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University of New Hampshire 1

at least through multivariate , and must have of basic AND and basic linear at the undergraduate level. STATISTICS (MATH) Applicants for the of master of for teachers (M.S.T.) usually possess a background equivalent to at least a minor in mathematics and must have either: completed courses Degrees Offered: Ph.D., M.S., M.S.T., sufficient for certification, have three years teaching experience, or Graduate Certificate currently hold a full- teaching position. This program is offered in Durham. https://ceps.unh.edu/mathematics-statistics

The mission of the Mathematics and Statistics program is twofold: to prepare students for a variety of exciting and rewarding career Programs opportunities in , industry, government and the teaching professions; and to advance forefront knowledge in the of pure • Mathematics (Ph.D.) mathematics, , statistics, and mathematics • (Ph.D.) education through world- cutting-edge . • Statistics (Ph.D.) The Department of Mathematics and Statistics offers programs • Mathematics (M.S.) leading to a master of science for teachers (M.S.T.) in mathematics, • Mathematics: Applied Mathematics (M.S.) master of science in mathematics, master of science in mathematics • Mathematics (M.S.T.) with an option in applied mathematics, and a master of science in • Statistics (M.S.) statistics. Students in the master of science in applied mathematics may choose approved courses in the doctoral program in Integrated Applied • Industrial Statistics (Graduate Certificate) Mathematics as part of their MS program.

The department also offers doctor of programs in Courses mathematics, integrated applied mathematics, statistics, and mathematics education. Mathematics & Statistics (MATH) In general, the master's degree programs offer the student a high level MATH 801 - Exploring Mathematics for Teachers I of preparation for professional employment as well as appropriate Credits: 3 preparation for programs leading to the Ph.D. The Ph.D. programs prepare Provides prospective elementary teachers with the opportunity to the student primarily for a career in university teaching and research. explore and master involving systems and operations, and . Additional topics may include , The graduate programs have limited enrollment, allowing students to , and algebraic thinking. Mathematical reasoning, problem work closely with faculty members in their areas of expertise. Research solving, and the use of appropriate manipulatives and are within the department is currently being conducted in many areas of integrated throughout the course. Readings, class discussions, and the mathematical , including: , Hilbert , assignments focus on mathematics content as well as applicable geometric theory, , theory, commutative of learning, curriculum resources, and and national algebra, , quantum groups, categories, recommendations. The course models instructional techniques that can , , , theory, nonlinear be adapted to the elementary curricula. Credit offered only to M.Ed. and dynamics and chaos, , chaotic prediction and control, M.A.T., certificate students, and in-service teachers. (Not offered for credit spectral analysis, asymptotic analysis, mathematical , if credit is received for MATH #821 or MATH 823.) environmental statistics, spatial and spatio-temporal statistics, Bayesian Prerequisite(s): (EDUC 500 with a minimum grade of D- or EDUC 935 with and computational statistics, in statistics, teaching and a minimum grade of B-). learning of K-12 mathematics and statistics, teaching and learning of Equivalent(s): MATH 601, MATH #821, MATH 823 undergraduate mathematics and statistics, mathematical curriculum and Grade Mode: Letter Grade teacher education, and calculus learning. MATH #821 - Number Systems for Teachers Additionally, a graduate certificate in industrial statistics is offered. Credits: 3 Ways of representing , relationships between numbers, number systems, the meanings of operations and how they relate to one another, Admission Requirements and computation with number systems as a foundation for algebra; Applicants for the M.S. and Ph.D. degrees in must episodes in history and development of the number system; and have completed significant undergraduate coursework in mathematics, examination of the developmental and learning trajectory as preferably in algebra, analysis, and topology. children learn number concepts. Credit offered only to M.Ed., M.A..T., Elementary Math Specialist certificate only students, and in-service Applicants for the M.S. with applied mathematics option must have teachers. Not offered for credit if credit received for MATH 621. completed significant coursework in analysis or applied analysis. Equivalent(s): MATH 621 Applicants for the M.S. in statistics will typically have an undergraduate Grade Mode: Letter Grade degree in the mathematical, physical, biological, or social sciences or in . Applicants must have completed mathematical coursework 2 Mathematics and Statistics (MATH)

