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An Introduction to Advanced Mathematics

An Introduction to Advanced MathematicsM. YotovDecember 9, 2017 For .. Y ou Know Who!1 These Notes constitute a version of the courseMAA 3200 Introduction to Advanced Mathematicstaught by the author at the Department of Mathematics and Statistics of FIU. The concepts ofclasses, sets, relations, and functions are introduced and studied with rigour. Care is taken in moti-vating the Introduction of the Zermelo-Fraenkel axioms. The natural numbers and the principle of(finite) mathematical induction are discussed in detail. The integer, rational, and real numbers areconstructed and thoroughly discussed. As a brief Introduction to Advanced Calculus, the classicaltopology, convergent sequences of real numbers, and continuity of real valued function of a realvariable are studied. The Bolzano- weierstrass Theorem, Intermediate Value Theorem, and weier - strass s Theorem are send comments and corrections to the author at.

The Bolzano-Weierstrass Theorem, Intermediate Value Theorem, and Weier-strass’s Theorem are proved. Please send comments and corrections to the author at yotovm@ u.edu . c 2016 M.Yotov. Single paper copies for noncommercial personal use may be made without explicit permission from the copyright holder. 2.

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