A non-calculus based course that highlights the nature and significance of mathematics and its widespread applicability across a variety of disciplines. Applications of mathematics and mathematical modeling may come from areas such as financial management, economics, political science, government, medicine, the natural sciences, and the arts. An emphasis will be placed upon developing the student's skills in critical thinking and in applying analytical skills to interpret quantitative information.[Q]
An introduction to the concepts and reasoning underlying the interpretation of data and chance. Emphasis is on understanding how statistical analysis is used to gain insight into a wide variety of areas of human interest. Topics include elements of descriptive statistics, design of experiments, laws of probability, and inference from a sample to a population (including confidence intervals and hypothesis testing). Not open to students who have credit for any mathematics course numbered above 120, except by permission of instructor. [Q]
An introduction to mathematical modeling and the use of differential calculus. Topics include: analysis and manipulation of elementary functions, including trigonometric, exponential, and logarithmic functions; the differential calculus of such functions; and optimization. An ongoing emphasis will be the use of elementary functions as well as the differential calculus to model phenomena in the natural, social and life sciences. Not open to students who have credit for MATH 161 or MATH 165. [Q]
This course in the differential calculus of one and several variables is intended for students who plan to major in Economics or Policy Studies. Mathematical concepts include exponentials and logarithms, limits, ordinary and partial derivatives, techniques of differentiation, contours, and optimization in both one and several variables. Economic concepts and models include supply and demand curves, market equilibrium, present and future value, marginal analysis, total and average cost, elasticity of demand, and optimization subject to a budget constraint. Not open to students who have credit for MATH 161 or MATH 165. [Q]
The sequence MATH 161, MATH 162, MATH 263 provides an introduction to calculus for students of mathematics, engineering, and the sciences. Topics include limits, derivatives, techniques of differentiation, definite integrals, the fundamental theorem of calculus, and applications of derivatives and integrals. [Q]
A continuation of MATH 161. Topics include techniques and applications of integration, introduction to differential equations, parametric curves and polar coordinates, infinite series and Taylor approximation.
A course which covers the same topics as MATH 161 while using a workshop experience and collaborative learning to give special emphasis to the development of problem-solving skills. Enrollment is by invitation of the Department of Mathematics. [Q]
An introduction to discrete structures and algorithms and some mathematical tools and methods of reasoning that aid in their development and analysis. Topics include: propositional and first-order logic, sets, counting, probability, algorithms, mathematical induction, relations, graphs, and trees.
An introductory course emphasizing standard methods and reasoning used in analyzing data. Topics include exploratory data analysis, design of experiments, least squares analysis, probability, sampling distributions and methods of inferential statistics. Includes an introduction to a statistical computing package. Not open to students who have credit for PSYC 120 or Biostatistics. [Q]
An introduction to the concepts, techniques, and application of evolutionary game theory. The mathematics of game theory and natural selection offer insights valuable to the study of economics, biology, psychology, anthropology, sociology, philosophy, and political science. This course is intended to serve students with interests in any of these fields learn the approach, requiring minimal mathematical background, with special attention to apparent paradoxes, such as the evolution of altruism. [V]
A continuation of MATH 162. Topics include vector algebra, vector calculus, partial derivatives, gradients and directional derivatives, tangent planes, the chain rule, multiple integrals and line integrals.
An introductory course in ordinary differential equations including techniques of elementary linear algebra. Emphasis is on first-order equations, and higher-order linear equations and systems of equations. Topics include qualitative analysis of differential equations, analytical and numerical solutions, Laplace transforms, existence and uniqueness of solutions, and elemental models in science and engineering.
An introductory course in linear algebra emphasizing applications to fields such as economics, natural sciences, computer science, statistics, and engineering. The course covers solutions of systems of equations, matrix algebra, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors. Not open to students who have credit for MATH 300.
A course that introduces students to the fundamentals of mathematical modeling through the formulation, analysis, and testing of mathematical models in a variety of areas. Modeling techniques covered include curve fitting, difference and differential equations, simulation and an introduction to computer programming.
This course will serve as a one-semester introduction to probability and mathematical statistics, with roughly half of the semester devoted to each. After learning basics of set theory and axiomatic probability, we review random variables, probability mass/density functions, expected value (including covariance and correlation), and expected value and variance of linear combinations. Then we begin inferential statistics (confidence intervals and hypothesis tests), correlation and simple linear regression, and, time permitting, one-way analysis of variance and/or x2 tests. Students may not receive credit for Math 286 if they have credit for Math 186.
This course will examine advanced methods for analyzing data. Topics will include experimental design concepts, one- and two-way ANOVA (and interaction), multiple regression and ANCOVA, analysis of categorical outcomes (including logistic regression), and power. Time permitting, additional topics may be covered. The course emphasizes the correct application and interpretation of these methods, including assessment of underlying assumptions. Applications will require use of statistical software (presumably R), which is left to the discretion of the instructor.
An introduction to the concepts and techniques that permeate advanced mathematics. Topics include set theory, propositional logic, proof techniques, relations, and functions. Special emphasis on developing students' facility for reading and writing mathematical proofs. Examples and additional topics are included from various branches of mathematics, at the discretion of the instructor.
A first course in theoretical linear algebra, emphasizing the reading and writing of proofs. Topics include systems of linear equations, matrix algebra, vector spaces and linear transformations, eigenvectors and diagonalization, inner product spaces, and the Spectral Theorem. Not open to students with credit for MATH 272.
