# Mathematics & Statistics Department

## 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: MATH 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: MATH 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: MATH 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: MATH 141. 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: MATH 141, or experience with linear regressions and programming with instructor approval. 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: MATH 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: MATH 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: MATH 202. Lecture-conference. Offered in alternate years.

### Mathematics 332 - Abstract Algebra

One-unit semester course. An elementary treatment of the algebraic structure of groups, rings, fields, and/or algebras. Prerequisite: MATH 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: MATH 202. Lecture-conference. May be repeated for credit. Offered in alternate years.

### 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: MATH 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: MATH 243, or MATH 241 with permission of the instructor. Conference-laboratory. May be repeated for credit. Offered in alternate years.

### Mathematics 346 - Bayesian Statistics

One-unit semester course. An introduction to the philosophy and practice of Bayesian statistics, an alternative framework to the classical frequentist approach. The course starts with foundational topics including Bayes’ theorem, conjugacy, and the philosophical and practical differences between Bayesian and frequentist approaches. We then take a deep dive into regression, hierarchical models, computational methods, and other advanced topics among missing data, mixture models, and prediction, all from a Bayesian perspective. Emphasis is placed on applying Bayesian methods to real-world datasets. Prerequisites: MATH 141 and 243, or consent of the instructor. Lecture-conference.

### 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: MATH 201. Concurrent MATH 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: MATH 113 and 201. Lecture-conference. Offered in alternate years.

Not offered 2023–24.

### Mathematics 382 - Algorithms and Data Structures

See CSCI 382 for description.

Computer Science 382 Description

### Mathematics 386 - Private and Fair Data Analysis

See CSCI 386 for description.

Computer Science 386 Description

### Mathematics 387 - Computability and Complexity

See CSCI 387 for description.

Computer Science 387 Description

### Mathematics 388 - Cryptography

See CSCI 388 for description.

Not offered 2023–24.

Computer Science 388 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: MATH 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: MATH 141 and 391, or consent of the instructor. Lecture-conference.

### 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: MATH 141 and 391, or consent of the instructor. Lecture-conference.

Not offered 2023–24.

### Mathematics 411 - Topics in Advanced Analysis

One-unit semester course. Topics selected by the instructor. Prerequisite: MATH 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: MATH 332 or consent of the instructor. Lecture-conference. May be repeated for credit.

### Mathematics 441 - Topics in Computer Science Theory

See CSCI 441 for description.

Computer Science 441 Description

### 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.