## Courses

### Mathematics 111 - Calculus

One-unit semester course. This includes a treatment of limits, continuity, derivatives, mean value theorem, integration—including the fundamental theorem of calculus, and definitions of the trigonometric, logarithmic, and exponential functions. Prerequisite: three years of high school mathematics. Lecture-conference.

### Mathematics 112 - Introduction to Analysis

One-unit semester course. Field axioms, the real and complex fields, sequences and series. Complex functions, continuity and differentiation; power series and the complex exponential. Prerequisite: Mathematics 111 or equivalent. Lecture-conference.

### Mathematics 113 - Discrete Structures

One-unit semester course. Sets, cardinality, number theory, combinatorics, probability. Proof techniques and problem solving. Additional topics may include graph theory, finite fields, and computer experimentation. Prerequisite: three years of high school mathematics. Lecture-conference.

### Mathematics 141 - Introduction to Probability and Statistics

One-unit semester course. The basic ideas of probability including properties of expectation, the law of large numbers, and the central limit theorem are discussed. These ideas are applied to the problems of statistical inference, including estimation and hypothesis testing. The linear regression model is introduced, and the problems of statistical inference and model validation are studied in this context. A portion of the course is devoted to statistical computing and graphics. Prerequisite: three years of high school mathematics. Lecture-conference and laboratory.

### Mathematics 201 - Linear Algebra

One-unit semester course. A brief introduction to field structures, followed by presentation of the algebraic theory of finite dimensional vector spaces. Topics include linear transformations, determinants, eigenvalues, eigenvectors, diagonalization. Geometry of inner product spaces is examined in the setting of real and complex fields. Prerequisite: Mathematics 112. Lecture-conference.

### Mathematics 202 - Vector Calculus

One-unit semester course. The derivative as a linear function, partial derivatives, optimization, multiple integrals, change of variables, Stokes’s theorem. Prerequisites: Mathematics 112 and 201, or permission of the instructor. Lecture-conference.

### Mathematics 241 - Data Science

One-unit semester course. Applied statistics class with an emphasis on data analysis. The course will be problem driven with a focus on collecting and manipulating data, using exploratory data analysis and visualization tools, identifying statistical methods appropriate for the question at hand, and communicating the results in both written and presentation form. Prerequisite: Mathematics 141 or equivalent. Lecture-conference.

### Mathematics 243 - Statistical Learning

One-unit semester course. An overview of modern approaches to analyzing large and complex data sets that arise in a variety of fields from biology to marketing to astrophysics. The most important modeling and predictive techniques will be covered, including regression, classification, clustering, resampling, and tree-based methods. There will be several projects throughout the course, which will require significant programming in R. Prerequisite: Mathematics 141, or experience with linear regressions and programming. Lecture-conference.

### Mathematics 311 - Complex Analysis

One-unit semester course. A study of complex valued functions: Cauchy’s theorem and residue theorem, Laurent series, and analytic continuation. Prerequisite: Mathematics 202. Lecture-conference.

### Mathematics 321 - Real Analysis

One-unit semester course. A careful study of continuity and convergence in metric spaces. Sequences and series of functions, uniform convergence, normed linear spaces. Prerequisite: Mathematics 202. Lecture-conference.

### Mathematics 322 - Ordinary Differential Equations

One-unit semester course. An introduction to the theory of ordinary differential equations. Existence and uniqueness theorems, global behavior of solutions, qualitative theory, numerical methods. Prerequisite: Mathematics 202. Lecture-conference. Offered in alternate years.

Not offered 2022–23.

### Mathematics 332 - Abstract Algebra

One-unit semester course. An elementary treatment of the algebraic structure of groups, rings, fields, and/or algebras. Prerequisite: Mathematics 201 and 113. Lecture-conference.

### Mathematics 341 - Topics in Geometry

One-unit semester course. Topics in geometry selected by the instructor. Possible topics include the theory of plane ornaments, coordinatization of affine and projective planes, curves and surfaces, differential geometry, algebraic geometry, and non-Euclidean geometry. Prerequisite: Mathematics 202. Lecture-conference. May be repeated for credit. Offered in alternate years.

Not offered 2022–23.

### Mathematics 342 - Topology

One-unit semester course. An introduction to basic topology, followed by selected topics such as topological manifolds, embedding theorems, and the fundamental group and covering spaces. Prerequisite: Mathematics 202 and 332, the latter of which may be taken concurrently. Lecture-conference.

### Mathematics 343 - Statistics Practicum

One-unit semester course. In this course, students will participate in a team-based, semester-long research project. Class time will be divided between supervised research time and a seminar focused on providing students with skills to facilitate their research. Seminar topics will include reproducible workflows, effective strategies for collaborative work, technical writing, statistical consulting, and scientific presentations. The course covers several components of the research process, such as literature reviews, technical writing, and scientific presentations. Emphasis is placed on developing a reproducible workflow. Prerequisite: Mathematics 243, or Mathematics 241 with permission of the instructor. Conference-laboratory. May be repeated for credit. Offered in alternate years.

