Mathematics & Statistics

• CAS MA 294: Applied Abstract Algebra
  Undergraduate Prerequisites: (CASMA293) 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. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
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• CAS MA 301: Writing in Mathematics
  Undergraduate Prerequisites: First Year Writing Seminar (WR120). - Prerequisite for this course: First Year Writing Seminar (WR120). Writing in mathematics is distinctive for at least two reasons: i) in addition to written language, mathematical writing involves numbers, symbols, and images; and ii) mathematicians write not only to communicate their work, but more perhaps importantly to clarify and refine their own thinking. In this class, we explore how writing is used to both communicate and facilitate mathematics by participating in the process of writing across a range of discipline-specific genres, including proof writing and expository writing, for pure or applied math majors who have not yet taken a course involving proof writing, but who intend to do so in the future. Students who do not meet these criteria may only take the course with instructor permission. Effective Spring 2023, this course fulfills a single unit in each of the following BU Hub areas: Writing-Intensive Course.
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  • Writing-Intensive Course
• CAS MA 341: Introduction to Number Theory
  Undergraduate Prerequisites: (CASMA242) 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. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
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• CAS MA 401: Senior Independent Work
  Undergraduate Prerequisites: approval by the Director of Undergraduate Studies. - This course is the first in a two-semester sequence during which the student conducts a substantial research project under the supervision of a faculty advisor. Effective Fall 2023, this course fulfills a single unit in the following BU HUB areas: Research and Information Literacy.
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  • Research and Information Literacy
• CAS MA 402: Senior Independent Work
  Undergraduate Prerequisites: approval by the Director of Undergraduate Studies. - This course is the second in a two-semester sequence during which the student conducts a substantial research project under the supervision of a faculty advisor. Effective Spring 2024, this course fulfills a single unit in the following BU HUB area: Oral and/or Signed Communication.
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  • Oral and/or Signed Communication
• CAS MA 411: Advanced Calculus
  Undergraduate Prerequisites: ( (CASMA225 OR CASMA230) & (CASMA242 OR CASMA442)) - 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: (CASMA225 OR CASMA230) - 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
  Undergraduate Prerequisites: (CASCS 111 or CDSDS 110 or ENGEK 125) AND (CASMA 113 or CASMA 115 or CASMA 116 or CASMA 213 or CASMA 214 or CASMA 582) or consent of instructor. - 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.
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  • Critical Thinking
• CAS MA 416: Analysis of Variance
  Undergraduate Prerequisites: CASMA 116 or CASMA 214 or consent of instructor. - 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.
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• CAS MA 433: Graph Theory
  Undergraduate Prerequisites: (CASMA242 & CASMA293) or consent of instructor. - Graph Theory can be used to generalize the concept of what it means for geometric objects to be connected and describe complex systems. Using vertices to represent objects and edges to represent which objects are adjacent to each other, students will be able to analyze the system as a whole. Students can study which geometrical objects can be placed on a plane, sphere, torus, etc. as well as generalize the concept of connected to more abstract settings. Students will explore these geometric aspects as well as analyze various algorithms and open problems in Graph Theory.
• CAS MA 442: Honors Level Linear Algebra
  Undergraduate Prerequisites: CASMA 121 or CASMA 123 or CASMA 129 or consent of instructor - 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 CASMA 242.) Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking.
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• CAS MA 491: Directed Study
  Undergraduate Prerequisites: consent of instructor and application made through the Mathematics Dep artment. - DIRECTED STUDY
• CAS MA 492: Directed Study
  Undergraduate Prerequisites: consent of instructor and application made through the Mathematics Dep artment. - DIRECTED STUDY
• CAS MA 505: History of Mathematics
  Undergraduate Prerequisites: (CASMA225 OR CASMA230) and (CASMA242 or CASMA442); or consent of instructor. - 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.
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  • Historical Consciousness
• CAS MA 511: Introduction to Analysis I
  Undergraduate Prerequisites: (CASMA225 OR CASMA230) - Graduate Prerequisites: (CASMA225 OR CASMA230) - 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: (CASMA511) - Graduate Prerequisites: (CASMA511) - 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 531: Mathematical Logic
  Undergraduate Prerequisites: (CASMA293) or consent of instructor. - Graduate Prerequisites: (CASMA293) or consent of instructor. - 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.
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  • Philosophical Inquiry and Life's Meanings
• CAS MA 532: Foundations of Mathematics
  Undergraduate Prerequisites: (CASMA531) - 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
  Undergraduate Prerequisites: (CASMA 225 or CASMA 230) & (CASMA 242 or CASMA 442) and programming experience or consent of instructor. - 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 1
  Undergraduate Prerequisites: (CASMA242 OR CASMA442) - Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings.