Mathematics and Statistics

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.

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.

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.

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

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

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. Restricted to Part-Time Studies

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.

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.

Functions, algebra of real functions, polynomials, allometric functions, exponential and logarithmic functions, trigonometric functions, graphing, log-log and semilog graphs, sequences, difference equations, limits, continuity, the derivative, the chain rule, higher order derivatives, maxima and minima, curve sketching, applications to biology.

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.

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.

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

The mean-value theorem, Taylor's polynomial approximations, the anti-derivative, the definite integral, area, numerical integration, applications of the integral, techniques of integration, indeterminate forms, L'Hospital's rule,improper integrals, introduction to differential equations with applications to biological systems, numerical solutions using the computer, applications in the life sciences.

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

Techniques of differentiation and integration, applications and further developments of calculus.

Analysis of single variable problems: problem formulation, translation between mathematical symbols and verbal descriptions, single variable modeling with real data, rates of change, techniques of differentiation, optimazation, post-optinality analysis, continuous probability distributions, integrals, Fundamental Theorem of Calculus.

Analysis of multivariable problems: problem formulation, translation between mathematical symbols and verbal descriptions, multivariable modeling with real data, regression analysis, partial derivatives and unconstrained optimization, Lagrange multipliers and constrained optimization, matrix algebra, linear programming.

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.

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.

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.

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.

Internship Elective

Internship Elective

The design and analysis of experiments, probability distributions, basic statistical inference, analysis of variance, block designs and factorial designs. For social and natural science majors.

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.

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.

Mathematical proofs: direct, indirect, induction. Logic, set theory, relations, functions. Optional topics from algebra, number theory, combinatorics, and analysis.

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

Development of mathematics from ancient times to the birth of calculus in the seventeenth century.

Internship

Internship

Lecture course in an area of mathematics or statistics. May be repeated for credit if topics are different.

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

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.

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.

Advanced topics selected from real analysis, complex analysis, or higher analysis.

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.

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.

Development of mathematics from ancient times to the birth of calculus in the seventeenth century.

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.

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.

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

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

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.

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.

Study of popular games, toys, and puzzles using recursions, counting techniques, graph theory, group theory, probability, Markov chains, and other mathematical tools.

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.

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

Topics selected from affine, hyperbolic, spherical, elliptic, Euclidean or projective geometry.

Congruences, quadratic reciprocity, Diophantine equations; applications.

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.

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

Geometry of curves and surfaces, curvature, first and second fundamental forms, minimal surfaces, use of MAPLE.

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

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

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

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

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

Lecture course in an area of applied mathematics. May be repeated for credit if topics are different.

Lecture course in an area of pure mathematics. May be repeated for credit if topics are different.

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

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

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

Workshop for teachers of the Advanced Placement (AP) Statistics course. Inference, design of experiments, exploratory data analysis, simulation, probability, investigative tasks, and AP Statistics exam overview.

A brief overview of statistical reasoning using both descriptive and inferential statistical methods. Special focus on the Advanced Placement statistics course.

Workshop for teachers of introductory statistics. Overview of material just beyond the AP/introductory statistics curriculum, including simulation-based inference, multiple regression, ANOVA, statistical programming, and selected topics.

For current or future teachers of statistics. Combines theoretical framework and hands-on experience in understanding and developing statistical reasoning and thinking necessary for teaching an introductory statistics course. Ideas for addressing common student misconceptions will be addressed. Prerequisites: MAT 1230 or MAT 4310 equivalent.

Data summarization and display, distributions; binomial, Poisson, normal, t, chi-square and F, estimation, hypothesis testing, linear regression, correlation, statistical software packages.

ANOVA: multiple comparison procedures, contrasts, random and fixed effect models, transformations, experimental design, nested designs, randomized blocks, factorials, latin squares, analysis of covariance, multiple regression, correlation, statistical software packages.

Use SAS and R for data manipulation, presentation, and summarization. Topics include inputting/importing/exporting data cleaning and manipulation, and numerical and graphical summaries/analyses. Students will be introduced to simulations, SAS macro programming, and R functions.

