Please note: The course descriptions displayed here are current as of Wednesday, July 29, 2015, but the official Course Catalog should be used for all official planning.

MATH 107
Elementary Statistics

For students in all disciplines. Provides the background needed to evaluate statistical arguments found in newspapers, magazines, reports, and journals and the logic and techniques necessary to perform responsible elementary statistical analysis. Topics include basic data analysis, one-variable regression, experimental and sampling design, random variables, sampling distributions, and inference (confidence intervals and significance testing). This course may not be taken on a Satisfactory/Unsatisfactory basis. Units: 6. Prerequisite: Sophomore standing.

MATH 120
Applied Calculus I

A course in the applications of mathematics to a wide variety of areas, stressing economics and the biological sciences. Topics may include recursive sequences and their equilibria, the derivative of a function, optimization, fitting abstract models to observed data. Emphasis placed on algebraic and numerical techniques and on understanding the role of mathematical thinking. Mathematics 120 and 130 do not prepare students for more advanced courses in mathematics. Units: 6. Prerequisite: Three years of high school mathematics;

MATH 130
Applied Calculus II

A continuation of math 120. Topics may include the indefinite and definite integral, elementary linear algebra including matrix arithmetic and solving linear equations, vectors, partial derivatives, Lagrange multipliers. Both algebraic and numerical computations. Units: 6. Prerequisite: MATH 120 or the equivalent

MATH 140
Calculus I

Functions, limits, derivatives, the Mean Value Theorem, definition and properties of integrals, the Fundamental Theorem of Calculus, and applications to related rates, curve sketching, and optimization problems. Placement exam not required. Units: 6. Prerequisite: Four years of high school mathematics

MATH 150
Calculus II

Applications of integration, exponential and logarithmic functions, techniques of integration, infinite sequences and series, and Taylor series. Units: 6. Prerequisite: Advanced placement, MATH 140, or MATH 120 and consent of instructor

MATH 160
Calculus III

Functions of two or more variables, partial derivatives, chain rules, optimization, vectors, derivatives of vector-valued functions, Lagrange multipliers, multiple integrals, line integrals, and Green’s Theorem. Units: 6. Prerequisite: MATH 150 or advanced placement

MATH 191
Directed Study in Mathematics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 210
Differential Equations with Linear Algebra

A study of differential equations and related techniques in linear algebra. Topics include first-order equations and their applications, existence and uniqueness of solutions, second-order linear equations and their applications, series solutions, systems of first-order equations, vector spaces and dimension, linear transformations, and eigenvalues. Units: 6. Prerequisite: MATH 160, or MATH 150 and consent of instructor

MATH 217
Applied Statistical Methods

A second course in statistics that covers analyses needed to solve more complicated data-driven problems. Time permitting, topics include multiple regression, analysis of variance, categorical data analysis, nonparametric tests, bootstrap methods, and permutation tests. Class meetings are a mixture of lecture, discussion, and use of statistical software to investigate real data. Units: 6. Prerequisite: AP examination credit in statistics or MATH 107

MATH 220
Applied Combinatorics

An introduction to logic, proofs by mathematical induction, and elementary combinatorics. Additional topics include recurrence relations, generating functions, and the principle of inclusion-exclusion. Units: 6. Prerequisite: MATH 150

MATH 223
Quantitative Decision-Making

The students will learn how to develop formal, quantitative approaches to structuring difficult problems, particularly those problems involving probabilistic factors. We will develop and practice the steps of defining a problem, gathering data, formulating a model, performing numerical calculations, evaluating numerical information, refining the model, analyzing the model's alternatives, and communicating the results. Units: 6. Prerequisite: Sophomore standing
Also listed as Economics 223

MATH 240
Probability

An introduction to probability and its applications. Topics will include combinatorial and axiomatic probability, conditional probability and Bayes' Theorem, random variables, expectation and variance, discrete and continuous probability distributions, joint and conditional distributions, and limit laws. Units: 6. Prerequisite: MATH 160, or MATH 150 and consent of instructor

MATH 300
Foundations of Algebra

An introduction to the rigorous study of mathematics. Topics include elementary theory of sets and mappings, number theory, equivalence relations, finite groups, homomorphisms, quotient groups, and rings. Units: 6. Prerequisite: MATH 210, 220, or 240

MATH 310
Foundations of Analysis

A study of the concepts that underlie mathematical analysis: the completeness of the real numbers, convergence, continuity, derivatives, integrals, infinite series, and, if time permits, an introduction to metric spaces or Fourier series. Units: 6. Prerequisite: MATH 300

MATH 390
Tutorial Studies in Mathematics

Advanced work in mathematics on topics not covered in regular offerings. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 391
Directed Study in Mathematics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 399
Independent Study in Mathematics

Guided independent study of an advanced topic in undergraduate mathematics or supervised work on an undergraduate research project, generally culminating in a final presentation and/or paper. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 400
Partial Differential Equations

A survey of techniques used in modeling physical systems, with particular emphasis on partial differential equations and methods used to attack problems that do not have clean or simple solutions. Topics include techniques for solving partial differential equations exactly, the Fourier transform, perturbation theory, variational methods, Monte Carlo techniques, and finite difference schemes. Units: 6. Prerequisite: MATH 300 or consent of instructor

