Mathematics and Statistics

Degrees and Certificates

Classes

MAT 1000 : Math and Stat Communities

Understanding the role of creative thinking, problem solving, and collaboration in mathematics and statistics; exploration of research and careers in the mathematical and statistical sciences; building community with fellow mathematics and statistics majors.

Credits

Credits 1

MAT 1220 : Discrete Math Social Sci

Discrete mathematics for the Liberal Arts student: voting methods, weighted voting, fair division, apportionment, circuits, network, trees, directed graphs, planning and scheduling, linear programming, growth and symmetry. Not open to students who have completed MAT 1505.

Credits

Credits 3

MAT 1280 : Mathematics of Fairness

Examining fairness in our personal lives and in society: Voting systems and power indices, strategic political positioning spatial models, fair division, congressional district apportionment, game theory, the GINI index of economic inequality, gerrymandering.

Credits

Credits 3

MAT 1290 : Topics in Core Mathematics

Course in an area of pure or applied mathematics or statistics. May be repeated for credit if areas of topical focus are different. Designed specifically to satisfy the core requirement in mathematics and statistics, for students in the humanities and social sciences.

Credits

Credits 3

MAT 1312 : Biocalculus

Discrete and continuous dynamics of biological systems: discrete dynamical systems, sequences, functions, discrete and continuous limits, the derivative, the integral, methods and applications of differentiation and integration, Taylor polynomials, modeling with differential equations, Euler's method, applications to Biology.

Credits

Credits 4

MAT 1314 : Modeling for the Life Sciences

Mathematical and statistical modeling in the Life Sciences. Topics selected from: dynamical systems, diffusion, Markov, Bayesian, connectionist, and information theory models, applied to epidemiology, ecology, neuroscience and neuron signaling, cell and molecular biology, genetics, physiology, psychology, and other areas. Pre-requisites MAT 1312 or Equivalent

Credits

Credits 3

Prerequisites

MAT 1310
MAT 1312
MAT 1320
MAT 1400
MAT 1500

MAT 1310 or MAT 1312 or MAT 1320 or MAT 1400 or MAT 1500

MAT 1320 : Calculus I for Liberal Arts

Calculus for Liberal Arts students: polynomial, rational and transcendental functions, the derivative, numerical and graphical introduction to integration.

Credits

Credits 3

MAT 1400 : Business Calculus

Functions, limits, and basic definitions of differential and integral calculus. Techniques of differentiation and integration. The Fundamental Theorem of Calculus. Applications in various areas of business and economics.

Credits

Credits 4

MAT 1500 : Calculus I

Limits, transcendental functions (logarithms, exponential functions, inverse trigonometric functions), differentiation (definition, tangent lines, rates of change, techniques, implicit differentiation, related rates), applications of differentiation (graphing, optimization), indeterminate forms and L'Hopital's Rule. Use of a computer algebra system, eg. MAPLE.

Credits

Credits 4

MAT 1505 : Calculus II

Integration (indefinite, definite), applications of integration (area, volume, applications to physics and economics, etc.), methods of integration, approximate integration (trapezoidal and Simpson's rules), improper integrals, differential equations, infinite sequences and series. Continued use of a computer algebra system.

Credits

Credits 4

Prerequisites

MAT 1312
MAT 1320
MAT 1400
MAT 1500

MAT 1312 or MAT 1320 or MAT 1400 or MAT 1500

MAT 2400 : Linear Algebra for Computing

Vectors, matrices, and matrix algebra; systems of linear equations; matrix inverses; least squares problems; eigenvalues and eigenvectors; using Python for computational linear algebra; applications from areas such as data science, computer graphics, graph algorithms, and web search.

Credits

Credits 4

Prerequisites

MAT 1500

MAT 1500

MAT 2500 : Calculus III

Parametric equations; polar, cylindrical, and spherical coordinates; vectors and the geometry of space; vector functions (derivatives, integrals, curvature, etc.); partial derivatives; optimization; multiple integration and its applications; vector calculus (line integrals, vector analysis). Continued use of a computer algebra system.

Credits

Credits 4

Prerequisites

MAT 1505

MAT 1505 :D-

MAT 2600 : Foundation of Math I

Topics selected from natural numbers, mathematical induction, irrational and transcendental real numbers, complex numbers, Fundamental Theorem of Algebra, infinite cardinals, symbolic logic, functions and relations, iterated functions, mathematical chaos.

Credits

Credits 3

Prerequisites

MAT 1500

MAT 1500 :D-

MAT 2705 : Diff Equation with Linear Alg

First order and linear second order differential equations, matrices and linear equation systems, eigenvalues and eigenvectors, and linear systems of differential equations.

