MATH 105
The Mathematical Experience
An introduction to the scope, power, and spirit of mathematics. Topics, chosen to convey the character of mathematical inquiry, may vary; they include euclidean and non-euclidean geometry, number theory, topology, graph theory, infinity, paradoxes, set theory, and logic. Intended for students with limited preparation in mathematics.
Units: 6.
Prerequisite: Sophomore standing
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). Students who have completed a calculus course should elect Mathematics 207 rather than Mathematics 107. This course may not be taken on a Satisfactory/Unsatisfactory basis.
Units: 6.
Prerequisite: Sophomore standing. Only one of MATH 107, 117, or 207 may be taken for credit
MATH 117
Elementary Statistics
For students in all disciplines. Provides background needed to evaluate statistical arguments found in newspapers, 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). Computer lab component is used to investigate real data using statistical software. Students who have completed a calculus course should elect Mathematics 207 rather than Mathematics 107 or 117. This course may not be taken on a Satisfactory/Unsatisfactory basis.
Units: 6.
Prerequisite: Sophomore standing. Only one of MATH 107, 117, or 207 may be taken for credit.
MATH 120
Applied Calculus I
An introduction to calculus that stresses applications to the life and social sciences. Topics include derivatives, integrals, optimization, and exponential and logarithmic functions. Mathematics 120 and 130 do not prepare students for more advanced courses.
Units: 6.
Prerequisite: Three years of high school mathematics;
MATH 130
Applied Calculus II
Differential and integral calculus in several variables, including optimization, partial derivatives, and multiple integrals. Also applications of integration and an introduction to differential equations. Stresses applications to the life and social sciences.
Units: 6.
Prerequisite: MATH 120
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 207
Introduction to Probability and Statistics
A survey of statistical methods including their mathematical foundation and their implementations on a computer. Topics include descriptive statistics and graphs, simple linear regression, random variables and their distributions, conditional probability, independence, sampling distributions, the Central Limit Theorem, and parametric and nonparametric tests of hypotheses. Computer lab component is used to investigate real data using statistical software.
Units: 6.
Prerequisite: MATH 120 or 140. Only one of MATH 207, 107, or 117 may be taken for credit
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, MATH 107, MATH 117, or MATH 207
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 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 207, 210, or 220
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
The development and study of statistical theory. Topics include sampling distributions, point and interval estimation, significance tests, categorical data analysis, bootstrap methods and permutation tests, and, time permitting, regression analysis and analysis of variance. Class meetings are a mixture of lecture, discussion, and use of statistical software to analyze real-world case studies and to investigate computer-intensive statistical methods.
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 540
Mathematical Logic and Set Theory
Establishes the basic syntactical tools needed to develop the semantics of first-order logic with equality, including the completeness and compactness theorems. Axiomatic set theory is developed culminating with the Axiom of Choice, some equivalents, and the Continuum Hypothesis.
Units: 6.
Prerequisite: MATH 300
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 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.
