Theory of functions of a real variable
I have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. The elements of the topology of metrics spaces are presented (in the nature of a rapid review) in Chapter I. The course itself consists of two parts: 1) measure theory and integration, and 2) Hilbert space theory, especially the spectral theorem
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Semi-Riemann Geometry and General Relativity
This book represents course notes for a one semester course at the undergraduate level giving an introduction to Riemannian geometry and its principal physical application, Einsteinâ€™s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus, preferably in the language of differential forms. This book covers the following topics: The principal curvatures; rules of calculus; Levi-Civita Connections; bundle of frames; connections on prin
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River City Project
As visitors to River City, students travel back in time, bringing their 21st century skills and technology to address 19th century problems. With funding from the National Science Foundation, we have developed an interactive computer simulation for middle grades science students to learn scientific inquiry and 21st century skills. River City has the look and feel of a video game but contains content developed from National Science Education Standards, National Educational Technology Standards, a
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Lie Algebras
This book addresses the following topics: The Campbell Baker Hausdor formula; sl(2) and its Representations; classical simple algebras; Engel-Lie-Cartan-Weyl; conjugacy of Cartan subalgebras; simple finite dimensional algebras; cyclic highest weight modules; Serre's theorem; Clifford algebras and spin representations; The Kostant Dirac operator; The center of U(g); and Chevalley's theorem.
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Dynamical Systems
This book addresses the following topics: Iterations and fixed points; bifurcations; conjugacy; space and time averages; the contraction fixed point theorem; Hutchinson's theorem and fractal images; hyperbolicity; and symbolic dynamics. 151 page pdf file.
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Saturn Educator Guide
This educators guide uses NASA's mission to Saturn (Cassini-Huygens) as real-world motivational context for learning fundamental, standards-based concepts in science. It includes six constructivist lessons, an FAQ, and a variety of connections to art, literature, and mythology.
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Population Growth
This series of activities explores the mathematical and environmental aspects of population growth. Using archived census and demographic data as well as up-to-the-minute population estimates from the U.S. Census Bureau, students will learn how to model population growth and study the implications of a changing population.
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Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis
Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis is a typed revision of the book originally published by Plenum Press in 1976 as Volume 2 in their series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.
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Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra
Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra is a typed revision that was originally published by Plenum Press in 1976 as Volume 1 in a series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.
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Open Data Kit
Open Data Kit (ODK) is a suite of tools to help organizations collect, aggregate and visualize their data. Our goals are to make open-source and standards-based tools which are easy to try, easy to use, easy to modify and easy to scale.
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Elementary Calculus: An Infinitesimal Approach (CA Textbook)
This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960. Robinson's modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits. This digital textbook was reviewed for its alignment with California content standards.
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Speed
This lesson reviews the basic "feel" we all have for what speed is and introduces the means for calculation and composition of various average speeds. Students calculate average speed of various snowmobiles and predict the outcome of a race.
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Virtual Worlds Almanac
This is a project to create a free, complete, up-to-date, and reliable guide to virtual worlds. So far we have 159 entries on virtual worlds written and edited by people from around the globe.
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Multivariable Calculus
This is a textbook for a course in multivariable calculus that has been used for the past few years at Georgia Tech.
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Complex Analysis
This is a textbook for an introductory course in complex analysis. It has been used for the undergraduate complex analysis course at Georgia Tech and at a few other places.
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Using Mars in a Teaching Plan
This area of the Web site is for teachers and those preparing lesson plans. It is our intention to provide enough material in enough subject areas to keep a class occupied for up to a whole term on a major project with "Exploring Mars" as its theme. That is not to say that this is how you should use the site, you may wish simply to pick something for a single lesson. That can be done too.
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Ask Dr. Math is a question and answer service for math students and their teachers. A searchable archive is available by level and topic, as well as summaries of Frequently Asked Questions (the Dr. Math FAQ)
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Mathematical Methods of Engineering Analysis
Mathematical Methods of Engineering Analysis
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Linear Programming: Foundations and Extensions
This book is an introductory graduate textbook on linear programming although upper-level graduate students and researchers will find plenty of material here that cannot be found in other books. It has also been used successfully to teach undergraduates majoring in Operations Research.
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From Stargazers to Starships
This is a self-contained book-on-the-web course on basic astronomy, Newtonian mechanics, the sun (and associated physics), and spaceflight and spacecraft. covers elementary astronomy, Newtonian mechanics, the Sun and related physics and spaceflight. Also included are a Spanish translation, 46 lesson plans, a short but complete math course (algebra + trig), teachers' guides, glossary, timelines, 345 questions (current tally) by users and their answers, over 100 problems to solve, and more.
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