MATH 823 - Statistics and Probability for Teachers MATH 836 - Advanced Statistical Methods for Research Credits: 3 Credits: 3 An introduction to probability, descriptive statistics and data analysis; An introduction to multivariate statistical methods, including principal exploration of , data representation and modeling. components, analysis, , , Descriptive statistics will include measures of central tendency, multidimensional scaling, and MANOVA. Additional topics include , distributions and regression. Analysis of generalized linear models, general additive models, depending on the requiring hypothesizing, experimental design and data gathering. Credit interests of class participants. This course completes a grounding offered only to M.Ed., M.A..T., Elementary Math Specialist certificate only in modern applications of statistics used in most research applications. students, and in-service teachers. Not offered for credit if credit received The use of statistical software, such as JMP, S PLUS, or R, is fully for MATH 623. integrated into the course. Prerequisite(s): (MATH 621 with a minimum grade of D- or MATH #821 Prerequisite(s): (MATH 835 with a minimum grade of B- or MATH 839 with a minimum grade of B-). with a minimum grade of B-). Equivalent(s): MATH 623 Grade Mode: Letter Grade Grade Mode: Letter Grade MATH 837 - Statistical Methods for Quality Improvement and Design MATH 831 - Mathematics for Geodesy Credits: 3 Credits: 3 Six Sigma is a popular, data-focused methodology used worldwide by A survey of topics from undergraduate mathematics designed for organizations to achieve continuous improvement of their existing graduate students in engineering and science interested in applications processes, products and services or to design new ones. This course to geodesy and Sciences. Topics include essential elements from provides a thorough introduction to the Six Sigma principles, methods, , geometry of , and statistics, and applications for continuous improvement (DMAIC process) and an , discrete Fourier transforms and software, filtering overview of Design for Six Sigma (DFSS). Both manufacturing and non- applications to tidal data. manufacturing (transactional Six Sigma) applications will be included. Prerequisite(s): (MATH 645 with a minimum grade of D- or MATH 645H Emphasis is placed on the use of case studies to motivate the use of, as with a minimum grade of D- or MATH 762 with a minimum grade of D- or well as the proper application of, the Six Sigma methodology. Formal Six MATH 862 with a minimum grade of B-). Sigma Green Belt certification from UNH may be attained by successfully Grade Mode: Letter Grade completing TECH 696. Students must have completed a calculus-based MATH 832 - Introduction to the R Software introductory statistics course. Credits: 1 Grade Mode: Letter Grade This course provides a basic introduction to the open-sources statistical MATH 838 - Data Mining and Predictive Analytics software R for students who have never used this software or have never Credits: 3 formally learned the basics of it. Topics include: Numeric , An introduction to supervised and unsupervised methods for exploring simple and advanced , object management and work-, large data sets and developing predictive models. Unsupervised methods RStudio, user-contributed packages, basic programming, writing of include: market basket analysis, principal components, clustering, functions, statistical modeling and related graphs, distributed computing, and variables clustering. Important statistical and machine learning reproducible research and document production via markup language. methods (supervised learning) include: Classification and Regression Cr/F. Tress (CART), Random Forests, Neural Nets, Vector Machines, Equivalent(s): MATH 859 and Penalized Regression. Additional topics focus Grade Mode: on metamodeling, validation strategies, bagging and boosting to improve MATH 835 - Statistical Methods for Research prediction or classification, and ensemble prediction from a of diverse Credits: 3 models. Required case studies and projects provide students with This course provides a solid grounding in modern applications of experience in applying these techniques and strategies. The course statistics to a wide range of disciplines by providing an overview of the necessarily involves the use of statistical software and programming fundamental concepts of and analysis, including t- languages. Students must have completed a calculus-based introductory tests and confidence intervals. Additional topics include: ANOVA, multiple statistics course. , analysis of cross classified categorical data, logistic Grade Mode: Letter