# Mathematics & Statistics Department

## Courses

### MATH 111 - Calculus

Description of Math 111 courses

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): Three years of high school mathematics
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 112 - Introduction to Analysis

Field axioms, the real and complex fields, sequences and series. Complex functions, continuity and differentiation; power series and the complex exponential.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 111 or equivalent
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 113 - Discrete Structures

Sets, cardinality, number theory, combinatorics, probability. Proof techniques and problem solving. Additional topics may include graph theory, finite fields, and computer experimentation.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): Three years of high school mathematics
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 141 - Introduction to Probability and Statistics

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): Three years of high school mathematics
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 201 - Linear Algebra

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 112
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 202 - Vector Calculus

The derivative as a linear function, partial derivatives, optimization, multiple integrals, change of variables, Stokes's theorem.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 112 and MATH 201
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 241 - Data Science

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 141
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 243 - Statistical Learning

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 141 or experience with linear regressions and programming with instructor approval
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 311 - Complex Analysis

A study of complex valued functions: Cauchy's theorem and residue theorem, Laurent series, and analytic continuation.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 202
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 321 - Real Analysis

A careful study of continuity and convergence in metric spaces. Sequences and series of functions, uniform convergence, normed linear spaces.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 202
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 322 - Ordinary Differential Equations

An introduction to the theory of ordinary differential equations. Existence and uniqueness theorems, global behavior of solutions, qualitative theory, numerical methods.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 202
Instructional Method: Lecture-conference
Notes: Offered in alternate years.
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 332 - Abstract Algebra

An elementary treatment of the algebraic structure of groups, rings, fields, and/or algebras.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 201 and MATH 113
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 341 - Topics in Geometry

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 202
Instructional Method: Lecture-conference
Repeatable for Credit: May be taken up to 8 times for credit if different topics.
Notes: Offered in alternate years.
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 342 - Topology

An introduction to basic topology, followed by selected topics such as topological manifolds, embedding theorems, and the fundamental group and covering spaces.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 202 and MATH 332. MATH 332 may be taken concurrently
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 343 - Statistics Practicum

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 243, or MATH 241 with instructor approval
Instructional Method: Conference-laboratory
Repeatable for Credit: May be taken up to 2 times for credit.
Notes: Offered in alternate years.
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 346 - Bayesian Statistics

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 141 and MATH 243
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 361 - Number Theory

A study of integers, including topics such as divisibility, theory of prime numbers, congruences, and solutions of equations in the integers.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 201
Instructional Method: Lecture-conference
Notes: Recommended: concurrent enrollment in MATH 332. Offered in alternate years.
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 372 - Combinatorics

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 113 and MATH 201
Instructional Method: Lecture-conference
Notes: Offered in alternate years.
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 382 - Algorithms and Data Structures

See CSCI 382 for description.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): CSCI 121 or equivalent and MATH 112 and MATH 113
Instructional Method: Lecture-conference
Cross-listing(s): CSCI 382
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 386 - Private and Fair Data Analysis

See CSCI 386 for description.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): CSCI 121 or MATH 141; and one of CSCI 382/MATH 382CSCI 387/MATH 387, or MATH 391
Instructional Method: Lecture
Cross-listing(s): CSCI 386
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 387 - Computability and Complexity

See CSCI 387 for description.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): CSCI 121 or equivalent and MATH 112 and MATH 113
Instructional Method: Lecture-conference
Cross-listing(s): CSCI 387
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 388 - Cryptography

See CSCI 388 for description.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): CSCI 382/MATH 382CSCI 387/MATH 387, or MATH 332
Instructional Method: Lecture-conference
Cross-listing(s): CSCI 388
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 391 - Probability

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 113 and MATH 202
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 392 - Mathematical Statistics

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 141 and MATH 391
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 394 - Causal Inference

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.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 141 and MATH 391
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 411 - Topics in Advanced Analysis

Topics vary, and are selected by instructor.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 321
Instructional Method: Lecture-conference
Repeatable for Credit: May be taken up to 3 times for credit if different topics.
Notes: Not all topics offered every year. Review schedule of classes for availability.
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 412 - Topics in Algebra

Topics vary, and are selected by the instructor, for example, commutative algebra, Galois theory, algebraic geometry, and group representation theory.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 332
Instructional Method: Lecture-conference
Repeatable for Credit: May be taken up to 3 times for credit if different topics.
Notes: Not all topics offered every year. Review schedule of classes for availability.
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 441 - Topics in Computer Science Theory

See CSCI 441 for description.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 201, and CSCI 382/MATH 382, and CSCI 387/MATH 387
Instructional Method: Lecture-conference
Cross-listing(s): CSCI 441
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 442 - Algebraic Topology

An introduction to algebraic topology, concentrating on homology of topological spaces as a coarse, yet highly computable algebraic invariant. Topics include singular and simplicial homology, homological algebra, and cohomology.

Unit(s): 1
Group Distribution Requirement(s): Distribution Group III
Prerequisite(s): MATH 332 and MATH 342
Instructional Method: Lecture-conference
Group Distribution Learning Outcome(s):
• Use and evaluate quantitative data or modeling, or use logical/mathematical reasoning to evaluate, test or prove statements.
• Given a problem or question, formulate a hypothesis or conjecture, design an experiment, and collect data or use mathematical reasoning to test or validate it.

### MATH 470 - Thesis

Unit(s): 2
Instructional Method: Independent study