Precalculus mathematics including basic algebraic operations, equations, inequalities, complex numbers, graphs, functions, zeros of polynomials, systems of equations and matrices.

A continuation of MATH 1100 covering precalculus mathematics including trigonometric functions and their properties, trigonometric identities and equations, applications of trigonometry, vectors, polar coordinates, exponential and logarithmic functions and conic sections.

Review of topics from college algebra and trigonometry required for the calculus sequence. Emphasis on understanding functions including polynomials and rational functions, trigonometric functions, and exponential and logarithmic functions.

Concepts of mathematics for liberal arts students. Emphasis on understanding and appreciating concepts rather than developing computational skills. Topics include the historical development of ideas, role of abstraction, and relationship between different areas of mathematics is given precedence over performance of arithmetic and algebraic manipulations.

Mathematics of finance, including simple and compound interest, present and future value of ordinary annuities, sinking funds, and amortization schedules. Matrices, linear systems and linear programming. Combinatorics and elementary probability theory.

The basic concepts and techniques of differential and integral calculus. Applications and examples chosen primarily from economics, biology, the social and behavioral sciences and business.

Developmental lab for MATH 1400. Learning through active participation with other students in small group settings.

Fundamental concepts and techniques of differential and integral calculus, logarithmic, exponential and trigonometric functions, examples and applications from biology and medicine.

Functions of one variable, limits and continuity. The derivative and the definite integral with applications.

The transcendental functions. Techniques of integration including numerical methods. Elementary differential equations. Infinite sequences and series, Taylor Series. Not regularly offered.

Techniques of integration, including numerical methods. Applications of integrals, Taylor polynomials, analytic geometry and vectors. The differential and integral calculus of functions of several variables.

Fundamental theory and methods of statistics without calculus. Descriptive statistics, elements of probability theory, estimation, tests of hypotheses, regression, correlation, introduction to computer methods of statistical tabulation and analysis. Recommended for students seeking a general introduction to statistical concepts and not intended to be a final course in statistics for students who need a thorough working knowledge of statistical methods.

Fundamental theory and methods of statistics without calculus. Descriptive statistics, elements of probability theory, estimation, tests of hypotheses, correlation, regression, ANOVA, introduction to computer methods of statistical tabulation and analysis. Offered with a laboratory component and is recommended for students seeking a general introduction to statistical concepts. Students learn to compute various statistical measures - both with and without the aid of a computer. Not intended to be a final course in statistics for students who need a thorough working knowledge of statistical methods. May not be taken for credit by students who have received college credit for another probability or statistics course. As an Honors Program course, includes a more intensive research or project component.

Mathematical content and processes. Mathematical techniques and ways of thinking are used to enhance mathematical power. Multiple ways of organizing and analyzing data, reasoning and communication skills, and multiple problem-solving strategies are used to solve non-routine problems. Provides a framework for deepening and expanding elementary mathematical ideas.

Mathematical content and processes for teachers. Uses a problem solving approach. Integrates early mathematics content with teaching methods and learning theory. Provides a framework for in-depth study of number concept, meaning of place value, whole numbers, exponents, fractions, decimals, percent, ratios, and proportions. In-depth study of whole and rational number systems including analyses of algorithmic procedures for addition, subtraction, multiplication and division.

Mathematical content and processes for elementary and secondary school teachers. Uses a problem solving approach. Integrates mathematics content with teaching methods and learning theory. In-depth study of the growth of algebraic and geometric reasoning. Provides a framework for the meaningful understanding and teaching of integers, patterns, algebraic expressions, functions, equations, graphs, spatial visualization, polygons and polyhedra, similarity and congruence, conjectures and deductions in geometry, and mathematical modeling.

Introduction to set theory, logic, mathematics induction, finite state machines, graph theory, modular arithmetic, Boolean algebra, and coding theory. Applications in computer science are emphasized. May not be taken for credit by those who have completed MATH 2350.

