Mathematics & Statistics

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  • CAS MA 230: Honors-Level Vector Calculus
    Undergraduate Prerequisites: CAS MA 124 or CAS MA 127 or CAS MA 129.
    Linear algebra: linear transformations and matrices, inner products, cross products. Differentiation: tangent spaces, directional derivatives, gradients, vector fields and flow, divergence, curl. Integration: multiple integrals, line integrals, Green's theorem, surface integrals, Stokes's theorem, the divergence theorem. (Cannot be taken for credit in addition to CAS MA 225.)
  • CAS MA 231: Honors-Level Differential Equations
    Undergraduate Prerequisites: CAS MA 225 or CAS MA 230.
    Ordinary differential equations with applications to mechanics, biology, and physics. First- and second-order equations, linear and nonlinear systems, Sturm-Louisville problems, vibrating strings, special functions, power series solutions, regular singular points, Laplace transforms, calculus of variations, isoperimetric problems, and Hamilton's principle. (Cannot be taken for credit in addition to CAS MA 226.)
  • CAS MA 242: Linear Algebra
    Matrix algebra, solution of linear systems, determinants, Gaussian elimination, fundamental theory, row-echelon form. Vector spaces, bases, norms. Computer methods. Eigenvalues and eigenvectors, canonical decomposition. Applications. (Cannot be taken for credit in addition to CAS MA 142, MA 442, or ENG EK 102.)
  • CAS MA 293: Discrete Mathematics
    Undergraduate Prerequisites: CAS MA 123.
    Propositional logic, set theory. Elementary probability theory. Number theory. Combinatorics with applications.
  • CAS MA 294: Applied Abstract Algebra
    Undergraduate Prerequisites: CAS MA 293; or consent of instructor.
    Abstract algebra and its applications to combinatorics. A first exposure to groups, rings, and fields via significant combinatorial applications. Students who have already received credit for MA 541 or MA 542 may not subsequently receive credit for MA 294.
  • CAS MA 341: Introduction to Number Theory
    Undergraduate Prerequisites: CAS MA 242; or consent of instructor.
    Study of integers and basic results of number theory. Topics include Linear Diophantine equations, prime numbers and factorization, congruences, and quadratic reciprocity.
  • CAS MA 411: Advanced Calculus
    Undergraduate Prerequisites: CAS MA 225 or CAS MA 230 and CAS MA 242 or CAS MA 442.
    Extends concepts and techniques of calculus and develops further applications. Topics include higher dimensional calculus, applications of vector analysis, uniform convergence of series, complex series, improper integrals, gamma and beta functions, Stirling's formula, Fourier series and transform.
  • CAS MA 412: Complex Variables
    Undergraduate Prerequisites: CAS MA 225 or CAS MA 230.
    Basic concepts, results, and applications of complex analysis. Emphasis on computation and applications. Complex plane and functions, differentiability, Cauchy-Riemann conditions, contour integrals, Cauchy formulas, complex series, residue calculus, applications. Extends the concepts of the calculus to the complex setting.
  • CAS MA 416: Analysis of Variance
    Undergraduate Prerequisites: CAS MA 116 or CAS MA 214; or equivalent.
    Fundamental concepts and analytical skills in analysis of variance, including crossed and nested designs, as well as fixed- and random- effect models. Trend analysis for repeated measures, expected mean squares, and non-parametric techniques. SAS is used throughout the course.
  • CAS MA 442: Honors Level Linear Algebra
    Undergraduate Prerequisites: CAS MA 225 or CAS MA 230.
    A thorough development of the fundamentals of linear algebra. Systems of linear equations; matrices, linear transformations, duality; determinants, characteristic and minimal polynomials; diagonalization and normal forms of linear transformations; inner products, unitary and self-adjoint operators, and spectral theory. Applications to physics, probability, and statistics. (Cannot be taken for credit in addition to CAS MA 242.)
  • CAS MA 471: Chaotic Dynamical Systems
    Undergraduate Prerequisites: CAS MA 124.
    Iteration of functions in one and higher dimensions. Periodic points; hyperbolicity; recurrence; topological conjugacy and structural stability; chaotic dynamics. Some numerical experimentation involving personal computers.
  • CAS MA 505: History of Mathematics
    Undergraduate Prerequisites: CAS MA 242 and CAS MA 293; or consent of instructor.
    Patterns of mathematical thought from antiquity to the seventeenth century. Emphasis throughout on the background and origins of the mathematical revolution of the seventeenth century in which Descartes, Newton, and Leibniz played key roles.
  • CAS MA 511: Introduction to Analysis I
    Undergraduate Prerequisites: CAS MA 225 or CAS MA 230.
    Graduate Prerequisites: CAS MA 225 or CAS MA 230.
    Fundamental concepts of mathematical reasoning. Properties of the real-number system, elementary point-set theory, metric spaces. Limits, sequences, series, convergence, uniform convergence, continuity. Differentiability for functions of a single variable, Riemann-Stieltjes integration.
  • CAS MA 512: Introduction to Analysis II
    Undergraduate Prerequisites: CAS MA 511.
    Graduate Prerequisites: CAS MA 511.
    Background of CAS MA 511 used to develop further topics of calculus. Exponential and logarithmic functions, Taylor series, power series, real analytic functions. Differential and integral calculus for functions of several variables. Line and surface integrals, divergence theorem, Stokes's theorem, inverse and implicit function theorems, change of variables. Fourier analysis.
  • CAS MA 528: Introduction to Modern Geometry
    Undergraduate Prerequisites: CAS MA 225 or CAS MA 230; or consent of instructor.
    Graduate Prerequisites: CAS MA 225 or CAS MA 230; or consent of instructor.
    The foundations of Euclidean geometry. Transformation and symmetries in the plane, inversive and projective planes, coordinates, conics and quadrics, the Golden Section, intermediary and Dedekind's axiom, models for non-Euclidean geometries.
  • CAS MA 531: Mathematical Logic
    Undergraduate Prerequisites: CAS MA 293; or consent of instructor.
    Graduate Prerequisites: CAS MA 293; or consent of instructor.
    The syntax and semantics of sentential and quantificational logic, culminating in the Gödel Completeness Theorem. The Gödel Incompleteness Theorem and its ramifications for computability and philosophy. Also offered as CAS PH 461.
  • CAS MA 532: Foundations of Mathematics
    Undergraduate Prerequisites: CAS MA 531.
    Axiomatic set theory as a foundation for mathematics and as a field of mathematics: Axiom of Choice, the Continuum Hypothesis, and consistency results. Also offered as CAS PH 461.
  • CAS MA 541: Modern Algebra I
    Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings.
  • CAS MA 542: Modern Algebra II
    Vector spaces and modules, Galois theory, linear transformations and matrices, canonical forms, bilinear and quadratic forms.
  • CAS MA 555: Numerical Analysis I
    Undergraduate Prerequisites: CAS MA 225 or CAS MA 230.
    Graduate Prerequisites: CAS MA 225 or CAS MA 230.
    Numerical solutions of equations, iterative methods, analysis of sequences. Theory of interpolation and functional approximation, divided differences. Numerical differentiation and integration. Polynomial theory. Ordinary differential equations.