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I believe the figures and graphs make students understand more easily.

Real Analysis

This textbook is for pure mathematics. So, I believe it has no inclusive issues about races, ethnicities, and backgrounds at all.

Overall, the textbook is very well-organized. I like the way how to organize the chapters.


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It is essential and nothing of unnecessary sections. Specifically, I like the composition adding the exercises after theorems and examples. If I use the book, I do not have to add more examples and suggest the students with the exercise problems.

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There are also some drawbacks to the book like ordering the topics. Nevertheless, I value this book in teaching the course Analysis. This is a short introduction to the fundamentals of real analysis.

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What Is Real Analysis in Economics?

Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof including induction , and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.

Dan Sloughter has been teaching Furman students since , and became Professor of Mathematics in He previously served as an assistant professor at Santa Clara University from , and at Boston College from He was also an instructor at Dartmouth College from This shows, I suppose, how much progress we have made in two thousand years, for it is a great deal more sophisticated than the Theorem of Pythagoras, which once received that title. All who have taught the subject know how patient one has to be, for the ideas take root gradually, even in students of good ability.

This is not too surprising, since it took more than two centuries for calculus to evolve into what we now call analysis, and even a gifted student, guided by an expert teacher, cannot be expected to grasp all of the issues immediately. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Mathematics Analysis. Buy eBook. Buy Softcover.

FAQ Policy. 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.

Real 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.

【Mathematical Analysis】Open and closed sets

It is an introductory analysis textbook, presented through the lens of history.