Mathematics and Computer Science

A course in modern machine learning via deep learning. Topics include statistical estimation, efficient gradient descent of nonlinear functions, convolutional models, attention-based models, and generative models. Emphasis is placed on maintaining a balance between theory and the ability to produce practically efficient implementation of these techniques leveraging GPU acceleration within a leading deep learning development framework. Practical implementation details also consider techniques for avoiding local optima and improving generalization.

The first of a two-semester sequence designed to introduce the ideas and applications of the Differential Calculus. This course focuses on the concepts of functions, limits, continuity and differentiation, exploring them in the context of algebraic functions. Prerequisites: none. 

The second of a two-semester sequence designed to introduce the ideas and applications of the Differential Calculus. This course focuses on the Differential Calculus of transcendental functions, including exponential, logarithmic and trigonometric functions. The course will introduce integration including the Fundamental Theorem of Calculus. The successful completion of MTH 113 is equivalent to successful completion of Calculus I. 

A comprehensive study of limits, continuity and differentiation of functions of one real variable and their applications. Introduction to integrals. Credit will not be granted for both MTH 113 and MTH 120. Prerequisites: For students in their first two years of college and an ACT mathematics score of 27 or higher. 

A continuation of MTH 120. Techniques and applications of integration. Infinite sequences and series. 

A thorough treatment of the techniques of formal reasoning. Topics include truth-functional logic, quantification logic and construction of correct deductions.

The theory and applications of vector spaces, matrix algebra, linear transformations and eigenvalues. 

A third-semester calculus course. Topics will include vectors and three-dimensional coordinate systems, partial differentiation with applications, multiple integrals, and vector calculus. 

Properties of the integers, the Euclidean Algorithm, divisibility, Diophantine equations, prime numbers, congruences and residues. 

An introduction to the theory and applications of discrete mathematics. Topics for the course include proof writing, logic, set theory, induction, recursion, combinatorics, relations, functions, and graph theory.

A study of the techniques and theory of solving ordinary and partial differential equations. Topics may include series solutions, numerical methods, Fourier and Laplace transforms, linearization, stability theory, periodic orbits, and bifurcations and chaos. Prerequisite: MTH 310 or PHY 304. Spring, typically odd-numbered years.

A college-level approach to Euclidean and non-Euclidean geometries. The course will pursue an in-depth investigation into the following topics: Hilbert's postulates for Euclidean geometry, the parallel postulates, neutral geometry and non-Euclidean geometry. 

Introduction to the mathematical theory of probability. Discrete probability spaces, conditional probability, discrete and continuous random variables, expectations and distributions.

Game theory is the study of the interaction of rational decision makers. This course uses game theory to study incentives and strategic behavior in practical situations of inter-dependent decision making and negotiations. The course will develop basic theoretical concepts in tandem with applications from a variety of areas, including bargaining, competition, and strategic voting. 

This course serves as an introduction to the formulation, analysis and interpretation of mathematical models in the study of problems in the natural, management and social sciences. Topics may include optimization, dimensional analysis, Markov chains and autonomous systems. The course will require the use of the Eaton Corporation Computer Laboratory and the software packages R, Mathematica, and Matlab. 

A course on mathematical interest theory. Topics discussed will include the time value of money, annuities and cash flows, loans, bonds, the yield rate of an investment, the term structure of interest rates, duration, and immunization. The course may also include topics from financial economics. Offered as needed.

A study of the historical development of various branches of mathematics from antiquity through the end of the nineteenth century. Topics include mathematics prior to classical antiquity, mathematics in ancient Greece, Islamic mathematics, the development of symbolic algebra, the invention of the calculus, and the nineteenth century evolution of algebra, geometry, and analysis. The course will emphasize primary source materials. 

An introduction to proof writing, oral presentations, literature research, and computer software applied to mathematics. Offered as needed.

A rigorous treatment of the calculus of one variable, including limits, continuity, sequences, differentiation and Riemann integrals. This course should be taken in the junior or senior year. 

The theory of functions of a single complex variable. Complex numbers, elementary complex functions, differentiation and integration of complex functions, complex series and residue theory.

Numerical methods for approximation of roots, systems of linear equations, interpolation and curve fitting, numerical integration and differentiation, and differential equations. Problems are generally approached through structured algorithms. 

An introduction to the theory of algebraic structures, including the elementary properties of groups, rings and fields. This course should be taken in the junior or senior year. 

This course serves as a sequel to MTH 370 (Theory of Probability), focusing on the application of concepts introduced in MTH 370 to the theory and practice of statistical inference. Emphasis will be placed both on the mathematical theory underlying the definition and evaluation of various estimators and statistical tests, as well as the application of this theory to the analysis of real-world data sets. 

An introductory course in the fundamental concepts of general topology, including metric spaces, topological spaces, connectedness and compactness. 

Students will be introduced to contemporary mathematics literature with an emphasis on undergraduate research. Instruction will be given on how to read and write mathematics papers, how to give and receive math talks, what to do at math conferences, how to perform literature searches, and other skills related to the mathematics profession and the practice of mathematics beyond the classroom.