Mathematics and Statistics
Programs
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Mathematics Major -
Statistics Major -
Mathematics Minor -
Statistics Minor
Courses
MAT 1000: Math and Stat Communities
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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.
MAT 1220: Discrete Math Social Sci
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Discrete math for Liberal Arts students: graphs (circuits, trees, directed graphs), discrete growth, symmetry, and select topics from planning and scheduling, linear programming, tiling, voting methods, and unit conversions. Not open to students who have completed MAT 1505.
MAT 1280: Mathematics of Fairness
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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.
MAT 1290: Topics in Core Mathematics
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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.
MAT 1312: Biocalculus
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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.
MAT 1314: Modeling for the Life Sciences
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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
MAT 1310 or MAT 1312 or MAT 1320 or MAT 1400 or MAT 1500
MAT 1320: Calculus I for Liberal Arts
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Calculus for Liberal Arts students: polynomial, rational and transcendental functions, the derivative, numerical and graphical introduction to integration.
MAT 1400: Business Calculus
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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.
MAT 1500: Calculus I
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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.
MAT 1505: Calculus II
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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.
MAT 1312 or MAT 1320 or MAT 1400 or MAT 1500
MAT 1903: Internship Elective
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Internship Elective
MAT 1906: Internship Elective
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Internship Elective
MAT 2400: Linear Algebra for Computing
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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.
MAT 1500
MAT 2500: Calculus III
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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.
MAT 1505 :D-
MAT 2600: Mathematical Reasoning & Proof
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Mathematical proofs: direct, indirect, induction. Logic, set theory, relations, functions. Optional topics from algebra, number theory, combinatorics, and analysis.
MAT 1500 :D-
MAT 2705: Diff Equation with Linear Alg
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First order and linear second order differential equations, matrices and linear equation systems, eigenvalues and eigenvectors, and linear systems of differential equations.
MAT 1505 :D-
MAT 2993: Internship
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Internship
MAT 2996: Internship
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Internship
MAT 3001: Topics in Mathematics & Stats
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Lecture course in an area of mathematics or statistics. May be repeated for credit if topics are different.
MAT 3011: Problem Solving Seminar
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Explore techniques for solving mathematical problems, including problems typical of the Putman Mathematical Competition. Students solve and present solutions to problems posed.
MAT 1500
MAT 3100: Applied Linear Algebra
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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.
MAT 1312 or MAT 1320 or MAT 1400 or MAT 1500
MAT 3300: Advanced Calculus
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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.
MAT 2500 :D- and (MAT 2600 :D- or HON 4151 :D-)
MAT 3400: Linear Algebra
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Theory of vector spaces, linear transformations, basis, and dimension. Selected topics from orthogonal transformations, least squares, eigenvalues and eigenvectors, similarity, diagonalization, matrix decompositions, infinite dimensional transformations.
MAT 2600 and (MAT 2400 or MAT 2705 or MAT 3100)
MAT 3500: Modern Algebra I
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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.
MAT 2600 :D- and MAT 2705 :D-
MAT 3930: History of Mathematics
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Development of mathematics from ancient times to the birth of calculus in the seventeenth century.
MAT 1505 :D- and MAT 2600 :D-
MAT 4110: Combinatorics
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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.
MAT 1505 :D-
MAT 4270: Numerical Analysis
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Numerical and computational aspects of root-finding methods, interpolation and polynomial approximation, numerical differentiation and integration, approximation theory.
MAT 1505 :D-
MAT 4410: Math Modeling
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Model formulation, the modeling process, graphs as models, examples from the physical and social sciences, parameter estimation, experimental modeling, dimensional analysis, modeling discrete and continuous dynamic behavior, implementation.
MAT 2705 :D-
MAT 4500: Mathematics of Games
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Study of popular games, toys, and puzzles using recursions, counting techniques, graph theory, group theory, probability, Markov chains, and other mathematical tools.
MAT 2600 and (STAT 1230 or STAT 1250 or STAT 1313 or STAT 1430 or STAT 4310)
MAT 4550: Math of Financial Derivatives
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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.
MAT 1505
MAT 4600: Deterministic Oper Res
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Deterministic methods: mathematical optimization, linear programming, formulation and solution techniques, duality, integer linear programming, transportation problem, assignment problem, network flows, dynamic programming.
MAT 2500 :D- and (MAT 2705 or MAT 3100 or MAT 3400)
MAT 4610: Stochastic Oper Research
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Probabilistic methods: brief review of probability, transient and asymptotic properties of Markov chains, queuing models and their applications, Markov decision processes, forecasting, game theory, simulation.