Grade regression, nonparametric statistics and data mining using CART. The MATH 839 - Applied Regression Analysis use of statistical software, such as JMP. S PLUS, or R, is fully integrated Credits: 3 into the course. Statistical methods for the analysis of relationships between response Grade Mode: Letter Grade and input variables: , multiple regression analysis, residual analysis , multi-collinearity, nonlinear fitting, categorical predictors, introduction to analysis of variance, analysis of covariance, examination of validity of underlying assumptions, logistic regression analysis. Emphasizes real applications with use of statistical software. Students must have completed an introductory statistics course. Grade Mode: Letter Grade University of New Hampshire 3

MATH 840 - I MATH 845 - Foundations of Applied Mathematics I Credits: 3 Credits: 3 First course in design of experiments with applications to quality An introduction to Partial Differential (PDEs) and associated improvement in industrial manufacturing, engineering research mathematical methods and the analytical foundation for applied and development, or research in physical and biological sciences. mathematics. Topics include: PDE classification, superposition, Experimental factor identification, statistical analysis and modeling , orthonormal functions, completeness, of experimental , randomization and blocking, full convergence, Fourier , Sturm-Liouville eigenvalue problems, and designs, random and mixed effects models, replication and sub- eigenfunctions. Methods are introduced for the analysis and solution strategies, fractional factorial designs, response methods, of boundary value problems, in particular, the Heat, , and Laplace mixture designs, and screening designs. Focuses on various treatment equations. Students are required to have a mastery of differential structures for designed experimentation and the associated statistical equations and ordinary differential equations. analyses. Use of statistical software. Students must have completed an Grade Mode: Letter Grade introductory statistics course. MATH 846 - Foundations of Applied Mathematics II Grade Mode: Letter Grade Credits: 3 MATH 841 - An introduction to special functions, asymptotic analysis, and transform Credits: 3 methods applied to partial differential equations. Topics include: Explorations of models and data-analytic methods used in medical, Boundary value problems in cylindrical coordinates, the Bessel biological, and reliability studies. Event-time data, censored data, and Bessel functions, Fourier-Bessel expansions in cylindrically reliability models and methods, Kaplan-Meier estimator, proportional symmetric spatial domains, the , the , hazards, Poisson models, loglinear models. The use of statistical Cosine and Transforms, problems on semi-infinite intervals, and software, such as SAS, JMP, or R, is fully integrated into the course. Asymptotic Analysis. Students are required to have a mastery of Prereq: MATH 839. (Offered in alternate years.) differential equations and ordinary differential equations. Grade Mode: Letter Grade Grade Mode: Letter Grade MATH 843 - Analysis MATH 847 - Introduction to Nonlinear Dynamics and Chaos Credits: 3 Credits: 3 An introduction to univariate time series models and associated methods An introduction to the mathematics of chaos and nonlinear dynamics. of data analysis and inference in the time and frequency domain. Topics include: linear and nonlinear systems of ordinary differential Topics include: Auto regressive (AR), moving average (MA), ARMA and equations; discrete maps; chaos; analysis; bifurcations; and ARIMA processes, stationary and non-stationary processes, seasonal computer simulations. Prereq: elementary differential equations; linear ARIMA processes, auto-correlation and partial auto-correlation functions, algebra; and multidimensional calculus. (Not offered every year.) identification of models, estimation of , diagnostic checking Grade Mode: Letter Grade of fitted models, forecasting, spectral density function, periodogram and MATH 853 - Introduction to Numerical Methods discrete Fourier transform, linear filters. parametric spectral estimation, Credits: 3 dynamic Fourier analysis. Additional topics may include wavelets and Introduction to mathematical and methods of . long memory processes (FARIMA) and GARCH Models. The use of A wide survey of approximation methods are examined including, statistical software, such as JMP, or R, is fully integrated in to the course. but not limited to, , root finding, numerical Offered in alternate years in the spring. integration, approximation of differential equations, and techniques used Prerequisite(s): (MATH 835 with a minimum grade of B- or MATH 839 in conjunction with linear systems. Included in each case is a study of the with a minimum grade of B-). accuracy and