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Mathematics : A Very Short Introduction

Mathematics : A Very Short Introduction


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The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?") It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.
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    1. Quartz - Silicon dioxide, or quartz, is the most common mineral in the earth's crust.
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    5. Calcite - Calcium carbonate is the major constituent of limestones and marbles.
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    Igneous rocks were once lava or magma, that is, a molten collection of minerals. The rate at which a lava or magma cools and solidifies influences rock texture, making it either fine, medium or coarse grained.

    7. Pumice - A light colored volcanic rock of rhyolitic composition; the texture results from bubbles formed by escaping gasses.
    8. Obsidian - Very rapid cooling caused this volcanic rock to have its glassy appearance.
    9. Basalt - This dark-colored, extrusive rock occurs as large flows, dikes, and sills.
    10. Rhyolite - Quartz and microcline are the major components of rhyolite.
    11. Andesite - The feldspar phenocrysts present in this light-colored, extrusive rock are the result of relatively slowly cooling lava at shallow depths.
    12. Granite - Feldspars and quartz made up the majority of this intrusive rock.


    Metamorphic rocks are rocks that have been changed (metamorphosed), by heat, pressure, and/or hydrothermal solutions. All three rock types can be metamorphosed.

    13. Mica Schist - This rock is a highly metamorphosed shale. All schists exhibit shistose structure; the generally parallel alignment of micaceous minerals.
    14. Slate - The low-grade metamorphism of shale results in slate.
    15. Quartzite - The "parent rock" of quartzite is quartz sandstone.
    16. Gneiss - All gneisses exhibit gneissic structure, that is, alternating layers of granular minerals and micaceous minerals.
    17. Garnet Schist - Shale that undergoes complete recrystallization due to metamorphism often contains high-pressure minerals such as garnet or andalusite.
    18. Marble - This rock results when limestones or certain dolomites are metamorphosed.


    Clastic sedimentary rocks are formed from layers of sediment (fragments of older, weathered rock) exposed to pressure. Other sedimentary rocks are of organic or chemical origin.

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    22. Conglomerate - Rounded pebbles cemented together with finer material make up this clastic, sedimentary rock.
    23. Breccia - is composed of re-consolidated angular fragments of gravel and/or sand size particles.
    24. Limestone - This sedimentary rock is made up primarily of calcite. Some limestones are chemical in origin, while other are clastic.

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