Introduction To Statistics Mendenhall Pdf 31 ((FULL))
Topics in mathematics that every educated person needs to know to process, evaluate, and understand the numerical and graphical information in our society. Applications of mathematics in problem solving, finance, probability, statistics, geometry, population growth. Note: This course does not cover the algebra and pre-calculus skills needed for calculus.
introduction to statistics mendenhall pdf 31
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Various topics that might enrich an elementary school mathematics program, including probability and statistics, the integers, rational and real numbers, clock arithmetic, diophantine equations, geometry and transformations, the metric system, relations and functions. For Pre-Early Childhood and Pre-Elementary Education majors only.
Basic calculus with applications to problems in the life and social sciences. Functions and graphs, the derivative, techniques of differentiation, curve sketching, maximum-minimum problems, exponential and logarithmic functions, exponential growth and decay, and introduction to integration.
Continuation of MATH 127. Elementary techniques of integration, introduction to differential equations, applications to several mathematical models in the life and social sciences, partial derivatives, and some additional topics.
Descriptive statistics, elements of probability theory, and basic ideas of statistical inference. Topics include frequency distributions, measures of central tendency and dispersion, commonly occurring distributions (binomial, normal, etc.), estimation, and testing of hypotheses.
This course is about how to write and use computer code to explore and solve problems in pure and applied mathematics. The first part of the course will be an introduction to programming in Python. The remainder of the course (and its goal) is to help students develop the skills to translate mathematical problems and solution techniques into algorithms and code. Students will work together on group projects with a variety applications throughout the curriculum.
An introduction to functions of a complex variable. Topics include: Complex numbers, functions of a complex variable and their derivatives (Cauchy-Riemann equations). Harmonic functions. Contour integration and Cauchy's integral formula. Liouville's theorem, Maximum modulus theorem, and the Fundamental Theorem of Algebra. Taylor and Laurent series. Classification of isolated singularities. Evaluation of Improper integrals via residues. Conformal mappings.
This is a rigorous introduction to some topics in mathematics that underlie areas in computer science and computer engineering, including: graphs and trees, spanning trees, colorings and matchings, the pigeonhole principle, induction and recursion, generating functions, and (if time permits) combinatorial geometry. The course integrates mathematical theories with applications to concrete problems from other disciplines using discrete modeling techniques. Small student groups will be formed to investigate a modeling problem independently, and each group will report its findings to the class in a final presentation. Satisfies the Integrative Experience for BS-Math and BA-Math majors.
This course is a proof-based introduction to elementary number theory. We will quickly review basic properties of the integers including modular arithmetic and linear Diophantine equations covered in Math 300 or CS250. We will proceed to study primitive roots, quadratic reciprocity, Gaussian integers, and some non-linear Diophantine equations. Some important applications to cryptography will be discussed.
This is an introduction to the history of mathematics from ancient civilizations to present day. Students will study major mathematical discoveries in their cultural, historical, and scientific contexts. This course explores how the study of mathematics evolved through time, and the ways of thinking of mathematicians of different eras - their breakthroughs and failures. Students will have an opportunity to integrate their knowledge of mathematical theories with material covered in General Education courses. Forms of evaluation will include a group presentation, class discussions, and a final paper. Satisfies the Integrative Experience requirement for BA-MATH and BS-MATH majors.
This course is an introduction to mathematical analysis. A rigorous treatment of the topics covered in calculus will be presented with a particular emphasis on proofs. Topics include: properties of real numbers, sequences and series, continuity, Riemann integral, differentiability, sequences of functions and uniform convergence.
The course will start with the study of transport equations, and an introduction to and classification of second-order partial differential equations and their applications. Subsequently, we will proceed to examine in more detail the wave equation, heat equation and Laplace equation. For instance, we will touch upon the D'Alembert solution to the wave equation, the solution of the heat equation, the maximum principle, energy methods, separation of variables, Fourier series and Fourier transform methods, as well as operator eigenvalue problems, starting with one spatial dimension and then considering generalizations of some of these ideas to higher dimensions.
This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing financial instruments, or "derivatives." The central topic will be options, culminating in the Black-Scholes formula. The goal is to understand how the models derive from basic principles of economics, and to provide the necessary mathematical tools for their analysis.
A practical overview of computational methods used in science, statistics, industry, and machine learning. Topics will include: an introduction to python programming and software for scientific computing such as NumPy and LAPACK, numerical linear algebra, optimization and root-finding, approximation of functions by splines and trigonometric polynomials, and the Fast Fourier Transform. Applications may include regression problems in statistics, audio and image processing, and the calculation of properties of molecules. Homework will be assigned frequently. Each assignment will involve both mathematical theory and python programming. There will be no exams. Instead, each student will pursue an open-ended project related to a topic discussed in class.
This proof-based course covers the fundamentals of linear optimization and polytopes and the relationship between them. The course will give a rigorous treatment of the algorithms used in linear optimization. The topics covered in linear optimization are graphical methods to find optimal solutions in two and three dimensions, the simplex algorithm, duality and Farkas' lemma, variation of cost functions, an introduction to integer programming and Chvatal-Gomory cuts. The topics covered simultaneously in polytopes are two- and three-dimensional polytopes, f-vectors, equivalence of the vertex and hyperplane descriptions of polytopes, the Hirsch conjecture, the secondary polytope, and an introduction to counting lattice points of polytopes.
This course is an introduction to differential geometry, where we apply theory and computational techniques from linear algebra, multivariable calculus and differential equations to study the geometry of curves, surfaces and (as time permits) higher dimensional objects.
This course is an introduction to the fundamental principles of statistical science. It does not rely on detailed derivations of mathematical concepts, but does require mathematical sophistication and reasoning. It is an introduction to statistical thinking/reasoning, data management, statistical analysis, and statistical computation. Concepts in this course will be developed in greater mathematical rigor later in the statistical curriculum, including in STAT 515, 516, 525, and 535. It is intended to be the first course in statistics taken by math majors interested in statistics. Concepts covered include point estimation, interval estimation, prediction, testing, and regression, with focus on sampling distributions and the properties of statistical procedures. The course will be taught in a hands-on manner, introducing powerful statistical software used in practical settings and including methods for descriptive statistics, visualization, and data management.
This course provides a calculus-based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling) and the beginning of statistical inference (continued in Stat516). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, probability inequalities, the central limit theorem, the Poisson approximation, and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals. 076b4e4f54