An introductory course for students who wish to develop quantitative skills. Topics covered include: mathematical problem solving, logic, counting and cardinality, number systems, relations and functions, ratios and proportional relationships, probability, statistics, and geometry.
A study of the nature and development of some of the most important mathematical ideas. Topics may include, but are not limited to: infinity, variation, symmetry, numbers and notation, topology, mathematics and calculating machines, dimension, coordinate systems, dynamical systems, randomness, and probability.
A study of the differentiation of algebraic and trigonometric functions with applications. Topics covered include limits, continuity, differentiation formulas, the Mean Value Theorem, curve sketching, optimization, and related rates.
A study of the integration of algebraic, trigonometric and transcendental functions with applications. Topics covered include the Fundamental Theorem of Calculus, calculating areas and volumes, the average value of a function, inverse functions, and integration techniques.
A study of vector analysis and ordinary differential equations and their applications. Topics include vector fields, line and surface integrals, first order differential equations, linear differential equations, and systems of differential equations.
Via the solution of interesting problems, this course isolates and draws attention to the most important problem-solving techniques encountered in undergraduate mathematics. The aim is to show how a basic set of simple techniques can be applied in diverse ways to solve a variety of problems.
An introduction to linear algebra and its applications. Topics covered include systems of linear equations, matrix algebra, vector spaces, determinants, eigenvalues and eigenvectors, and diagonalization of matrices.
A study of probability distributions and their application to statistical inference. Topics include conditional probability and independence, Bayes' Rule, discrete and continuous probability distributions, Tchebysheff's Theorem, and the Central Limit Theorem.
Topics for discussion include complex numbers and their properties, analytic functions, integration in the complex plane, Cauchy's integral formula, Taylor and Laurent series, and methods of contour integration.
Designed to bridge the gap between manipulative elementary calculus and theoretical real analysis. The fundamentals of elementary calculus are treated in a more rigorous manner. Topics covered include mathematical induction, sequences, series, and continuity.
Designed to bridge the gap between manipulative elementary calculus and theoretical real analysis. The fundamentals of elementary calculus are treated in a more rigorous manner. Topics covered include sequences and series of functions, differentiation, and the Riemann integral.
This course will consist of a detailed investigation of a topic important to contemporary mathematics. The topic will be chosen by the department for its relevance to current mathematical thought and its accessibility to students.
Prerequisite(s):MA 180 or permission of the instructor.