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10-24-2009, 05:08 PM
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Modern Differential Geometry in Gauge Theories: YangMills Fields, Volume II

Anastasios Mallios, "Modern Differential Geometry in Gauge Theories: YangMills Fields, Volume II"
Birkhäuser Boston | 2009 | ISBN: 0817643796 | 234 pages | PDF | 2,2 MB




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Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications.


Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Volume 1 focused on Maxwell fields. Continuing in Volume II, the author extends the application of his sheaf-theoretic approach to Yang–Mills fields in general. The important topics include: cohomological classification of Yang–Mills fields, the geometry of Yang–Mills A-connections and moduli space of a vector sheaf, as well as Einstein's equation in vacuum.


The text contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity.
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10-24-2009, 05:10 PM #2

Judith A. Muschla, Gary Robert Muschla, "The Math Teacher's Book of Lists"
Prentice-Hall | 1994 | ISBN: 0131803573 | 377 pages | Djvu | 4,6 MB



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This unique information source and time-saver for mathematics teachers provides over 300 useful lists for developing instructional materials and planning lessons for elementary and secondary students. Some of the lists supply teacher background; others are to copy for student use, many give new twists to studied topics.

For quick access and easy use, the lists are numbered consecutively, organized into eight sections focusing on eight different areas of math, and printed in a big 8 ½" x 11" format for easy photocopying of any lists as many times as you need it. Here's just an overview of the ready-to-use lists you'll find in each section:

I. NUMBERS presents 49 lists featuring number theory and operations from "Classification of Real Numbers" and rules for various operations to "Bases" ... "Big Numbers ... "Mathematical Signs and Symbols" ... and "Problem-Solving Strategies."
II. MEASUREMENT includes over 30 lists, ranging from "Things That Measure" and "Measurement Abbreviations" to lists of metric units and customary US units, "Temperature Formulas" ... "Measurement of Time" ... and "US MoneyCoins and Bills."
III. GEOMETRY offers more than 50 lists such as "Facts about Pairs of Angles" ... "Figure Number Formulas" ... "Basic Figures in Geometry" ... "Properties of Similar Triangles" ... "Pythagorean Triples" ... "Solids" ... and "Formulas for Surface Area."
IV. ALGEBRA gives you over 40 lists from "How to Express Operations Algebraically" ... "Order of Operations" ... and "Algebraic Grouping Symbols," to "The Absolute Facts on Absolute Value" ... "Powers and Boots" ... "Types of Functions" ... and "Conjugate Complex Numbers."
V. TRIGONOMETRY CALCULUS provides more than 30 lists for example, "The Quadrant Signs of the Functions" ... "How to Express Angles in Circular Measure" ... "Graphs of the Inverse Trigonometric Functions" ... "Limits" ... and "Curve Drawing."
VI. MATH IN OTHER AREAS offers 38 lists that tie math to other content areas, such as "Probability and Odds" ... "Ways People Are Paid" ... "How to Balance a Checkbook" ... "Stock Market Words" ... "How to Read the New Food Label" ... "Physical Activities and Calorie Expenditure" ... and "The Number in Popular Sports."
VII. POTPOURRI features 19 lists that show how math is used in everyday life activities, for example, "Careers in Mathematics" ... "World Firsts" ... "Numbers and Symbolism" ... "Tricky Math Problems" ... and "Math and Superstition."
VIII. TEACHER' REFERENCE presents 26 lists to help you in various aspects of your work including "Steps to Help Students Develop Problem-Solving Skills" ... "How to Run a Cooperative Math Class" ... "Math Bulletin Board Ideas" ... "Steps for Evaluating Portfolios" ... and "How to Have a Parents' math Night."
You'll also find a special section at the end with over 20 full-page activity sheets that reinforce the concepts and skills presented in the lists. "Nets for Regular Polyhedra," for example, involves students in making models so they can examine their properties.

In Short, The Math Teacher's Book of Lists gives you an unparalleled source of good examples, key words, teachable content, and teaching ideas that might otherwise take many years and much effort to compile! It will save you time and help you instill in your students a genuine appreciation for the world of mathematics.
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