MATH 410
Linear Algebra

A study of vector spaces, linear transformations, and their representations. The focus will be on algebraic and coordinate-free methods, and topics will include dimension, dual spaces, determinants, canonical forms, inner product spaces, and the spectral theorem. Units: 6. Prerequisite: MATH 300

MATH 420
Numerical Analysis

Computer approximated (numerical) solutions to a variety of problems with an emphasis on error analysis. Interpolation, evaluation of polynomials and series, solution of linear and non-linear equations, eigenvectors, quadrature (integration), and differential equations. Units: 6. Prerequisite: MATH 300 and CMSC 110 or CMSC 150

MATH 435
Optimization

The study of local and global maximums and minimums of function, given various sorts of constraints. Linear problems and the simplex algorithm, general non-linear problems and the Kuhn-Tucker conditions, convex problems. Perturbation of problem parameters and duality. Applications to a wide variety of fields, including economics, game theory, and operations research. Units: 6. Prerequisite: MATH 310

MATH 440
Probability Theory

The mathematics of chance: probability, discrete and continuous random variables and their distributions, moments, jointly distributed random variables, conditional distributions, the Central Limit Theorem, and weak and strong convergence. Units: 6. Prerequisite: MATH 310

MATH 445
Mathematical Statistics

Development of the mathematical theory of statistics and its application to the real world. The course will focus on the principles of estimation and testing from both the frequentist and Bayesian perspectives. Resampling methods (permutation tests and bootstrap intervals) will also be explored. Units: 6. Prerequisite: MATH 310 and MATH 440

MATH 525
Graph Theory

A survey of graph theory that balances the abstract theory of graphs with a wide variety of algorithms and applications to “real world” problems. Topics include trees, Euler tours and Hamilton cycles, matchings, colorings, directed graphs, and networks. Units: 6. Prerequisite: MATH 300

MATH 530
Topics in Geometry

The axiomatic development of euclidean and non-euclidean geometry, including the historical and philosophical issues raised by the “non-euclidean revolution.” Additional topics, such as projective or differential geometry and convexity, may be included. Units: 6. Prerequisite: MATH 300

MATH 535
Complex Analysis

An introduction to functions of a complex variable, the Cauchy-Riemann equations, conformal mappings, Cauchy’s theorem, Cauchy’s integral formula, Taylor and Laurent series, and a sampling, as time and interest permit, of the corollaries to Cauchy’s theorem. Units: 6. Prerequisite: MATH 310

MATH 545
Rings and Fields

Modern algebra with topics selected from group theory, ring theory, field theory, classical geometric construction problems, and Galois theory. Emphasis on the use of mathematical abstraction to illuminate underlying relationships and structure. Units: 6. Prerequisite: MATH 300

MATH 550
Topics in Analysis

Selected topics in analysis covering a wide variety of spaces and leading to applications of classical importance. In recent years, topics have included fixed point theory, inverse and implicit function theorems, abstract theory of differential equations, Lebesgue measure and integration, Fourier series and transforms. Units: 6. Prerequisite: MATH 310

MATH 555
Topics Algebra & Combinatorics

A study of interconnections between abstract algebra (especially finite group theory) and combinatorics (especially graph theory). Topics will include classical results (such as the matrix-tree theorem), as well as recent subjects and advances (such as the abelian sandpile model and the Riemann-Roch theorem for graphs). Units: 6. Prerequisite: MATH 300

MATH 560
Topology

A study of metric and topological spaces, including continuity, compactness, connectedness, product and quotient spaces. Additional topics may include Zorn’s Lemma, separation properties, surfaces, the fundamental group, and fixed point theorems. Units: 6. Prerequisite: MATH 310

MATH 565
Number Theory

A study of the integers, including unique factorization, congruences, and quadratic reciprocity. Other topics may include finite fields, higher reciprocity laws, and algebraic number theory. Units: 6. Prerequisite: MATH 300

MATH 590
Tutorial Studies in Mathematics

Advanced work in mathematics on topics not covered in regular offerings. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 591
Directed Study in Mathematics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 599
Independent Study in Mathematics

Guided independent study of an advanced topic in undergraduate mathematics or supervised work on an undergraduate research project, generally culminating in a final presentation and/or paper. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 600
History of Mathematics

A study of the history of mathematics from the ancient Greeks through the present, emphasizing the role of mathematics in scientific advances, the work of great mathematicians, and the modern branching of the subject into a multitude of specialties. Units: 6. Prerequisite: MATH 310

MATH 690
Tutorial Studies in Mathematics

Advanced work in mathematics on topics not covered in regular offerings. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 691
Directed Study in Mathematics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work. Units: 1 TO 98. Prerequisite: Counter Registration Required.

MATH 699
Independent Study in Mathematics

Guided independent study of an advanced topic in undergraduate mathematics or supervised work on an undergraduate research project, generally culminating in a final presentation and/or paper. Units: 1 TO 98. Prerequisite: Counter Registration Required.

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