Yet Another Introduction to Analysis 1st Edition by Victor Bryant (PDF)

Description

Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be well-motivated, relevant and practical. When such students reach higher education the traditional development of analysis, often rather divorced from the calculus which they learnt at school, seems highly inappropriate. Shouldn’t every step in a first course in analysis arise naturally from the student’s experience of functions and calculus at school? And shouldn’t such a course take every opportunity to endorse and extend the student’s basic knowledge of functions? In Yet Another Introduction to Analysis the author steers a simple and well-motivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate the new ideas are related to school topics and are used to extend the reader’s understanding of those topics. A first course in analysis at college is always regarded as one of the hardest in the curriculum. However, in this book the reader is led carefully through every step in such a way that he/she will soon be predicting the next step for him/herself. In this way the subject is developed naturally: students will end up not only understanding analysis, but also enjoying it.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Bryant’s book on analysis is a great illustration of what a textbook should be. He takes what many upper level college mathematics students consider to be the most tedious and boring topic – analysis- and presents it in a clear, interesting and effective way. Calculus at the college undergraduate level is usually taught in 3 semester long classes where integrals and derivatives are seen as tools for finding areas under curves, or volumes of objects, etc. which is the way engineers are made to view Calculus during their scholastic careers. Past that introductory level, in their junior years students of pure mathematics must be reintroduced to Calculus in a rigorous proof-driven way – thus enters the dreaded subject of “analysis”, also sometimes called “advanced calculus” and thankfully, thus also enters this book. Bryant starts off assuming that rational numbers behave as we know from elementary school and then constructs the real numbers by adding a completeness axiom. From there he introduces the concept of limits and also the epsilon-delta technique in an accessible way before going on to the topics of differentiation and integration. Even though this is a mathematically rigorous book, the author manages to keep things interesting by introducing topics and theorems in bite-sized chunks. Basically, the book doesn’t go beyond the analysis of calculus normally taught at the undergraduate level, but rather reintroduces it properly and puts it on the rigorous plane with which all graduate mathematics students shall become familiar. Along with all that, there’s an excellent selection of interesting exercises with solutions at the back. These exercises range from the rather simple to the very tricky. If you are a mathematics major, you will probably not be lucky enough to have this as your textbook in analysis class, but you should buy a copy and read it before and during the class so that you know what is really trying to be conveyed.

⭐Unlike many of the other reviewers of this work, I found Dr. Bryant’s informal writing style a hassle. While I can appreciate the conversational approach, I found his writing to be very lacking in detail and too casual to yield in-dpeth knowledge. I suppose this work was intended to introduce Analysis in a non-scary, casual style, but so much substance gets left out because of it. I’ve always been fond of rigor, and I deperately need rigor when learning higher math. Some people equate rigor with obfuscation, but I have found that you can have rigor wth clarity. I found Kosmala’s “Advanced Calculus: A Friendly Approach” (now called “A Friendly Introduction to Analysis”) to be a much more rigorous and complete introduction that is also very “friendly” indeed. Although this book will serve as a “breezy” (and somewhat shallow) introduction to Analysis I would recommend Kosmala’s work over this one to anyone who wants a complete and in depth treatment of the subject that also gently guides the first time student through it.

⭐I found this book an excellent introduction to real analysis. The math courses I took during my US undergraduate engineering degree (your standard Calc I – Calc III) focused more on computation than theory. This book gave me a deeper understanding of the real number line, sequences and series, functions, differentiation, and integration, as well as some much-needed practice in writing proofs.I was a bit worried starting the book that it would be too difficult, but fortunately, the book started at just the right level for me and continued at a good pace. The book is written in a friendly and conversational style and all the concepts are well-explained, with lots of graphs to make things clear.The exercises often have you proving some key theory that is referred to later on, which gives a strong motivation to work through all the exercises. For someone with little experience writing proofs like myself, the exercises were not overly difficult, but provided a good challenge. The book provides full, worked-out solutions to all the exercises, which makes it great for self-study (I used the book to get some background on analysis over summer before I started my master’s).Overall, I found this to be an excellent book. I highly recommend it for self-study or as a supplement to a course.

⭐This book is the easiest book on real analysis in the market. However, this book leaves out numerous important topics.

⭐very good introduction to analysis, lots of examples, good text book.

⭐Unless you’re looking for the usual opaque tome this is good stuff.

⭐I was happy that I received the book on time, but the description of the book as “high use” I did not think that there would be 20 pages missing from chapter 1.

⭐Cannot be used on its own for beginner students to analysis. Recommend to use with other books on proofs.Also, basic calculus is necessary.

⭐Good coverage of introductory material. Complete set of solutions is very helpful for self-study.

⭐good introductory book

⭐His approach seems idiosyncratic – sometimes irritatingly long winded and doesn’t get to the heart of the matter fast enough.The only thing good about the book is that you can check out the solutions to the chapter questions at the back.There are better books out there.

⭐一変数の微積の教科書です。説明もわかりやすいし、天下り式の数学書でもないので読みやすい本。ただ、厳密であるかといえばちょっと疑問が残るかもしれない。証明は本全体に渡って直感的にわかりやすいものを取り上げている。高校で習う微積＋α（このαは結構小さいかも）程度。よって、高校生には最適でしょう。大学初年級の人には簡単すぎると思います。ε－δ式の極限の定義もないし、上積分、下積分の話をするところで話が終わる。ただ演習問題は面白いモノもあり、全部解答付き。しかし、考えさせるっていう程難しくはない。一部の証明をフローチャートを使って流れを説明するなど独特の部分があって面白い。Not rigorous enough

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