EC/MA 490
Advanced Financial Economics
(Prerequisites: EC 301, FIN 301, MA 299; Recommended: MA 491)
This is an advanced course that makes substantial use of mathematical methods. In general, the topics covered can be viewed as that subset of general equilibrium theory which focuses on complete and incomplete financial markets and their impact on the allocation of consumption goods and efficiency. The course focuses on the operation of financial markets and pricing of financial assets. In the first part of the course, basic techniques and principles of decision making under uncertainty will be developed. These principles will then be applied to portfolio selection problems in financial asset markets. Microeconomic models of financial asset markets and their implications for valuation of stocks, bonds and derivative assets will be examined. The analysis will explore the impact of risk and ambiguity on asset prices and allocations in asset markets. For the most part, it will be assumed that there are two dates and a single consumption good. This basic setting is suitable for the study of the relation between risk and return on securities, and the role played by securities in allocation of risk.
EC/MA 491
Mathematical Economics
(Prerequisites: EC 301, EC 302; Recommended: MA 299)
The purpose of this course is to introduce students to basic but rigorous mathematical methods and models widely applied in modern economic theory, and relative economic applications (e.g., convex analysis, unconstrained and constrained optimization, basic topology and metric spaces, introductory Game Theory). The material is fairly basic, yet emphasis is placed on rigor and mathematical proofs. The course will be at the level of the material covered in such texts in the field as Wade Hands’ Introductory Mathematical Economics, and Aliprantis and S.K. Chakrabarti’s Games and Decision Making. The material taught also draws from A. Mclennan`s lecture notes Introduction to Mathematical Economics.
MA 100
Finite Mathematics
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.
MA 101
Intermediate Algebra
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.
MA 197
Pre-Calculus
(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.
MA 198
Calculus I
(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.
MA 200
Introduction to Mathematical Reasoning
(Prerequisites: Placement into MA 197 or completion of MA 100 or MA 101 with a grade of C- or above)
The course introduces the basics of mathematical reasoning, the aspect of mathematics that is concerned with the development and analysis of logically sound and rigorous arguments, which lie at the core of problem-solving and theorem-proving techniques. The course will explore fundamental mathematical concepts such as sets, relations, and functions, and proof techniques based on formal logic and mathematical induction.
MA 208
Statistics I
(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.
MA 209
Statistics II
(Prerequisites: MA 208 with a grade of C- or above; Co-requisite: CS 110 OR CS 160)
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.
MA 210
Statistics for Science and Engineering
(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.
MA 281/381
Independent Study
MA 298
Calculus II
(Co-requisite: MA 350 Linear Algebra)
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.
MA 350
Linear Algebra
(Pre-requisite: 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.
MA 481
Independent Research
(Prerequisite: Permission of the intructor)
MA 482
Independent Study
(Prerequisite: Permission of the intructor)
MA 490
Calculus III
(Prerequisites: MA 299 Calculus II and MA 491 Linear Algebra (both with a grade of C or above))
This course builds on the material presented in Calculus II. It covers vector and multivariable calculus. The mathematical tools and methods introduced in the course are used extensively in the physical sciences, engineering, and economics. The main aim is to arrive at two of the most important theorems in vector calculus: Green’s Theorem and Stokes’ Theorem.
MA 491
Linear Algebra
(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.
MA 492
Mathematical Statistics
(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.
MA 493
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.
MA 495
Differential Equations
(Prerequisites: MA 298 and MA 350 or permission of the instructor)
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.
MA 497
Real Analysis
(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.
MA/PH 103
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, but it is also extremely helpful in day-to-day life. The course focuses on three related areas. The first is what is called "formal logic", and consists in learning how to formalize natural language into statements that can be evaluated as true or false. The second is techniques of mathematical proof (direct proof, proof by contradiction, proof by induction), which will be explored using a range of diverse examples. The third main topic of the course will be learning to recognize many of the most common logical fallacies, that is, errors of reasoning, found in discourses both inside and outside of Mathematics. This last topic will be explored mainly with the aim of giving the student a powerful tool against misinformation, and will be illustrated with many up-to-date examples.
PH/MA 103
Introduction to Logic
This course introduces you to the study of logic, essential for clear thinking and argument in all disciplines. We will study how the validity of arguments can be evaluated in formal and symbolic terms, and the issues regarding language, truth, and rationality that this raises. As examples to analyze, we will use arguments from diverse fields, such as politics, sociology, mathematics, science, and philosophy.