stability of a given technique, as well as its efficiency and Grade Mode: Letter Grade . It is assumed that the student is familiar and comfortable MATH 844 - Design of Experiments II with programming a high-level computer language. (Also offered as Credits: 3 CS 853.) Second course in design of experiments, with applications in quality Equivalent(s): CS 853 improvement and industrial manufacturing, engineering research and Grade Mode: Letter Grade development, research in physical and biological sciences. Covers MATH 855 - Probability with Applications experimental design strategies and issues that are often encountered in Credits: 3 practice complete and incomplete blocking, partially balanced incomplete Introduces the theory, methods, and applications of randomness and blocking (PBIB), partial confounding, intra and inter block information, random processes. Probability concepts, random , expectation, split plotting and strip plotting, repeated measures, crossover designs, discrete and continuous probability distributions, joint distributions, squares and rectangles, Youden squares, crossed and nested conditional distributions; -generating functions, convergence of treatment structures, variance components, mixed effects models, random variables. analysis of covariance, optimizations, filling designs, and modern Grade Mode: Letter Grade screening design strategies. Prerequisite(s): MATH 840 with a minimum grade of B-. Grade Mode: Letter Grade 4 Mathematics and Statistics (MATH)

MATH 856 - Principles of Statistical Inference MATH 872 - Combinatorics Credits: 3 Credits: 3 Introduces the basic principles and methods of statistical estimation (including planar graphs, graph coloring, Hamiltonian and model fitting. One- and two-sample procedures, and circuits, trees); principles (including , efficiency, likelihood methods, confidence regions, significance testing, , , inclusion-exclusion principle); and , nonparametric and re-sampling methods, decision related topics. theory. Grade Mode: Letter Grade Prerequisite(s): MATH 855 with a minimum grade of B-. MATH 876 - Grade Mode: Letter Grade Credits: 3 MATH 857 - Mathematical Optimization for Applications Induction and ; sentential logic; first- logic; completeness, Credits: 3 consistency, and decidability; recursive function. (Not offered every year.) This course introduces the foundations of mathematical optimization Grade Mode: Letter Grade and reinforces them via applications. The content includes convex MATH 883 - optimization, first and second-order methods, constrained problems, Credits: 3 , linear and quadratic programming, as well as discrete and Axiomatic set theory, including its history, Zermelo-Fraenkel , non-. Applications will focus on machine learning ordinal and cardinal numbers, consistency, independence, and methods but also include problems from engineering and operations undecidability. (Not offered every year.) research. Students are required to have programming proficiency in Grade Mode: Letter Grade MATLAB, R, Java, C, Python, and mastery of Calculus II. Equivalent(s): CS 857 MATH 884 - Topology Grade Mode: Letter Grade Credits: 3 Open sets, , , and continuous functions. , MATH 861 - compactness, separation axioms, and metrizability. Credits: 3 Prerequisite(s): (MATH 767 with a minimum grade of D- or MATH 867 This course establishes the axiomatic framework that underlies number with a minimum grade of B-). systems and similar mathematical structures, investigating basic Grade Mode: Letter Grade properties of groups, rings, fields and their homomorphisms. Grade Mode: Letter Grade MATH 888 - Complex Analysis Credits: 3 MATH 863 - Abstract Algebra II Complex functions, , limits, differentiability and Cauchy- Credits: 3 Riemann equations, elementary functions, Cauchy's and , This course extends the investigations of MATH 861 into more Taylor's and Laurent's series, residues, conformal mapping. specialized situations related to old and new problems in mathematics, Prerequisite(s): MATH 867 with a minimum grade of B-. such as the of solutions of polynomial equations. It presents Grade Mode: Letter Grade advanced properties of groups, rings, fields and their applications. Prerequisite(s): MATH 861 with a minimum grade of B-. MATH 896 - Topics in Mathematics and Statistics Grade Mode: Letter Grade Credits: 1-4 New or specialized courses not covered in regular course offerings. MATH 865 - Introduction to and Algebraic Repeat Rule: May be repeated for a maximum of 99 credits. Geometry Grade Mode: Letter Grade Credits: 3 Methods of determining solution sets of polynomial systems; affine MATH 898 - Master's Project varieties and their ideals; the 'algebra-geometry correspondence'; theory Credits: 1-6 and applications of Grobner bases. May be repeated to a maximum of 6 credits. IA (continuous grading). Cr/ Grade Mode: Letter Grade