Mathematics

Units: 1

Fulfills General Education Requirement (FSSR)

Topics to demonstrate power of mathematical reasoning. Course has two components: (1) introduction to the fundamentals of mathematical proof, and (2) the application of these fundamentals to at least one particular area of mathematics. The area is dependent on the instructor. MATH 102 is not open to MATH, CMSC, MTEC, BUAD, or ACCT majors.

Units: .25-1

Special topics satisfying neither major nor minor requirements.

Units: 1

Topics will include exploratory data analysis, correlation, linear and multiple regression, design of experiments, basic probability, the normal distribution, sampling distributions, estimation, hypothesis testing and randomization approach to inference. Exploratory graphical statistics, model building and model checking techniques will be emphasized with extensive use of statistical software for data analysis.

Pre-calculus.

Units: 1

Fulfills General Education Requirement (FSSR)

Limits, continuity, derivatives, and integrals. Derivatives of trigonometric, exponential, logarithmic, and inverse trigonometric functions; the derivative as a rate-of-change; linear approximations; Fundamental Theorem of Calculus; applications to the sciences, social sciences, and economics.

High school precalculus.

Units: 1

Fulfills General Education Requirement (FSSR)

Techniques of integration; applications of integration; improper integrals; Taylor's Theorem and applications; infinite series; differential equations; applications to the sciences, social sciences, and economics.

Units: 1

Fulfills General Education Requirement (FSSR)

N-dimensional Euclidean space, functions of several variables, partial derivatives, multiple integrals, line and surface integrals, classical integral theorems, applications.

MATH 212.

Units: 1

Vector spaces, matrices, systems of linear equations, linear transformations, applications.

MATH 212 or CMSC 222.

Units: .25-.5

Participation in practical application of mathematics skills, such as statistics, data science, or mathematical modeling, with supervision of mathematics or statistics faculty. Does not count for mathematics major or minor or for mathematical economics major. No more than a total of 1.5 units of MATH 288 may count toward the total number of units required for a degree.

Units: 1

Multiple linear regression, logistic regression, ANOVA and other modeling based topics. Exploratory graphical methods, model selection and model checking techniques will be emphasized with extensive use a statistical programming language (R) for data analysis.

Math 209 OR CMSC150 OR Bio 320 OR Econ 270.

Units: 1

Logic, quantifiers, negations of statements with quantifiers, set theory, induction, counting principles, relations and functions, cardinality. Includes introductory topics from real analysis and abstract algebra. Emphasis on methods of proof and proper mathematical expression.

MATH 212.

Units: 1

Mathematical models in modern biological and medical applications. Primary focus on practical understanding of the modeling process, and development of requisite modeling skills. Topics include discrete and continuous dynamical systems, including parameter estimation.

MATH 235, 245 or 300.

Units: 1

An introduction to the theory of groups. Topics include subgroups, cyclic groups, permutation groups, homomorphisms, isomorphisms, cosets, Lagrange's Theorem, normal subgroups, and the Fundamental Theorem of Finite Abelian Groups.

MATH 245 and MATH 300.

Units: 1

An introduction to the theory of rings and fields. Topics include rings, integral domains, ideals, factor rings, polynomial rings, ring homomorphisms, fields, and extension fields.

MATH 306.

Units: 1

Develops a practical understanding of financial mathematics and interest theory in both discrete and continuous time. This theory includes the fundamentals of how annuity functions are applied to the concepts of present and accumulated value for various cash flow streams and how this is used for future planning in valuation, pricing, duration, immunization, and investment. Topics include: rates of interest and discount, the force of interest, level and varying annuities, evaluation of financial instruments (e.g. bonds, stocks, leveraged strategies), measures of interest rate sensitivity, and the term structure of interest rates.

MATH 235 or 245 or 300.

Units: 1

Differentiation of vector-valued functions, Jacobians, integration theorems in several variables. Fourier series, partial differential equations.

MATH 235.