MAT 2705 :D-
MAT 5110: Topics in Geometry
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Topics selected from affine, hyperbolic, spherical, elliptic, Euclidean or projective geometry.
MAT 2600 :D-
MAT 5200: Theory of Numbers
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Congruences, quadratic reciprocity, Diophantine equations; applications.
MAT 2600 :D-
MAT 5400: Complex Analysis
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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.
(MAT 2500 :D- and MAT 2600 :D-)
MAT 5500: Topology
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Topological equivalence, connectedness, compactness, topology of subsets of Rn, manifolds, topological embeddings, topological spaces.
MAT 3300 :Y
MAT 5600: Differential Geometry
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Geometry of curves and surfaces, curvature, first and second fundamental forms, minimal surfaces, use of MAPLE.
MAT 2500 :D-
MAT 5900: Seminar in Mathematics
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Supervised study of selected topics or problems in mathematics, student presentations. May be repeated for credit if content is different.
MAT 3300 :D- or MAT 3500 :D-
MAT 5920: Topics in Applied Mathematics
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Lecture course in an area of applied mathematics. May be repeated for credit if topics are different.
MAT 5991: Independent Study
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Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.
MAT 1505 :D-
MAT 5992: Independent Study
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Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.
MAT 1505 :D-
MAT 5993: Independent Study
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Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.
MAT 1505 :D-
STAT 1230: Intro Statistics I
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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.
STAT 1235: Intro Statistics II
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Probability concepts, hypothesis testing, inferences about means, variances and proportions, contingency tables, analysis of variance. Not open to students who have completed MAT 1505.
MAT 1230 or STAT 1230
STAT 1250: Stats in Health Care Research
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Descriptive and inferential statistics: graphical displays, estimation, & hypothesis testing. Restricted to nursing students; others by special permission only.
STAT 1260: Elementary Statistics
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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.
STAT 1313: Statistics for Life Sciences
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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.
STAT 1430: Business Statistics
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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.
STAT 3021: Topics in Statistics
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Lecture course on a topic from Statistics. May be repeated for credit if topics are different.
STAT 4210: Bayesian Statistical Analysis
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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.
MAT 4310 or STAT 4310 or STAT 4315
STAT 4310: Stat Methods
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Data displays and summarization, probability distributions, point and interval estimation, hypothesis testing, categorical data analysis, regression and correlation.
MAT 1505 :Y
STAT 4315: Applied Statistical Models
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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.
MAT 1505 and (MAT 1430 or STAT 1430 or MAT 4310 or STAT 4310)
STAT 4380: Data Science
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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.
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 4414: Categorical Data Analysis
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Analysis of categorical response data, including contingency tables, logistic regression, multinomial logistic regression, and generalized linear models.
STAT 4315
STAT 4416: Design of Experiments
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Completely randomized, randomized block, and Latin square designs; full and fractional factorial designs; nested and split plot designs; response surface methology.
MAT 4310 or STAT 4310 or STAT 4315
STAT 4444: Applied Time Series Analysis
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Time series modeling, forecasting, and diagnostics, with an emphasis on applications from business and the sciences.
STAT 4315
STAT 4450: Regression for Biostatistics
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Regression methods for analyzing medical and biological data, including multiple regression, logistic regression, survival modeling, and longitudinal mixed modeling.
MAT 4310 or STAT 4310 or STAT 4315
STAT 4452: Nonparametric Statistics
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One-sample, two-sample, and multi-sample rank tests; nonparametric confidence intervals; permutation tests; nonparametric regression and correlation; the bootstrap.
MAT 4310 or STAT 4310 or STAT 4315
STAT 4480: Data Mining
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Supervised and unsupervised data mining techniques, including clustering, classification, and association rule learning.
MAT 4310 or STAT 4310 or STAT 4315
STAT 5700: Probability
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Probability, random variables, joint distributions, expected values, limit theorems, distributions derived from the normal distribution.
MAT 2500
STAT 5705: Theory of Stat Inference
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Transformation of random variables, Distributions related to the normal, Central Limit Theorem, Law of Large Numbers, Point estimation, Maximum likelihood estimation, Bias, Consistency, Sufficiency, Confidence intervals, Hypothesis testing, Likelihood ratio tests.
MAT 2500 and (MAT 5700 or STAT 5700)
STAT 5905: Seminar in Statistics
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Supervised study of selected topics or problems in statistics, with student presentations and papers. May be repeated for credit if content is different.
(MAT 4315 or STAT 4315) and (MAT 5700 or STAT 5700)
STAT 5910: Topics in Statistics
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Lecture course in an area of statistics. May be repeated for credit if topics are different. Prerequisites: Dependent on Topic.