F. Repeat Rule: May be repeated for a maximum of 6 credits. MATH 867 - One-Dimensional Grade Mode: Credits: 3 Theory of limits, continuity, differentiability, integrability. MATH 899 - Master's Thesis Grade Mode: Letter Grade Credits: 1-6 May be repeated up to a maximum of 6 credits. Cr/F. MATH 869 - Introduction to Repeat Rule: May be repeated for a maximum of 6 credits. Credits: 3 Grade Mode: Introduction to the study of the geometric properties of and surfaces in 3-dimensional space. MATH 900 - Bridges from the Classroom to Mathematics Grade Mode: Letter Grade Credits: 1 An introduction to the goals of the MST program. Students have the MATH 870 - Foundations of opportunity to explore mathematical problems; to complete activities Credits: 3 that make connections between several , including and numbers, functions, congruences, the mathematical content in the MST degree program and the secondary reciprocity laws, quadratic forms, Diophantine equations, computational school mathematics classroom; and to participate in readings/on- number theory. Offered in alternate years. discussion on the nature of mathematics. Permission required. Cr/F. Grade Mode: Letter Grade Grade Mode: University of New Hampshire 5

MATH 902 - Classroom Mathematics Practicum MATH 916 - Theory of Numbers for Teachers Credits: 1 Credits: 3 A follow-up course to the six core mathematics content courses Divisibility and primes; congruences; quadratic reciprocity; number of the MST degree program. During the course, students choose a theoretic functions; Diophantine equations; perfect and amicable mathematical topic and/or set of concepts learned in one of the core numbers. MST courses and develop and teach a unit based on these concepts at Grade Mode: Letter Grade the or secondary school level. Permission required. Cr/F. MATH #917 - Mathematical and Repeat Rule: May be repeated up to 3 . Credits: 3 Grade Mode: Introduction to abstract mathematics with an emphasis on problem MATH 905 - Euclidean and non-Euclidean from a Synthetic solving and proof structure, methods and techniques. Content includes Perspective logic, set theory and basic number theory. Credits: 3 Grade Mode: Letter Grade An axiomatic development of geometry, beginning with finite geometries; MATH 918 - Analysis of Real Numbers emphasis is given to the fundamental concepts of Euclidean and non- Credits: 3 Euclidean geometries from a synthetic perspective. Permission required. An introduction to the fundamental concepts in real analysis that provide Grade Mode: Letter Grade the mathematical foundation for calculus. Content focuses on properties MATH 906 - Analytic and Transformational Geometry of sequences and series; properties of functions, including continuity, the Credits: 3 and the Riemann . Permission required. Fundamental concepts of transformational, , and Grade Mode: Letter Grade inversive geometry, including properties of conics and quadratic surfaces. MATH 925 - Problem Solving Seminar Permission required. Credits: 3 Grade Mode: Letter Grade A study of variety of problem solving strategies and techniques in the MATH 909 - Probability and Statistics for Teachers context of solving mathematical problems. Problems will emphasize Credits: 3 the connections between the core areas of algebra, geometry and Permutations and combinations; finite sample spaces; random variables; analysis. Other mathematical topics may be included. Typically taken in binomial distributions; statistical applications. conjunction with the Concluding Experience Problem Set. Cr/F. Grade Mode: Letter Grade Grade Mode: MATH #910 - Selected Topics in Mathematics Education for Teachers MATH 928 - Selected Topics in Mathematics for Teachers Credits: 1-4 Credits: 1-3 developments and issues in mathematics education; content, New or specialized topics not covered in the regular course offerings. curricula, methods, and psychology of teaching mathematics. Can be May be repeated for credit. repeated for credit. Grade Mode: Letter Grade Grade Mode: Letter Grade MATH 929 - Directed Reading MATH 913 - Graph Theory and Topics in Credits: 1-3 Credits: 3 A directed reading project on a selected topic in mathematics or Key theoretical and computational aspects of graph theory and related mathematics education, planned in collaboration with a faculty member. areas of discrete mathematics. Applications of graph theory as well as Repeat Rule: May be repeated for a maximum of 6 credits. current "open" problems are explored. Permission required. Grade Mode: Letter Grade Grade Mode: Letter Grade MATH 931 - Mathematical MATH #914 - Topology for Teachers Credits: 3 Credits: 3 Complex variables, differential equations, asymptotic methods, integral Fundamental concepts of elementary topology; network and transforms, special functions, linear vector spaces and matrices, Green's problems; sets, spaces, and