This work is an outline of the main definitions and theorems of modern mathematics. It is intended as a reference for non-mathematicians whose work requires knowledge and use of advanced mathematical techniques, as well as a guide for those intimidated by the proliferation of nomenclature and notation. The material is arranged pedagogically, beginning with first principles and building new definitions on top of prior ones. This is not a math textbook. It is no substitute for a disciplined and proof-based study of mathematics.
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