Units: 1

Introduction to ordinary differential equations and their use as models of physical systems. Linear and nonlinear equations and systems of equations, including existence and uniqueness theorems, analytical solution techniques, numerical methods, and qualitative analysis. Includes studies of global behavior and local stability analysis of solutions of nonlinear autonomous systems; bifurcation analysis. Application and modeling of real phenomena included throughout.

MATH 212 and MATH 245.

Units: 1

Geometry of surfaces in 3-dimensional space. Arc length, Frenet frame, parallel translation and geodesics. Gaussian curvature, constant curvature surfaces, Gauss-Bonnet theorem. Topological classification of compact surfaces.

MATH 235 or 245.

Units: 1

Mathematical introduction to game theory. Foundational material on rationality and the expected utility theorem; problems for single decision-makers who maximize utility in uncertain circumstances; classical two-person matrix games and Nash equilibria; dynamic games, behavioral strategies, and repeated games; population games and evolutionarily stable strategies in biology; evolutionary dynamics.

MATH 245.

Units: 1

Topological properties of the real line and Euclidean space. Convergence, continuity, differentiation, integration properties of real-valued functions of real variables.

MATH 235 and 300.

Units: 1

Analysis and implementation of algorithms used in applied mathematics, including root finding, interpolation, approximation of functions, integration, solutions to systems of linear equations. Computer error. (Same as Computer Science 328.)

MATH 245 and CMSC 150.

Units: 1

Introduction to the theory, methods, and applications of randomness and random processes. Probability concepts, independence, random variables, expectation, discrete and continuous probability distributions, moment-generating functions, simulation, joint and conditional probability distributions, sampling theory, laws of large numbers, limit theorems.

MATH 235 and MATH 245. MATH 245 can be taken concurrently.

Units: 1

Introduction to basic principles and procedures for statistical estimation and model fitting. Parameter estimation, likelihood methods, unbiasedness, sufficiency, confidence regions, Bayesian inference, significance testing, likelihood ratio tests, linear models, methods for categorical data, resampling methods.

MATH 329.

Units: 1

Introduction to the calculus of functions of a single complex variable, including series, calculus of residues, and conformal mapping.

MATH 235 OR PHYS 301.

Units: 1

Linear and Integer Programming: algorithms, complexity, sensitivity, and duality. Applications such as assignments, networks, scheduling.

MATH 245 and either MATH 300 or CMSC 222, which can be taken concurrently.

Units: .25-1

For well-qualified students who wish to work independently in areas not included in curriculum. Proposal must be approved by departmental committee.

Permission of department chair and instructor.

Units: 1

Error-correcting codes are used to ensure reliable electronic communication in everything from Blue Ray players to deep-space transmission. Cryptographic systems are developed to keep communication secret in everything from e-commerce to military communication. This course develops the mathematics underlying the transmission of messages. In coding theory, we will develop theoretical constraints on codes, construction methods for good codes, and algorithms for encoding and decoding efficiently. In cryptography, we will explore historically important systems as well as modern public-key cryptosystems.

MATH 245 and either MATH 300 or CMSC 222 or permission of instructor.

Units: .25-1

No more than 1.5 units of internship in any one department and 3.5 units of internship overall may be counted toward required degree units.

Permission of department chair.

Units: 1

Computational statistics and statistical algorithms for building predictive models from large data sets. Topics include model complexity, hyper-parameter tuning, over- and under-fitting, and the evaluation of predictive performance. Models covered include linear regression, penalized regression, additive models, gradient-boosted trees, and neural networks. Applications are drawn from many areas, with a particular focus on processing unstructured text and image corpora.

Math 289 or Math 329.

Units: 1

Selected topics in mathematics.

Varies with topic.

Units: 1

Selected topics in mathematics for mathematical economics.

Units: 0

Documentation of the work of students who receive summer fellowships to conduct research [or produce a creative arts project] in the summer. The work must take place over a minimum of 8 weeks, the student must engage in the project full-time (at least 40 hours per week) during this period, and the student must be the recipient of a fellowship through the university. Graded S/U.

Approval for summer Arts and Sciences fellowship by faculty mentor