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There is no quick way around the need for prerequisite knowledge. When King Ptolemy asked for an easier way of learning mathematics, Euclid is famously said to have replied, "there is no royal road to geometry". Some background reading is expected when learning a new mathematical subject, and different readers will have greatly different needs ...
In order to enhance the attractiveness of this book as a textbook, we have included worked-out examples at appropriate points in the text and have included lists of exercises for Chapters 1 — 9. These exercises range from routine problems to alternative proofs of key theorems, but containing also material going beyond what is covered in the text.
The term workbook is also used to describe other compilations of questions that require the reader to complete scratch-work when dealing with higher-level mathematics. In industry, they may be customized interactive manuals which are used to help provide structure to an otherwise complex problem. The workbook format can also be used as a ...
An anonymous manuscript dated 1570 [7] said: "Multiplication is vexation, / Division is as bad; / The Rule of three doth puzzle me, / And Practice drives me mad." Charles Darwin refers to his use of the rule of three in estimating the number of species in a newly discerned genus. [ 8 ]
There are various ways of approaching the subject, each of which focuses on a slightly different flavor of Chern class. The original approach to Chern classes was via algebraic topology: the Chern classes arise via homotopy theory which provides a mapping associated with a vector bundle to a classifying space (an infinite Grassmannian in this case).
In the particular case that Y equals A 1 the regular maps f:X→A 1 are called regular functions, and are algebraic analogs of smooth functions studied in differential geometry. The ring of regular functions (that is the coordinate ring or more abstractly the ring of global sections of the structure sheaf) is a fundamental object in affine ...