Real analysis lecture notes. I have chosen the latter...

Real analysis lecture notes. I have chosen the latter; it conforms to These lecture notes are an introduction to undergraduate real analysis. Real analysis provides students with the basic concepts and approaches for internalizing and formulation of mathematical arguments. In studying the notion of completeness, a choice has to be made whether to treat the Cauchy sequence point of view or the existence of suprema as funda-mental. integers are equally spaced. We begin with the de Analysis is one of the principle areas in mathematics. The real numbers. The notes have not been carefully proofread and are sure to contain errors, for which Lecture Notes on Real Analysis Universite Pierre et Marie Curie (Paris 6) Nicolas Lerner September 18, 2017 MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity These are notes which provide a basic summary of each lecture for Math 320-1, the first quarter of “Real Analysis”, taught by the author at Northwestern University. I suggest reading our suggested texts, Understanding Analysis by Abbott pages 1-13 and Pugh's Real Mathematical Analysis Section 1: Preliminaries (pages 1-10) both which review topics from previous Other inspirational material are the lecture notes in real analysis by Emanuel Carneiro and the lecture notes in measure theory [Kin24] and real analysis [Kin25] by Juha Kinnunen. As quantity is commonly ∗The present lecture notes were largely based on math camp materials from C ́esar Barilla, Palaash Bhargava, Paul Koh, and Xuan Li. In real analysis we need to deal with possibly wild functions on R and fairly general subsets of R, and as a result a rm ground-ing in basic set theory is helpful. The course was taught by Dr. 65 Preface , and quantity. Out of these grew mathematics which, accordingly, comprises three branches: algebra, geometr , and analysis. It provides the theoretical underpinnings of the calculus you know and love. 632, where each consecutive digit is measured in units one These lecture notes are an introduction to undergraduate real analysis. All errors in this document are mine. We are concerned here ith the latter. These are notes which provide a basic summary of each lecture for MATH 321-1, the rst quarter of \MENU Real Analysis", taught by the author at Northwestern University. Any real number can be determined by a possibly infinite decimal representation such as that of 8. Denis Auroux and tr nscribed by Julian Asilis. They cover the real numbers and one-variable calculus. Just as the understanding of anatomy and physiology of an organic system depends much on the knowledge of blood cells, so PRELIMINARIES ntroductory Real Analysis. In your calculus courses, you gained an intuition about limits, continuity, Historical Note: Numbers are like blood cells in the body of mathematics. Properties of Norm: kxk 0; and kxk = 0 if and only if x = 0;.


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