A course which engages students in the creation of mathematical models to answer questions about a variety of phenomena. Students work in small teams on a sequence of projects which require the formulation, analysis, and critical evaluation of a mathematical model and conclude with the submission of a written report by each student. [W]
A study of some mathematical methods of decision making. Topics include: linear programming (maximizing linear functions subject to linear constraints), the simplex algorithm for solving linear programming problems, sensitivity analysis, networks and inventory problems and applications.
A course in the theory and applications of ordinary differential equations which emphasizes qualitative aspects of the subject. Topics include analytic and numerical solution techniques for systems of equations, graphical analysis, stability, existence-uniqueness theorems, and applications.
An introduction to partial differential equations and their applications. Formulation of initial and boundary value problems for these equations and methods for their solution are emphasized. Separation of variables and Fourier analysis are developed. The course includes interpretation of classical equations and their solutions in terms of applications.
Various geometries are considered including absolute, Euclidean, and the classical non-Euclidean geometries. General properties of axiomatic systems, models, and the role of Euclidean geometry in the development of other branches of mathematics are discussed.
An introduction to the techniques and theory of enumeration of finite sets. Topics include combinations, permutations, generating functions, recurrence relations, the inclusion-exclusion principle, block designs, and graph theory.
An introduction to the theory of the integers and techniques for their study and application. Topics include primality, modular arithmetic, arithmetic functions, quadratic residues, and diophantine equations.
A development of basic probability theory including the axioms, random variables, expected value, the law of large numbers and the central limit theorem. Additional topics include distribution functions and generating functions.
A mathematical development of fundamental results and techniques in statistics. Topics include estimation, sampling distributions, hypothesis testing, correlation and regression.
A stochastic process is any collection of random variables and is a mathematical model or random phenomena that occur in time or space. They have application in many areas including physics, engineering, biology, mathematical finance, computer science, geology, and actuarial science, to name a few. This course includes fundamental stochastic processes and their applications, including Markov chains, martingales, Poisson processes, and Brownian motion.
Topics include simple linear regression, multiple linear regression, and nonlinear regression. More specifically, the course covers applications of least squared techniques, inference, diagnostics such as residual analysis and the associated remedial measures, and the use of ANOVA in regression. The course uses a matrix-based approach. In addition, this course shows how regression is used in many other fields through practical application of the techniques covered in this class in real-world scenarios.
A continuation of multivariable calculus from MATH 263 , using concepts from linear algebra. Topics include the derivative as a linear transformation, the Chain Rule, the Inverse and Implicit Function Theorems, the Change of Variables Theorem, and the integral theorems of Green, Gauss and Stokes; additional topics may include differential forms and series of functions.
An introductory course in the calculus of complex functions including the algebra and geometry of complex numbers, elementary mappings, complex derivatives and integrals,Cauchy-Riemann equations, harmonic functions, Cauchy's Integral Theory, Taylor and Laurent series, residues.
A wide range of topics in mathematical finance are covered, including: continuous time models such as the Brownian motion model for stock prices, the Black-Scholes model for options prices, the Ho-Lee, Vasicek and other models for interest rates, also different hedging strategies and numerical approaches for derivative pricing such as binomial trees, Monte-Carlo simulation and finite difference methods, and price models for credit derivatives such as asset swaps, credit default swaps and collateralized debt obligations.
An introduction to some of the fundamental ideas and structures of abstract algebra. Homomorphisms and isomorphisms, substructures and quotient structures are discussed for algebraic objects such as fields, vector spaces, rings, and groups. Other topics may include factorization in rings, and finite group theory. [W]
The course covers field extensions and Galois Theory. Additional topics are included at the discretion of the instructor.
A rigorous development of the calculus of functions of one real variable including the topology of the real line, limits, uniform convergence, continuity, differentiation and integration. [W]
An introduction to metric spaces and measure theory. Topics covered include metric space topology, compactness and completeness, uniform convergence of functions; basic measure theory, construction of Lebesgue measure on the real line, and the definition and basic convergence properties of the Lebesgue integral.
The main topics are set theory, the separation axioms, connectedness, compactness, and the continuity of functions. Classical general topological spaces are studied including regular spaces, normal spaces, first or second countable spaces, and metrizable spaces.
Mathematics is a living, changing subject whose truths, once identified, have remarkable staying power. In this course students analyze various episodes in the history of mathematics that illustrate how mathematical knowledge has developed over the years. Topics include: Egyptian and Babylonian mathematics, indigenous mathematics from outside of the Western tradition, the contributions of Euclid and Ancient Greek mathematics, the birth of calculus, and selected topics from the 19th and 20th centuries. [W]
Chosen from among a wide range of mathematical topics accessible to junior and senior mathematics majors. When offered, the special topic to be studied will be listed in the Semester Course and Hour Schedule, and course descriptions will be available in the department office.
Study by an individual student, under the supervision of a mathematics faculty member, of a mathematical subject not covered by courses offered by the department. The program of study must be drawn up by the student and the faculty supervisor and approved by an ad hoc committee of the department.
A course in which each student undertakes a thorough and independent study of one or more topics in mathematics. Students are required to make oral presentations on their work and to prepare written reports on their topics. [W]
Students desiring to take Honors in Mathematics should inform their department advisers early in the second semester of the junior year. Honors work involves a guided program of independent study culminating in a thesis on a topic to be selected by the student in consultation with his or her adviser and approved by the department. [One W credit only upon completion of both 495 and 496]