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Courses

Mathematics professors are especially interested in helping students understand and appreciate the importance and usefulness of mathematics in the modern world. Assignments and projects emphasize the real-life applications of math in other fields of study. For example, the faculty recently developed a new two-semester scientific calculus course (MATH 231-232) that combines the core calculus concepts with other math topics important to the natural sciences. 

Math professors recognize that not all students will decide to study mathematics at the graduate level. In response, the department prepares students for a variety of career paths including education, industrial and governmental research and careers in actuarial science and economics. For students who do want to go on to graduate school, professors try to expose them to pure and applied mathematics in balanced doses so that they can make decisions about the kind of math they want to pursue in graduate school. Professors recognize that the best preparation students can have for graduate school is to participate in undergraduate research projects. Research leads to close student and faculty collaboration, which seniors cite in their annual exit interviews as the single greatest strength of the department. Faculty members are consistently willing and excited to work one-on-one with students as they wrestle with complex material.

Courses
Mathematics Courses
MATH 102 Problem Solving Using Finite Mathematics
Units: 1
Fulfills General Education Requirement (FSSR)
Description
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.

MATH 195 Special Topics
Units: .25-1
Description
Special topics satisfying neither major nor minor requirements.

MATH 209 Introduction to Statistical Modeling
Units: 1
Description
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.
Prerequisites
Pre-calculus.

MATH 211 Calculus I
Units: 1
Fulfills General Education Requirement (FSSR)
Description
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.
Prerequisites
High school precalculus.

MATH 212 Calculus II
Units: 1
Fulfills General Education Requirement (FSSR)
Description
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.

MATH 235 Multivariate Calculus
Units: 1
Fulfills General Education Requirement (FSSR)
Description
N-dimensional Euclidean space, functions of several variables, partial derivatives, multiple integrals, line and surface integrals, classical integral theorems, applications.
Prerequisites
MATH 212.

MATH 245 Linear Algebra
Units: 1
Description
Vector spaces, matrices, systems of linear equations, linear transformations, applications.
Prerequisites
MATH 212 or CMSC 222.

MATH 288 Mathematics Apprenticeship
Units: .25-.5
Description
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.

MATH 289 Introduction to Data Science
Units: 1
Description
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.
Prerequisites
Math 209 OR CMSC150 OR Bio 320 OR Econ 270.

MATH 300 Fundamentals of Abstract Mathematics
Units: 1
Description
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.
Prerequisites
MATH 212.

MATH 304 Mathematical Models in Biology and Medicine
Units: 1
Description
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.
Prerequisites
MATH 235, 245 or 300.

MATH 306 Abstract Algebra I
Units: 1
Description
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.
Prerequisites
MATH 245 and MATH 300.

MATH 307 Abstract Algebra II
Units: 1
Description
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.
Prerequisites
MATH 306.

MATH 309 Financial Mathematics: The Theory of Interest and Investment
Units: 1
Description
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.
Prerequisites
MATH 235 or 245 or 300.

MATH 310 Advanced Multivariable Calculus
Units: 1
Description
Differentiation of vector-valued functions, Jacobians, integration theorems in several variables. Fourier series, partial differential equations.
Prerequisites
MATH 235.

MATH 312 Differential Equations
Units: 1
Description
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.
Prerequisites
MATH 212 and MATH 245.

MATH 315 Modern Geometry
Units: 1
Description
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.
Prerequisites
MATH 235 or 245.

MATH 319 Game Theory
Units: 1
Description
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.
Prerequisites
MATH 245.

MATH 320 Real Analysis I
Units: 1
Description
Topological properties of the real line and Euclidean space. Convergence, continuity, differentiation, integration properties of real-valued functions of real variables.
Prerequisites
MATH 235 and 300.

MATH 328 Numerical Analysis
Units: 1
Description
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.)
Prerequisites
MATH 245 and CMSC 150.

MATH 329 Probability
Units: 1
Description
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.
Prerequisites
MATH 235 and MATH 245, which can be taken concurrently.

MATH 330 Mathematical Statistics
Units: 1
Description
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.
Prerequisites
MATH 329.

MATH 331 Complex Analysis
Units: 1
Description
Introduction to the calculus of functions of a single complex variable, including series, calculus of residues, and conformal mapping.
Prerequisites
MATH 235 OR PHYS 301.

MATH 336 Operations Research
Units: 1
Description
Linear and Integer Programming: algorithms, complexity, sensitivity, and duality. Applications such as assignments, networks, scheduling.
Prerequisites
MATH 245 and either MATH 300 or CMSC 222, which can be taken concurrently.

MATH 340 Directed Independent Study
Units: .25-1
Description
For well-qualified students who wish to work independently in areas not included in curriculum. Proposal must be approved by departmental committee.
Prerequisites
Permission of department chair and instructor.

MATH 350 Coding Theory and Cryptography: The Mathematics of Communication
Units: 1
Description
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.
Prerequisites
MATH 245 and either MATH 300 or CMSC 222 or permission of instructor.

MATH 388 Individual Internship
Units: .25-1
Description
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.
Prerequisites
Permission of department chair.

MATH 389 Statistical Learning
Units: 1
Description
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.
Prerequisites
CMSC 221 or MATH 245 or MATH 289.

MATH 395 Special Topics
Units: 1
Description
Selected topics in mathematics.
Prerequisites
Varies with topic.

MATH 396 Selected Topics in Mathematics
Units: 1
Description
Selected topics in mathematics for mathematical economics.

MATH 406 Summer Undergraduate Research
Units: 0
Description
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.
Prerequisites
Approval for summer Arts and Sciences fellowship by faculty mentor