Mathematics Track

Math 123 is a one semester introduction to statistics. Topics will include basic probability, discrete and continuous random variables, the Central Limit Theorem, sampling distributions for normal populations, confidence intervals, hypothesis tests, the chi-squared test, and simple linear regression. Students will use R software to explore these ideas on actual data.  Students will work with statistical models that occur in the natural and social sciences.

Prerequisites: MATH 120 – Calculus I

Course Designation/Attribute: FA

Anticipated Terms Offered: Each Semester

A requirement for mathematics and physics majors; highly recommended for all computer-science majors. Topics include systems of linear equations and their solutions, matrices and matrix algebra, inverse matrices; determinants and permutations; real n-dimensional vector spaces, abstract vector spaces and their axioms, linear transformations; inner products (dot products), orthogonality, cross products, and their geometric applications; subspaces, linear independence, bases for vector spaces, dimension, matrix rank; eigenvectors, eigenvalues, matrix diagonalization. Some applications of linear algebra will be discussed, such as computer graphics, Kirchoff’s laws, linear regression (least squares), Fourier series, or differential equations.

Prerequisites: MATH 121 or MATH 125.

Course Designation/Attribute: FA

Anticipated Terms Offered: Offered every year

A continuation of calculus (MATH 120, MATH 121, or MATH 124, MATH 125). Multivariate calculus uses linear algebra to extend the important concepts of single-variable calculus to higher-dimensional settings. Topics include scalar-valued and vector-valued functions, graphs, level sets, limits and continuity; partial derivatives, gradients, tangent planes, differentiability, total derivatives, directional derivatives; paths, velocity, acceleration, arclength, curvature, vector fields, divergence, curl; extrema, Hessians; multiple integrals, change of variables, Jacobians; line integrals, Green’s theorem; surface integrals, Stokes’ theorem, and Gauss’s theorem.

Prerequisites: MATH 121 or MATH 125 or MATH 130

Anticipated Terms Offered: Offered every year

Mathematical models are fundamental for understanding, predicting, and decision-making in almost every field. The goal of this course is to enable students to build mathematical models of real-world phenomena, analyze them, and make predictions about their behavior. A variety of models will be addressed with examples taken from natural and social sciences such as biology, chemistry, economics, and physics. Students are expected to actively engage in the modeling process by showing understanding and questioning the models constituents and extrapolating the presented examples to other situations. This course is project based. By the end of this course students are expected to present a report on their project with a focus on describing the modeling procedure and an analysis of the extent to which their model is accurate and its limitations.

Prerequisites: MATH 121 – Calculus II  or MATH 125 – Honors Calculus II

Course Designation/Attribute: POP

Anticipated Terms Offered: Spring

This course is ideal for students who want a rigorous introduction to finance.  The course covers the following fundamental topics: the time value of money, portfolio theory, capital market theory, and security price modeling.  We shall dissect financial models by isolating their central assumptions and conceptual building blocks, showing rigorously how their governing equations and relations are derived, and weighing critically their strengths and weaknesses.

Prerequisites: MATH 131 or Permission

Anticipated Terms Offered: Offered Periodically

An introduction to probability theory and mathematical statistics that emphasizes the probabilistic foundations required to understand probability models and statistical methods. Topics covered will include the probability axioms, basic combinatorics, random variables and their probability distributions, mathematical expectation and common families of probability distributions.

Prerequisites: MATH 130, MATH 131

Anticipated Terms Offered: Offered every year

The emphasis of this course is to develop the fundamental statistical concepts of inference and hypothesis testing from a classical perspective using the tools of probability theory. Topics investigated include sampling and sample distributions, graphical data analysis, point and interval estimation, hypothesis testing and an introduction to Bayesian inference.

Prerequisites: MATH 217

Anticipated Terms Offered: Offered every other year

A course in linear regression analysis which explores statistical methods for modeling a linear functional relationship between a response variable and one or more predictor variables. First the underlying theory for simple regression models involving one response and one predictor variable is developed, and then the results are extended to the case of one response variable and multiple predictor variables (multiple regression). Underlying model assumptions are explored and the implications of their violation. Besides the development of the statistical theory, we will emphasize the practical application of the theory to real world examples.

Prerequisites:MATH 217

Anticipated Terms Offered: Offered every year

A stochastic process is a collection of random variables indexed by a time parameter and used to model phenomena over time. Markov chains, the focus of this course, are one class of stochastic processes. They possess the Markov property which asserts that future random behavior of the system under study depends only on its current state, and not its past. Such processes find wide modeling applications in fields such as physics, chemistry, biology, business, information theory, and many others. Additionally, Markov chains are an effective tool in numerical estimation, for instance in solving multi-dimensional integrals that appear in statistical learning models. This course will consider both discrete- and continuous- time Markov chains. Topics will include Markov chains with finite and countable state spaces; continuous-time Markov chains such as the Poisson process, birth and death process, and queueing systems; Markov chain Monte-Carlo algorithms.

Prerequisites:MATH 217

Anticipated Terms Offered: Every other Spring

Most ordinary differential equations occurring in mathematical models of physical, chemical and biological phenomena cannot be solved analytically. Numerical integrations do not lead to a desired result without qualitative analysis of the behavior of the equation’s solutions. This course studies the flows of scalar and planar ordinary differential equations. Stability and bifurcation are discussed.

Prerequisites:MATH 130

Anticipated Terms Offered: Offered every other year