Introduction to set theory, logic, mathematical induction, graph theory, modular arithmetic, and higher mathematical thinking through proof and applications. Mathematical proof is emphasized.

Improper integrals, infinite sequences, and series including the Taylor series. Other advanced topics in vector calculus and multivariable calculus such as Lagrange multipliers, Green's Theorem, Divergence Theorem, and Stokes Theorem.

Three-dimensional analytic geometry including parametric equations, vectors and vector functions. The differential and integral calculus of functions of several variables.

Methods and techniques applicable to first order, nth order, and systems of first order differential equations. Eigenvalues, eigenvectors, the Wronskian, Laplace transforms, linearization and phase portraits.

Methods and techniques for solving differential equations and systems of differential equations, with applications to biomedical and civil engineering. Restricted to students in BIEN or CEEN.

Basic concepts of supervised learning, simple linear regression, multiple linear regression, diagnostic analysis, model selection, logistic regression, classification and regression trees (CART), random forest and use of statistical software R.

N-dimensional vector spaces, bases and coordinate systems, linear transformations and matrices, systems of equations, characteristic values, applications to differential equations and geometry.

Functions of a complex variable. Laplace and Fourier transforms and applications. Introduction to the calculus of variations.

A initial course in visualizing and extracting information from data and models. Topics include introduction to Python or R, clustering, dimension reduction, regression and basis functions.

Project-based modeling. Focuses on using computational software R and Matlab in mathematics and statistics: plotting, version control, simple/useful data structures and basic data i/o. Topics include population dynamics, SIR models, agent-based models, linear regression, Monte Carlo techniques and principal component analysis.

Studies mathematical problems, examine their solutions and formulate general problem solving methods and techniques. Prepares students for the Putnam Mathematical Competition. S/U grade assessment.

Historical background, problems, curricular materials, and teaching procedures in the various areas of mathematics pertinent to the needs of a secondary school mathematics teacher. In addition, a three-hour time block on one day each week between 8 a.m. and 3 p.m. must be kept free for clinical experience.

Topics chosen primarily from geometry and calculus, taught from an advanced standpoint to enrich and deepen the student's understanding. Emphasis on alternative approaches, generalizations, historical contexts and connections with prior mathematical studies.

Topics closely related to the high school mathematics curriculum, chosen primarily from algebra and number theory, taught from an advanced standpoint to enrich and deepen the student's understanding. Emphasis on alternative approaches, generalizations, historical contexts and connections with prior mathematical studies. Course is offered for graduate credit only to students enrolled in MSST.

Sets, mappings, operations on sets, relations and partitions. A postulational approach to algebraic systems including semigroups, groups, rings and fields. Homomorphisms of groups and rings, number systems, polynomial rings.

A continuation of MATH 4120 with emphasis on groups, rings, fields and modules.

Limits and continuity, differentiability, Riemann integration. Topology of N-dimensional spaces.

Transformations of N-spaces, line and surface integrals, sequences and series, uniform convergence.

Complex numbers, analytic functions, differentiation, series expansion, line integrals, singularities and residues.

Topics selected from the following: development of the number system (need for irrational and complex numbers); development of geometry including the effects of the discovery of non-Euclidean geometry; limit concept; need for axiomatic structures; twentieth-century problems. Current mathematics research and place of mathematics in today's world.

Integers, unique factorization theorems, arithmetic functions, theory of congruences, quadratic residues, partition theory.

Modern postulational development of Euclidean and non-Euclidean geometries.

Topological spaces, mappings, metric spaces, product and quotient spaces. Separation axioms, compactness, local compactness and connectedness.

Existence and uniqueness theorems, linear and non-linear systems, numerical techniques, stability.

Fourier series, method of separation of variables, eigenfunction expansions, application of eigenfunctions to partial differential equations, Green's functions and transform methods.

