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4434Interactive Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=85542
Quoted from the site: "Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, and more."Thu, 5 Jan 2006 00:00:00 -0800Cogent Mathematics
https://www.merlot.org/merlot/viewMaterial.htm?id=1113081
Cogent Mathematics is a fully peer-reviewed, open access, international scholarly journal with a mission to help researchers communicate with a global audience and interact with experts across the mathematics community and beyond. Cogent Mathematics considers original research articles in any of the following branches of mathematical and statistical research: Apllied and Interdisciplinary Mathematics; Computational Science; Pure Mathematics; and Statistics. Cogent Mathematics open access articles are distributed under a Creative Commons Attribution (CC-BY) 4.0 International license agreement.Sat, 26 Dec 2015 19:54:02 -0800A Short Course in Information Theory
https://www.merlot.org/merlot/viewMaterial.htm?id=89011
A Short Course in Information Theory.Tue, 8 May 2001 00:00:00 -0700Application of six sigma in Quality
https://www.merlot.org/merlot/viewMaterial.htm?id=79064
Talking about quality it is producing better with less waste of money and time. Applying the six sigma can help to reduce cost of production. Through this web anybody can apply to become menber of ASQ, for training and take online courses about quality and the updating of ISO 9000.Fri, 28 Mar 2003 00:00:00 -0800Elementary Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=905925
'This book is the second edition of an undergraduate level Real Analysis textbook formerly published by Prentice Hall (Pearson) in 2001. It is designed to be a user-friendly text that is suitable for a one year course. Additional elementary material designated asenrichment can be included for students with minimal background. Material designated asadvanced is intended for students with stronger backgrounds. Such topics are of a more sophisticated nature. The text consists of two volumes, each covering a semester course.'Mon, 3 Nov 2014 18:12:53 -0800FUNCTIONS DEFINED BY IMPROPER INTEGRALS
https://www.merlot.org/merlot/viewMaterial.htm?id=826915
'This is a supplement to the author’s Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute’s Open Textbook Initiative. It may be copied, modiﬁed, redistributed, translated, and built upon subject to the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. A complete instructor’s solution manual is available by email to wtrench@trinity.edu, subject to veriﬁcation of the requestor’s faculty status.'Introduction to Real Analysis: http://www.merlot.org/merlot/viewMaterial.htm?id=516759 NOTE: This book meets the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. http://www.aimath.org/textbooks/Wed, 15 Jan 2014 14:26:27 -0800How We Got from There to Here: A Story of Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=1071171
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.Wed, 14 Oct 2015 09:45:36 -0700How We Got from There to Here: A Story of Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=1221225
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.Thu, 11 Aug 2016 18:25:34 -0700Introduction to Mathematical Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=1221235
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.The textbook contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.Thu, 11 Aug 2016 18:33:38 -0700Introduction To Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=516759
״This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.״NOTE: This book meets the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. http://www.aimath.org/textbooks/Tue, 25 Jan 2011 14:19:47 -0800