This course develops the quantitative skills which a liberal-arts educated student should acquire. It is intended to give the student an appreciation for the use of mathematics as a tool in business and science, as well as developing problem solving and critical thinking abilities. The course introduces the student to important topics of applied linear mathematics and probability. Topics include sets, counting, probability, the mathematics of finance, linear equations and applications, linear inequalities, an introduction to matrices and basic linear programming.
This course provides a review of elementary algebra for students who need further preparation for pre-calculus. Students enroll in this course on the basis of a placement examination. The course covers the basic operations of addition, subtraction, multiplication, and division involving algebraic expressions; factoring of polynomial expressions; exponents and radicals; solving linear equations, quadratic equations and systems of linear equations; and applications involving these concepts. This course does not satisfy the General Distribution Requirement in Mathematics and Science.
(Prerequisite: Placement or completion of MA 101 with a grade of C- or above)
This course provides an introduction to Calculus that focuses on functions and graphs. The properties of absolute value, polynomial, rational, exponential, logarithmic, and trigonometric functions will be studied, along with the techniques for solving equations and inequalities involving those functions.
(Prerequisite: Placement or completion of MA 197 with a grade of C- or above)
This is a Standard Calculus course using an intuitive approach to the fundamental concepts in the calculus of one variable: limiting behaviors, difference quotients and the derivative, definite integrals, antiderivative and indefinite integrals and the fundamental theorem of calculus.
(Prerequisite: Placement into MA 197 or completion of MA 100 or MA 101 with a grade of C- or above)
An introduction to descriptive statistics, elementary probability theory and inferential statistics. Included are: mean, median, mode and standard deviation; probability distributions, binomial probabilities and the normal distribution; problems of estimation; hypothesis testing, and an introduction to simple linear regression.
(Prerequisites: CS 110, MA 208 with a grade of C- or above)
A continuation of Statistics I. Topics include more advanced hypothesis testing, regression analysis, analysis of variance, non-parametric tests, time series analysis and decision- making techniques.
Statistics for Science and Engineeting
(Prerequisite: MA 198)
This course provides an introduction to descriptive statistics, elementary probability theory, and inferential statistics for students of Science and Engineering. Included are: mean, median, mode and standard deviation; random variables and their probability distributions; problems of estimation; hypothesis testing, and an introduction to simple linear regression.
(Prerequisite: MA 198 with a grade of C- or above)
This course builds on the fundamentals of the calculus of one variable, and includes infinite series, power series, differential equations of first and second order, numerical integration, and an analysis of improper integrals. It also covers the calculus of several variables: limits, partial derivatives, and multiple integrals.
(Prerequisite: MA 198)
This course introduces students to the techniques of linear algebra and to the concepts upon which the techniques are based. Topics include: vectors, matrix algebra, systems of linear equations, and related geometry in Euclidean spaces. Fundamentals of vector spaces, linear transformations, eigenvalues and associated eigenvectors.
(Prerequisites: MA 198, MA 208, MA 209; Recommended: MA 299)
This is a calculus-based introduction to mathematical statistics. While the material covered is similar to that which might be found in an undergraduate course of statistics, the technical level is much more advanced, the quantity of material much larger, and the pace of delivery correspondingly faster. The course covers basic probability, random variables (continuous and discrete), the central limit theorem and statistical inference, including parameter estimation and hypothesis testing. It also provides a basic introduction to stochastic processes.
Stochastic Calculus for Finance
(Pre-requisites: MA 208, MA 299)
This course provides an introduction to stochastic calculus and some of its applications to Finance. It is designed for students who want to develop knowledge and skills for the analysis of continuous-time stochastic models involving stochastic integrals and stochastic differential equations. Topics include: construction of Brownian motion; martingales in continuous time; the Itô integral and an introduction to Itô calculus. Applications to financial instruments are discussed throughout the course.
(Prerequisites: MA 299, MA 491 (Multivariable calculus and Matrix Algebra))
This course provides an introduction to ordinary differential equations. These equations contain a function of one independent variable and its derivatives. The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. Ordinary differential equations and applications, with integrated use of computing, student projects; first-order equations; higher order linear equations; systems of linear equations, Laplace transforms; introduction to nonlinear equations and systems, phase plane, stability.
(Prerequisite: MA 198 Calculus I. Recommended: MA 299 Calculus II)
This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, and the Riemann integral. In this course the concepts learnt in calculus classes will be looked at more deeply and in greater detail, especially those relating to the calculus of a single real variable. While in prior courses students had experience computing limits, derivatives, and integrals to solve specific problems, in this class the focus will be on what makes the computations work, as well as on the precise definitions of the notions used. The goal is to develop a deeper understanding of the various concepts defined, and to train the critical thinking and rigorous reasoning skills of the students.
A major component of this course will be exposing students to proofs, with the aim of having them learn how to read, write, and understand a proof.
Introduction to Logic
The course offers an introduction to the study of Logic. Logic is
relevant for many disciplines, most notably Mathematics, Computer
Science, and Philosophy. The course focuses on the syntax and semantics
of the logic of propositions in the formal setting of modern
mathematical logic. The formalization of language and of the notions of
truth and proof is treated in detail. Attention is devoted to the
historical development of Logic and to the formalization and analysis
of arguments drawn from such diverse fields such as philosophy,
mathematics, politics, etc.