Mathematics & Statistics

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  • CAS MA 293: Discrete Mathematics
    Propositional logic, set theory. Elementary probability theory. Number theory. Combinatorics with applications. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
    • Critical Thinking
  • CAS MA 294: Applied Abstract Algebra
    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. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
    • Critical Thinking
  • CAS MA 341: Introduction to Number Theory
    Study of integers and basic results of number theory. Topics include Linear Diophantine equations, prime numbers and factorization, congruences, and quadratic reciprocity. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
    • Critical Thinking
  • CAS MA 400: Tpcs:Math
  • CAS MA 411: Advanced Calculus
    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
    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 415: Data Science in R
    Introduction to R, the computer language written by and for statisticians. Emphasis on data exploration, statistical analysis, problem solving, reproducibility, and multimedia delivery. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
    • Critical Thinking
  • CAS MA 416: Analysis of Variance
    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. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
    • Critical Thinking
  • CAS MA 433: Graph Theory
  • CAS MA 442: Honors Level Linear Algebra
    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.) Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
    • Critical Thinking
  • CAS MA 505: History of Mathematics
    The development of mathematics from Antiquity through the 18th Century. Assuming background in modern mathematics, its roots are systematically pursued in terms of modern techniques, structures, and results. Providing the emergence of mathematical concepts and procedures, a coherent, unifying view of number, geometry, algebra, calculus, and mathematical analysis is presented. Effective Fall 2018, this course fulfills a single unit in the following BU Hub area: Historical Consciousness.
    • Historical Consciousness
  • CAS MA 511: Introduction to Analysis I
    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
    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
    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
    The investigation of logical reasoning with mathematical methods. The syntax and semantics of sentential logic and quantificational logic. The unifying Godel Completeness Theorem, and models of theories. A look at the Godel Incompleteness Theorem and its ramifications. Effective Fall 2018, this course fulfills a single unit in the following BU Hub area: Philosophical Inquiry and Life's Meanings.
    • Philosophical Inquiry and Life's Meanings
  • CAS MA 532: Foundations of Mathematics
    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 539: Methods of Scientific Computing
    (Meets with CAS CS 539.) An introduction to topics including computational linear algebra, solutions of linear equations, numerical integration and solution of differential equations, finite element methods, and methods of stochastic simulation (i.e., Monte Carlo methods).
  • 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 547: Topics in Number Theory
    An exploration of rational arithmetic and its generalizations. Foundations of arithmetic, Euclid's algorithm; the fundamental theorem of arithmetic; arithmetic modulom; continued fractions; Diophantine approximation; Pell's equation; sums of squares; the arithmetic of polynomials over a field; quadratic reciprocity; arithmetic in quadratic number field; lattice point-free regions; Minkowski's theorem on convex bodies. This course is offered only during Summer Term.

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