A Course In Algebraic Number Theory
This is a text for a basic course in algebraic number theory.
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Where in the World? Understanding Latitude and Longitude
Students play a grid-based game and devise clues to help classmates locate spots on the globe. In doing so, they come to recognize the value of using latitude and longitude for identifying locations.
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Predicting the Greening of Spring with Red Emperor Tulips
As the earth revolves around the sun in its annual cycle we experience seasonal change. Where will spring arrive first? What kind of patterns will we see as the wave of spring progresses? Start in the fall to think about these questions, and make some predictions. Then in the spring revisit your predictions with each Journey North news update and real-time map.
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Predicting the Route of the Monarch's Spring Migration
As the monarchs pour out of Mexico in the spring, where do you think they will arrive first, and what pathway do you suppose they will travel? Think about this question and make some predictions as you watch the butterflies spread throughout their northern breeding range. Then form a hypothesis as to why the monarchs travel where they do.
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Practice With Latitude and Longitude
In this lesson students find their own homes on Google maps and determine their precise latitude and longitude coordinates. They learn how to pinpoint the location visually and then move north, east, south, or west on the map by changing latitude and longitude values.
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Journey North Map Basics
This teacher's lesson explains how to access and use updated Journey North maps and related data.
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How Does a Migration Move Forward?
As students gather and review migration data, they calculate how fast and far a migration travels and ponder what influences its progression.
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Choosing Random Samples: Mapping Data Made Manageable
Students explore how to chose random samples as they map Journey North data.
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Time Tracker
Time Tracker teaches young children how to tell time using an analog clock. There are ten educational levels ranging from simple hour hand manipulation to complex double-digit subtraction. Upper level equations show a deactivated clock representing the "current" time in conjunction with the main active play clock representing the "configurable" time. Time Tracker uses dynamic leveling algorithm to adjust to the child's ability.
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Balance Keeper
Balance Keeper is an educational tool that helps children practice addition, subtraction, logical thinking, and basic algebra. The purpose of the game is to balance the scale by clicking and dragging weights. Complex problems consist of unknown mystery weights. Through deductive reasoning and trial and error techniques, a child can determine these unmarked weights. Balance Keeper implements fifteen skill levels that automatically adjust in difficulty. Mastering all the levels will definitely jum
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Generating Functionology
This book is about generating functions and some of their uses in discrete mathematics. The subject is so vast that the author has not attempted to give a comprehensive discussion, but to communicate some of the main ideas.
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Basics of Algebra and Analysis for Computer Science
Basics of Algebra and Analysis for Computer Science
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A=B
This book is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks.
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Cutting It Down to Nano
The challenge of this activity is to determine the number of times the student needs to cut the strip of paper in half in order to make it between zero and ten nanometers long.
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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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