groups of polynomials and matrices. Properties of mappings that preserve algebraic structures are studied. Topics include cyclic groups, homomorphisms and isomorphisms, normal subgroups, factor groups, the structure of finite abelian groups, and Sylow theorems.

Terms offered: 2021 Fall Semester; 2022 Fall Semester; 2025 Fall Semester

Building on the theoretical underpinnings of calculus, develops the rudiments of mathematical analysis. Concepts such as limits and convergence from calculus are made rigorous and extended to other contexts, such as spaces of functions. Specific topics include metric spaces, point-set topology, sequences and series, continuity, differentiability, the theory of Riemann integration, and functional approximation and convergence.

Terms offered: 2021 Fall Semester; 2022 Fall Semester; 2024 Spring Semester; 2024 Fall Semester; 2025 Fall Semester

An introduction to the fundamentals of mathematical statistics. General topics include likelihood methods, point and interval estimation, and tests of significance. Applications include inference about binomial, Poisson, and exponential models, frequency data, and analysis of normal measurements.

Terms offered: 2022 Spring Semester; 2023 Spring Semester; 2024 Spring Semester; 2025 Spring Semester

An introduction to algebraic structures based on the study of rings and fields. Structure of groups, rings, and fields, with an emphasis on examples. Fundamental topics include: homomorphisms, ideals, quotient rings, integral domains, polynomial rings, field extensions. Further topics may include unique factorization domains, rings of fractions, finite fields, vector spaces over arbitrary fields, and modules. Mathematics 2502 is helpful but not required.

Terms offered: 2023 Fall Semester; 2024 Fall Semester

An introduction to the mathematical theory and practice of machine learning. Supervised and unsupervised learning problems, including regression, classification, clustering, and component analysis, focusing on techniques most relevant to the study and applications of neural networks. Additional topics may include dimension reduction, data visualization, denoising, norms and loss functions, optimization, universal approximation theorems, and algorithmic fairness. Class will include computer lab and projects, but no formal programming experience is necessary.

Terms offered: 2022 Spring Semester; 2023 Spring Semester; 2024 Fall Semester

A study of mathematical modeling, with emphasis on how to identify scientific questions appropriate for modeling, how to develop a model appropriate for a given scientific question, and how to interpret model predictions. Applications drawn from the natural, physical, environmental, and sustainability sciences. Model analysis uses a combination of computer simulation and theoretical methods and focuses on predictive capacity of a model.

Terms offered: 2022 Spring Semester; 2024 Spring Semester

A study of infinite-dimensional optimization, including calculus of variations and optimal control. Classical, analytic techniques are covered, as well as numerical methods for solving optimal control problems. Applications in many topic areas, including economics, biology, and robotics.

Terms offered: 2021 Fall Semester; 2023 Fall Semester

One or more specialized topics in abstract or linear algebra. Possible topics include: representations and modules, quivers, categories, homological algebra, spectral and operator theory, and algebraic combinatorics, as well as others that explore the connection of algebra with other areas of modern mathematics.

Terms offered: 2025 Spring Semester

A mathematical study of shape. Examination of surfaces, knots, and manifolds with or without boundary. Topics drawn from point-set topology, algebraic topology, knot theory, and computational topology, with possible applications to differential equations, graph theory, topological data analysis, and the sciences.

Terms offered: 2022 Fall Semester; 2024 Fall Semester

A study of nonlinear dynamical systems arising in applications, with emphasis on modern geometric, topological, and analytical techniques to determine global system behavior, from which predictions can be made. Topics chosen from local stability theory and invariant manifolds, limit cycles and oscillation, global phase portraits, bifurcation and resilience, multiple time scales, and chaos. Theoretical methods supported by simulations. Applications drawn from across the sciences.

Terms offered: 2022 Fall Semester

A study of some of the partial differential equations that model a variety of systems in the natural and social sciences. Classical methods for solving partial differential equations are covered, as well as modern, numerical techniques for approximating solutions. Applications to the analysis of a broad set of topics, including air quality, traffic flow, and imaging. Computer software is used as an important tool.

Terms offered: 2023 Spring Semester; 2024 Fall Semester; 2025 Spring Semester; 2025 Fall Semester

A second course in complex analysis. Topics may include conformal mappings, harmonic functions, and analytic functions. Applications drawn from boundary value problems, elliptic functions, two-dimensional potential theory, Fourier analysis, and topics in analytic number theory.

Terms offered: 2022 Fall Semester

An introduction to advanced topics in geometry, including Euclidean and non Euclidean geometries in two dimensions, unified by the transformational viewpoint of Klein’s Erlangen Program. Additional topics will vary by instructor and may include isometry groups of Euclidean and hyperbolic spaces, alternate models of hyperbolic geometry, differential geometry and projective geometry. Math 2404, or any higher numbered course, is helpful but not required.

Terms offered: 2021 Fall Semester; 2023 Fall Semester

The study of group actions on geometric objects; understanding finite and discrete groups via generators and presentations. Applications to geometry, topology, and linear algebra, focusing on certain families of groups. Topics may include Cayley graphs, the word problem, growth of groups, and group representations.

Terms offered: 2022 Spring Semester; 2023 Spring Semester

Measure theory and integration with applications to probability and mathematical finance. Topics include Lebesgue measure and integral, measurable functions and random variables, convergence theorems, analysis of random processes including random walks and Brownian motion, and the Ito integral.

Terms offered: 2022 Spring Semester; 2025 Spring Semester

One or more specialized topics in probability and statistics. Possible topics include regression analysis, nonparametric statistics, logistic regression, and other linear and nonlinear approaches to modeling data. Emphasis is on the mathematical derivation of the statistical procedures and on the application of the statistical theory to real-life problems.

Terms offered: 2021 Fall Semester; 2023 Fall Semester; 2024 Spring Semester; 2025 Fall Semester

Advanced topics in modern algebra based on rings and fields. Possible topics include: Galois theory with applications to geometric constructions and (in)solvability of polynomial equations; algebraic number theory and number fields such as the p-adic number system; commutative algebra; algebraic geometry and solutions to systems of polynomial equations.

Terms offered: 2024 Spring Semester