Credits

Credits 4

Prerequisites

MAT 1505

MAT 1505 :D-

MAT 3011 : Problem Solving Seminar

Explore techniques for solving mathematical problems, including problems typical of the Putman Mathematical Competition. Students solve and present solutions to problems posed.

Credits

Credits 1

Prerequisites

MAT 1500

MAT 1500

MAT 3100 : Applied Linear Algebra

Vectors, matrices, transpose and inverse of a matrix, systems of linear equations, the four fundamental subspaces, eigenvalues and eigenvectors, symmetric matrices, matrix factorizations, applications such as information retrieval, ranking web pages, graphs and networks, least squares, and data compression.

Credits

Credits 3

Prerequisites

MAT 1312
MAT 1320
MAT 1400
MAT 1500

MAT 1312 or MAT 1320 or MAT 1400 or MAT 1500

MAT 3300 : Advanced Calculus

Real numbers, sequences, convergence, supremum and infimum, completeness of the reals, continuous functions, Intermediate Value Theorem, differentiable functions, Mean Value Theorem, Riemann integral, Fundamental Theorem of Calculus, Taylor's Theorem.

Credits

Credits 3

Prerequisites

MAT 2500
MAT 2600
HON 4151

MAT 2500 :D- and (MAT 2600 :D- or HON 4151 :D-)

MAT 3400 : Linear Algebra

Vector spaces, linear transformations, basis and dimension, orthogonal transformations, least squares, eigenvalues and eigenvectors, similarity, diagonalization, symmetric, applications.

Credits

Credits 3

Prerequisites

MAT 2705

MAT 2705 :D-

MAT 3500 : Modern Algebra I

Topics selected from groups and subgroups, cyclic groups, permutation groups, isomorphisms, direct products, cosets and Lagrange's Theorem, normal subgroups and factor groups, group homomorphisms, the Fundamental Theorem of Finite Abelian Groups, rings, fields.

Credits

Credits 3

Prerequisites

MAT 2600
MAT 2705

MAT 2600 :D- and MAT 2705 :D-

MAT 4110 : Combinatorics

Induction, permutations and combinations, general counting methods, generating functions, recurrence relations, principle of inclusion-exclusion, graph theory, trees, planarity, crossing numbers, Hamiltonian cycles, Eulerian tours.

Credits

Credits 3

Prerequisites

MAT 1505

MAT 1505 :D-

MAT 4270 : Numerical Analysis

Numerical and computational aspects of root-finding methods, interpolation and polynomial approximation, numerical differentiation and integration, approximation theory.

Credits

Credits 3

Prerequisites

MAT 1505

MAT 1505 :D-

MAT 4550 : Math of Financial Derivatives

Basic tools of financial markets; options; asset price random walks; estimation of parameters; arbitrage put-call parity; Black-Scholes Model; implied volatility; portfolio-optimization; hedging.

Credits

Credits 3

Prerequisites

MAT 2705

MAT 2705 :D-

MAT 4600 : Deterministic Oper Res

Deterministic methods: mathematical optimization, linear programming, formulation and solution techniques, duality, integer linear programming, transportation problem, assignment problem, network flows, dynamic programming.

Credits

Credits 3

Prerequisites

MAT 2500
MAT 2705
MAT 3100
MAT 3400

MAT 2500 :D- and (MAT 2705 or MAT 3100 or MAT 3400)

MAT 5400 : Complex Analysis

Algebra of complex numbers, analytic functions, Cauchy- Riemann equation, Laplace equations, conformal mapping, integrals of complex functions, Cauchy's theorem, power series, Taylor's theorem, Laurent's theorem, residues, entire functions.

Credits

Credits 3

Prerequisites

MAT 2500
MAT 2600

(MAT 2500 :D- and MAT 2600 :D-)

Corequisites

MAT 5500 : Topology

Topological equivalence, connectedness, compactness, topology of subsets of Rn, manifolds, topological embeddings, topological spaces.

Credits

Credits 3

Prerequisites

MAT 3300

MAT 3300 :Y

MAT 5900 : Seminar in Mathematics

Supervised study of selected topics or problems in mathematics, student presentations. May be repeated for credit if content is different.

Credits

Credits 3

Prerequisites

MAT 3300
MAT 3500

MAT 3300 :D- or MAT 3500 :D-

MAT 5991 : Independent Study

Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.

Credits

Credits 1

Prerequisites

MAT 1505

MAT 1505 :D-

MAT 5992 : Independent Study

Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.

Credits

Credits 2

Prerequisites

MAT 1505

MAT 1505 :D-

MAT 5993 : Independent Study

Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.

Credits

Credits 3

Prerequisites

MAT 1505

MAT 1505 :D-

STAT 1230 : Intro Statistics I

Displaying and summarizing data, basic probability concepts, normal distributions, sampling distributions, estimation for a single population parameter, regression and correlation. Not open to students who have completed MAT 1505.