Not offered 2022–23.

### Mathematics 344 - Advanced Statistical Modeling

One-unit semester course. This course focuses on a generalization of the classical linear model: the multilevel/hierarchical model. This Bayesian framework has become a common tool to analyze more complex study designs in biology and psychology as well as observational data in political science and economics. The course establishes the foundation of the model in probability and discusses its estimation through Markov chain Monte Carlo. These components allow for extensive practice fitting models to real-world data sets drawn from across the sciences. Prerequisites: Mathematics 111 and either Mathematics 243 or 392. Lecture.

Not offered 2022–23.

### Mathematics 345 - Spatial Data and Analysis

One-unit semester course. How do you perform statistical analysis when your observations are distributed in a space? This course will introduce tools for analyzing and visualizing data that has a spatial component. Topics include coordinate systems, distance and clustering metrics, interpolation, spatial autocorrelation, and spatial regression models. Most analysis will be done using R; however, the course will also include a short introduction to QGIS. Prerequisite: Mathematics 141 and Mathematics 241 or 243, or significant experience with programming. Lecture.

Not offered 2022–23.

### Mathematics 361 - Number Theory

One-unit semester course. A study of integers, including topics such as divisibility, theory of prime numbers, congruences, and solutions of equations in the integers. Prerequisite: Mathematics 201. Concurrent Mathematics 332 is recommended. Lecture-conference. Offered in alternate years.

### Mathematics 372 - Combinatorics

One-unit semester course. Emphasis is on enumerative combinatorics including such topics as the principle of inclusion-exclusion, formal power series and generating functions, and permutation groups and Pólya theory. Selected other topics such as Ramsey theory, inversion formulae, the theory of graphs, and the theory of designs will be treated as time permits. Prerequisite: Mathematics 113 and 201. Lecture-conference. Offered in alternate years.

### Mathematics 382 - Algorithms and Data Structures

See Computer Science 382 for description.

### Mathematics 387 - Computability and Complexity

See Computer Science 387 for description.

### Mathematics 388 - Cryptography

See Computer Science 388 for description.

### Mathematics 391 - Probability

One-unit semester course. A development of probability theory in terms of random variables defined on discrete sample spaces. Special topics may include Markov chains, stochastic processes, and measure-theoretic development of probability theory. Prerequisites: Mathematics 113 and 202. Lecture-conference.

### Mathematics 392 - Mathematical Statistics

One-unit semester course. Theories of statistical inference, including maximum likelihood estimation and Bayesian inference. Topics may be drawn from the following: large sample properties of estimates, linear models, multivariate analysis, empirical Bayes estimation, and statistical computing. Prerequisite: Mathematics 141 and 391, or consent of the instructor. Lecture-conference.

### Mathematics 393 - Stochastic Processes

One-unit semester course. A brief introduction to calculus-based probability theory, as well as a study of the main discrete- and continuous-time stochastic processes. Topics include Markov chains, martingales, Poisson processes, renewal processes, continuous-time Markov chains, and Brownian motion. A portion of the course is devoted to modeling stochastic processes using computer software. Prerequisites: Mathematics 202 and one of Mathematics 113, 141, or 391. Lecture-conference.

Not offered 2022–23.

### Mathematics 394 - Causal Inference

One-unit semester course. Overview of the statistical tools used to estimate causal effects. This course uses the potential outcomes framework and structural causal models to define causal estimates, and introduces the methods and assumptions needed to estimate them. Topics include randomized experiments, regression adjustment, propensity scores, matching, weighting, doubly robust and augmented estimation, instrumental variables, regression discontinuity, and sensitivity analysis. Students will present on advanced topics. Assignments involve using R to apply course topics on real and simulated data, and mathematical proofs and derivations. Prerequisites: Mathematics 141 and 391, or consent of the instructor. Lecture-conference.

### Mathematics 411 - Topics in Advanced Analysis

One-unit semester course. Topics selected by the instructor. Prerequisite: Mathematics 321 or consent of the instructor. Lecture-conference. May be repeated for credit.

### Mathematics 412 - Topics in Algebra

One-unit semester course. Topics selected by the instructor, for example, commutative algebra, Galois theory, algebraic geometry, and group representation theory. Prerequisite: Mathematics 332 or consent of the instructor. Lecture-conference. May be repeated for credit.

### Mathematics 441 - Topics in Computer Science Theory

See Computer Science 441 for description.

Not offered 2022–23.

### Mathematics 470 - Thesis

Two-unit yearlong course; one unit per semester.

### Mathematics 481 - Independent Study

One-half-unit semester course. Independent reading primarily for juniors and seniors. Prerequisite: approval of the instructor and the division.