Probability, random variables, univariate and multivariate distributions, mathematical expectation, Central Limit Theorem, Law of Large Numbers.

Sampling, estimation, hypothesis testing, decision theory, least squares, regression, analysis of variance, Bayesian statistics.

Linear regression, correlation, multiple regression, weighted least squares, residuals and influence diagnostics, model building, variable selection, nonlinear regression.

Multivariate normal distribution, principal component analysis, Hotelling T2 test, discriminant function analysis, multivariate analysis of variance, covariance and repeated measurements, canonical correlation analysis, factor analysis, claffication and cluster analysis.

Prior distributions, Posterior distributions, Conjugate priors, the Metropolis-Hastings algorithm, the Gibbs sampler, Markov chain Monte Carlo, Convergence diagnostics, Credible Intervals Hierarchical modeling, Differences between Bayesian and frequentist inference.

Analysis of general linear models, fixed and random effects, variance components, unbalanced data.

Estimation, maximum likelihood, weighted least squares, log- linear models, logistic regression.

Completely randomized, randomized block, latin square, nested, split plot, balanced incomplete block and crossover designs, factorials, systems of confounding, fractional factorials and response surface designs.

Applications of regression analysis, analysis of variance, multivariate data analysis, presentation of results, statistical graphics, interpretation of results, issues relevant to the practice of statistical consulting. Analysis of a selected dataset, with written report and accompanying presentation required. Must have completed 24 credits in the Applied Statistics Program.

Industrial applications of statistical techniques, Deming's 14 points, Ishikawa's charting techniques, control charts for attributes and variables, acceptance sampling, military standards, process capability studies, introduction to Taguchi designs.

Frequency domain approaches to the analysis of time series, autoregressive models, forecasting.

Analysis of survival of lifetime data; life tables and Kaplan-Meier estimation, survival analysis with covariates, Cox proportional hazard models.

Basic principles of clinical trials, rationale, history, organization and planning, randomization and ethical issues, sample size determination, study designs: parallel, crossover, repeated measurements, statistical analysis of clinical trials data, interim analyses.

Longitudinal data plots, univariate and multivariate repeated measures ANOVA, generalized linear models, response profile models, linear mixed models, generalized linear mixed models, residual diagnostics, missing data, clinical trials applications, analysis in SAS.

One sample rank tests, estimates and confidence intervals, paired replicates, two sample rank tests, nonparametric correlation and regression techniques.

Sampling and survey methodology, basic sampling theory, random and stratified sampling, systematic sampling errors, estimation procedures.

Monte Carlo Simulation, Markov chains, generating functions, random walk models, gambler's ruin problem, queuing processes, Poisson processes, Gaussian processes.

Data preparation, Predictive modeling via decision trees, regression models and neural network, Model assessment and implementation, Pattern discovery, Association rule discovery, Text mining.

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.

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

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

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.

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.

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.

The design and analysis of experiments, probability distributions, basic statistical inference, analysis of variance, block designs and factorial designs. For social and natural science majors.

Lecture course on a topic from Statistics. May be repeated for credit if topics are different.

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.

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

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.

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.

Analysis of categorical response data, including contingency tables, logistic regression, multinomial logistic regression, and generalized linear models.

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

Time series modeling, forecasting, and diagnostics, with an emphasis on applications from business and the sciences.

Regression methods for analyzing medical and biological data, including multiple regression, logistic regression, survival modeling, and longitudinal mixed modeling.

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

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

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

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.

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

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

ANOVA: multiple comparison procedures, contrasts, random and fixed effect models, transformations, experimental design, nested designs, randomized blocks, factorials, latin squares, analysis of covariance, multiple regression, correlation, statistical software packages.

Methodologies for analyzing genetic data, including genome-wide association studies, population genetics, and phylogenetics; emphasis on discussing recent research literature in these areas.

Artificial neural networks, convolutional neural networks, recurrent neural networks, self-organizing maps, autoencoders.