Numerical solution of algebraic and transcendental equations, linear systems and the algebraic eigenvalue problem, interpolation and approximation, numerical integration, difference equations, numerical solution of differential equations and finite difference methods.

Construction and analysis of mathematical models from biological, behavioral and physical sciences.

Fundamental theorems describing the solution of linear programs and matrix games. Minimax, duality, saddle point property, simplex and specialized algorithms. Zero sum games, transportation and assignment problems, applications to economics.

Permutations and combinations, recurrence relations, inclusion and exclusion, Polya's theory of counting, graph theory, transport networks, matching theory.

Random variables, distributions, moment generating functions of random variables, various derived probabilistic models and applications. Recommended, with MATH 4710, for students in mathematics, engineering, and the physical and behavioral sciences.

Sampling theory and distributions, estimation and hypothesis testing, regression, correlation, analysis of variance, non-parametric methods, Bayesian statistics.

Probability, discrete and continuous distributions. Treatment of data, point and interval estimation, hypothesis testing. Large and small sample method, regression, non-parametric methods. An introductory applications-oriented course recommended for students who wish to acquire a basic understanding of statistical methods.

An introductory course to the statistical analysis software R. Topics include basic R programming, importing and cleaning data, data visualization, performing descriptive and inferential statistics, and creating reproducible reports.

Introduction to the statistics of life science and the use of mathematical models in biology. Data analysis and presentation, regression, analysis of variance, correlation, parameter estimation and curve fitting. Biological sequence analysis, discrete and continuous mathematical models and simulation.

Explores computational data analysis, an essential part of modern statistics. Introduces statistical computing including statistical programming, Monte Carlo simulation and parallel computing, smoothing and density estimation, implementing numerical methods in R (e.g., Expectation-Maximization algorithm), fitting models to data, statistical prediction and cross-validation.

Basic concepts of probability. Stationary time series. Autocorrelation and spectrum. Descriptive methods for time series data. ARMA and ARIMA models: estimation and forecasting. Identification and diagnostic techniques. Periodogram and spectral analysis. Use of software for time series analysis.

Object recognition and tracking for automatic machine vision systems. Topics include image representation, convolution, filter design, statistical deconvolution, discrete Fourier transform, automated object identification, text analysis, video object tracking and line tracing. Real-world applications such as object tracking within sequence of images, identification of item placement location in industrial settings, and autonomous lane departure identification. Additional topics may include object feature representations and statistical classification of objects. Computational implementation and examples utilize high-level programming language.

Basic concepts of statistical inference, simple linear regression, multiple linear regression, diagnostic analysis, selecting the best equation, stepwise methods, nonlinear regression and use of statistical software.

Bivariate, conditional and marginal distributions. The Bayesian philosophy, quantification of a priori information, prior, likelihood and posterior distributions. Bayesian linear models, posterior parameter estimation including maximum posteriori and marginal expectations. Topics may include numerical integration and Markov chain Monte Carlo techniques. Use of a high-level software package.

Topics selected from one of the various branches of mathematics or statistics. Specific topics to be announced in the Schedule of Classes.

Designed to initiate a selected group of qualified undergraduates into the techniques and discipline of scholarly research by concentrated work in a restricted field. Emphasis on critical reading and analysis of sources. Specific topics to be announced in the Schedule of Classes.

Students work full-time during fall or spring terms in a cooperative education program work assignment approved in advance by the department. Responsibilities include relevant academic content. Grading and credits are accomplished by registering for MATH 4988 during the following term. Fee. SNC/UNC grade assessment.

Grading for preceding co-op work assignment is accomplished by completing a report on the work assignment, a report on academic material related to the work assignment, and other materials as required. Grading is completed during the school term following the work assignment. May be taken more than once, but a maximum of two credits may be counted toward a major in the department.

Faculty-supervised, independent study/research of a specific area or topic in in Mathematics or Statistics.

Preparation of a thesis by approved students under the direction of an adviser from the staff.