transformations. functions, and additional topics selected from integral equations, Grade Mode: Letter Grade variational methods, numerical methods, tensor analysis, and MATH 915 - Algebraic Structures theory. Students are required to have a mastery of differential equations; Credits: 3 linear algebra; multidimensional calculus. An exploration of the structural similarities between and among Equivalent(s): PHYS 931 seemingly disparate number systems, beginning with counting numbers, Grade Mode: Letter Grade and progressing to , the rational numbers, the real numbers, and the complex numbers; and leading to a discussion of as an analogue and to fields as polynomial "quotients" through the basic concepts of splitting fields and . Permission required. Grade Mode: Letter Grade 6 Mathematics and Statistics (MATH)

MATH 941 - Bayesian and Computational Statistics MATH 951 - Algebra I Credits: 3 Credits: 3 Current approaches to Bayesian modeling and data analysis and Groups and their homomorphisms, products and sums, structure of related statistical methodology based on computational simulation. groups; rings and their homomorphisms, ideals, factorization properties. Fundamentals of Bayesian estimation and testing. Multi- Prerequisite(s): MATH 861 with a minimum grade of B-. level and hierarchical Bayesian modeling for correlated data. Introduction Grade Mode: Letter Grade to Markov chain Monte Carlo based estimation approaches such as MATH 952 - Algebra II the Gibbs sampler and the Metropolis-Hastings . Mastery of Credits: 3 intermediate statistics is required for this course, including: distributions, extensions; Galois theory; theory. discrete and continuous random variables, transformation of variables Prerequisite(s): MATH 951 with a minimum grade of B-. (calculus based), bivariate and multivariate normal distribution, maximum Grade Mode: Letter Grade likelihood estimation; working knowledge of linear regression and analysis of variance; basic linear algebra: vectors and matrices, linear MATH 953 - Analysis I spaces, , inverse of a matrix, positive definiteness. Credits: 3 Matrix-vector for linear regression and ANOVA. Measurable spaces and functions, measures, Lebesgue , Grade Mode: Letter Grade convergence . Prerequisite(s): MATH 867 with a minimum grade of B-. MATH 944 - Spatial Statistics Grade Mode: Letter Grade Credits: 3 Frequentist and Bayesian methods for estimation of characteristics MATH 954 - Analysis II measured in space (usually 2-dimensional ). Spatial Credits: 3 averaging. Spatial processes: models for clustering and inhibition. Cauchy theory and local properties of analytic functions, Riemann Cluster detection. Point referenced data: variogram estimation, Kriging, mapping theorem, representation theorems, harmonic functions. spatial regression. based data: spatial auto-regression, Markov Prerequisite(s): MATH 888 with a minimum grade of B-. random field models. Spatial regression models. Non-Gaussian response Grade Mode: Letter Grade variables. Hierarchical Bayesian spatial models and Markov chain Monte MATH 955 - Topology I Carlo methods. Multivariable spatial models. Mastery of intermediate Credits: 3 statistics including basics of maximum likelihood estimation; , , and quotient ; ; separation regression modeling including familiarity with matrix notation, basic and countability axioms; connectedness; compactness and concepts of calculus including partial is required for this compactifications; paracompactness, metrization, and course. completions. Grade Mode: Letter Grade Prerequisite(s): MATH 884 with a minimum grade of B-. MATH 945 - Advanced Theory of Statistics I Grade Mode: Letter Grade Credits: 3 MATH #956 - Topology II Introduction to the theory and practice of statistical modeling and Credits: 3 inference. Basic multivariate analysis: covariance and expectation, Chain complexes; of simplicial complexes, singular homology multivariate-normal and non-central chi-squared distributions, linear and and ; axiomatic homology; cup and cap products. quadratic forms. Basic inequalities for and expectations: Prerequisite(s): MATH 861 with a minimum grade of B- and MATH 884 Markov, Chebyshev, Jensen, and Cauchy-Schwartz. Basic decision with a minimum grade of B-. theory, sufficiency, minimal sufficiency, ancillarity and completeness, Grade Mode: Letter Grade Point estimation: method of moments, maximum likelihood, Bayesian MATH 958 - Foundations of Math Education procedures, likelihood procedures and information inequalities. Measures Credits: 1 of performance, notions of optimality, and construction of optimal Topics include: major issues and trends in mathematics education procedures in simple situations. Convergence in distribution and in research, the profession and infrastructure of mathematics education, probability. theoretical perspectives, cultural and historical aspects of