Credits

Credits 3

STAT 1235 : Intro Statistics II

Probability concepts, hypothesis testing, inferences about means, variances and proportions, contingency tables, analysis of variance. Not open to students who have completed MAT 1505.

Credits

Credits 3

Prerequisites

MAT 1230
STAT 1230

MAT 1230 or STAT 1230

STAT 1250 : Stats in Health Care Research

Descriptive and inferential statistics: graphical displays, estimation, & hypothesis testing. Restricted to nursing students; others by special permission only.

Credits

Credits 3

STAT 1260 : Elementary Statistics

Introduction to statistics including topics such as study design, graphical and numerical descriptive statistics, bivariate data analysis, probability, sampling distributions, confidence intervals, hypothesis testing, goodness of fit tests, analysis of variance; resampling and simulation using statistical software; interpreting output from and understanding selected algorithms used in statistical packages.

Credits

Credits 3

STAT 1313 : Statistics for Life Sciences

Statistical concepts and methods with applications in biological and life sciences; data visualization, descriptive statistics, probability distributions, interval estimation and hypothesis testing for one and two variables, statistical software.

Credits

Credits 3

STAT 1430 : Business Statistics

Statistical concepts and methods useful in analyzing problems in all areas of business. Descriptive statistics, probability, sampling distributions, confidence intervals, hypothesis testing, regression analysis, and time series. Applications in various areas of business and economics.

Credits

Credits 4

STAT 4210 : Bayesian Statistical Analysis

Application of Bayesian statistical procedures. Implementation using the programming language R. Bayes's Theorem. Bayesian statistical inference. Various types of prior distributions. Computer-intensive methods. Assessing the prior. Robustness analysis. Writing Bayesian statistical reports.

Credits

Credits 3

Prerequisites

MAT 4310
STAT 4310

MAT 4310 or STAT 4310

STAT 4310 : Stat Methods

Data displays and summarization, probability distributions, point and interval estimation, hypothesis testing, categorical data analysis, regression and correlation.

Credits

Credits 3

Prerequisites

MAT 1505

MAT 1505 :Y

STAT 4315 : Applied Statistical Models

Simple and multiple linear regression, including prediction, correlation, model building, multicollinearity, influential observations, and model fit; ANOVA for designed experiments, including completely randomized, randomized block and factorial designs; Time Series including linear time series models, moving averages, autoregressive and ARIMA models, estimation and forecasting.

Credits

Credits 3

Prerequisites

MAT 1505
MAT 1430
STAT 1430
MAT 4310
STAT 4310

MAT 1505 and (MAT 1430 or STAT 1430 or MAT 4310 or STAT 4310)

STAT 4380 : Data Science

Combining and summarizing real-world data to inform decision-making and predictions; data wrangling, visualization, text mining, ethics; uses R programming language. Some programming experience recommended.

Credits

Credits 3

Prerequisites

MAT 1230
STAT 1230
MAT 1250
STAT 1250
MAT 1313
STAT 1313
MAT 1430
STAT 1430
MAT 4310
STAT 4310
CSC 2300

MAT 1230 or STAT 1230 or MAT 1250 or STAT 1250 or MAT 1313 or STAT 1313 or MAT 1430 or STAT 1430 or MAT 4310 or STAT 4310 or CSC 2300

STAT 4416 : Design of Experiments

Completely randomized, randomized block, and Latin square designs; full and fractional factorial designs; nested and split plot designs; response surface methology.

Credits

Credits 3

Prerequisites

MAT 4310
STAT 4310

MAT 4310 or STAT 4310

STAT 4452 : Nonparametric Statistics

One-sample, two-sample, and multi-sample rank tests; nonparametric confidence intervals; permutation tests; nonparametric regression and correlation; the bootstrap.

Credits

Credits 3

Prerequisites

MAT 4310
STAT 4310

MAT 4310 or STAT 4310

STAT 4480 : Data Mining

Supervised and unsupervised data mining techniques, including clustering, classification, and association rule learning.

Credits

Credits 3

Prerequisites

MAT 4310
STAT 4310

MAT 4310 or STAT 4310

STAT 5700 : Math Statistics I

Probability, random variables, joint distributions, expected values, limit theorems, distributions derived from the normal distribution.

Credits

Credits 3

Prerequisites

MAT 2500

MAT 2500

STAT 5705 : Math Statistics II

Survey sampling, parameter estimation, hypothesis testing, two sample tests, analysis of variance, analysis of categorical data, linear least squares.

Credits

Credits 3

Prerequisites

MAT 2500
MAT 5700
STAT 5700

MAT 2500 and (MAT 5700 or STAT 5700)

STAT 5910 : Topics in Statistics

Lecture course in an area of statistics. May be repeated for credit if topics are different. Prerequisites: Dependent on Topic.

Credits

Credits 3