mathematics Prerequisite(s): MATH 856 with a minimum grade of B-. education, and the research-practice interface. Examples span the K-16 Grade Mode: Letter Grade . MATH 946 - Advanced Theory of Statistics II Grade Mode: Letter Grade Credits: 3 MATH 959 - Introduction to Research Design in STEM Education Asymptotic statistical inference: consistency, asymptotic normality Credits: 3 and efficiency. Hypothesis testing: Neyman-Pearson lemma, uniformly This course provides an overview of research design including most powerful , generalized likelihood ration tests, Chi squared preliminary considerations that go into selecting a qualitative, goodness-of-fit tests, Wald tests and related confidence intervals, quantitative, or mixed methods design. Topics include the definition pivotal , optimality properties. Modern likelihood methods of the various approaches, developing research questions and/or (quasi, pseudo and composite). Algorithmic inference: Gibbs sampling, hypotheses, reviewing the literature, the use of theory, bootstrapping, simultaneous inferences in high-dimensional data and anticipating ethical issues, and developing writing strategies. data. Nonparametric and semiparametric estimation methods, Grade Mode: Letter Grade asymptotic estimation theory and large sample tests. Prereq: MATH 945; or permission. Grade Mode: Letter Grade University of New Hampshire 7

MATH 966 - Topics in Algebraic Topology I MATH 997 - Statistics Seminar Credits: 3 Credits: 1 An introduction to topics in algebraic topology. A seminar of weekly and bi-weekly meetings organized by the statistics Prerequisite(s): MATH #956 with a minimum grade of B-. Ph.D. students with supervision by a statistics faculty member. Repeat Rule: May be repeated for a maximum of 99 credits. Informal presentations of faculty members, students, and outside guest Grade Mode: Letter Grade presenters; also discussion of topics that are of mutual interest to its MATH 968 - Topics in Mathematics Education I participants. Dissertation proposal presentations. Seminar presentations Credits: 3 are open to the greater public. Statistics Ph.D. students are required A) The Teaching and Learning of Mathematics; B) Curriculum and History to enroll for at least 3 semesters. Attendance is mandatory by those in Mathematics Education. Topics selected from: of students who are enrolled in the seminar. Credits do not count towards knowledge applied to mathematics; theories of learning and teaching the Master's degree. Cr/F. mathematics; theoretical perspectives in research; mathematics Repeat Rule: May be repeated for a maximum of 6 credits. education research programs K-16; research methods for studying Grade Mode: mathematics teaching, learning, and curricula; theoretical frameworks MATH 998 - Reading Courses for curriculum development, implementation of new curricula, and Credits: 1-6 research on curricula; historical perspectives of research in mathematics A) Algebra; B) Analysis; C) ; D) Geometry; E) General education; the evolution and history or K-16 mathematics curricula both Topology; F) Algebraic Topology; G) Applied Mathematics; H) in United States and internationally. Versions A and B offered alternately. Mathematics Education; I) Probability and Statistics. Prerequisite(s): MATH 958 with a minimum grade of B-. Grade Mode: Letter Grade Repeat Rule: May be repeated for a maximum of 99 credits. MATH 999 - Doctoral Research Grade Mode: Letter Grade Credits: 0 MATH #969 - Topics in Probability and Statistics I Cr/F. Credits: 3 Grade Mode: Selected advanced topics from one or several of the following areas: probability, processes, design of experiments, , Faculty Bayesian theory and methods, spatial and spatio-temporal statistics, time series analysis, nonparametric statistics. Repeat Rule: May be repeated for a maximum of 99 credits. See https://ceps.unh.edu/directory/all for faculty. Grade Mode: Letter Grade MATH 973 - Topics in Operator Theory Credits: 3 Selected topics in operator theory. Prerequisite(s): MATH 863 with a minimum grade of B-. Repeat Rule: May be repeated for a maximum of 99 credits. Grade Mode: Letter Grade MATH 978 - Topics in Mathematics Education II Credits: 1-3 An exploration of an of research in mathematics education. Repeat Rule: May be repeated for a maximum of 99 credits. Grade Mode: Letter Grade MATH 979 - Research Topics in Statistics Credits: 3 An exploration of the main statistical issues and computational methods associated with research problems from such areas as survival analysis, reliability, latitudinal data, categorical data, spatio-temporal data, and industrial processes. Student term projects require: literature searches, presentation, use of modern statistical software, and written reports. May be repeated barring duplication of topic. Repeat Rule: May be repeated up to unlimited times. Grade Mode: Letter Grade