Mathematics and Its History (Undergraduate Texts in Mathematics) 3rd Edition by John Stillwell (PDF)

Description

From a review of the second edition:”This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved…If one constructs a list of topics central to a history course, then they would closely resemble those chosen here.”(David Parrott, Australian Mathematical Society)This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

User’s Reviews

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

⭐Fascinating and mathematically rigorous history of math. Quite easy to follow with basic college math (calculus and analytic geometry sequence).It is also great to have this book to follow along with the YouTube video sequence from Norman Wildberger on the history of mathematics that teaches through most of the book.

⭐The book arrived promptly and is a wonderful addition to my personal library. I will have many years of rewarding reading to look forward to!

⭐I was fully prepared to give 5 stars for an informative book. Historical mathematics is presented in a manner modern readers interested in math can clearly follow.Until I came across the first of many blank pages, where paragraphs of text are inexcusably missing. I am not talking where the printing plates mis-struck, or or the pages slipped the binding, but pages without continuing text. Right page 9 stops mid paragraph in one section of the chapter, and left page 12 picks up mid paragraph in the next section. There are single pages blank mid proof and 3 continuous pages blank of text.The only reason I did not rate it less are the chapters that are stil intact are very good.Update (2014 January 20): ordered new copy of this book and was gratified that there were no missing pages this time. The quality is consistent through out and I will enjoy reading it.updated rating to 5 stars.

⭐Stillwell’s Math and its History is the one book I would pack in my suitcase for spending a few years alone on an island. This text is also the book I wish I’d received in high school – or at least read as an undergrad. Why? Because Math and its History fullfills Stillwell’s promise in his preface that he would integrate the disparate areas of mathematics and show how they “play” together. He also vividly demonstrates the constant baton passing in the relay race of inventing math, one mathematician influencing another to go farther, often with surprising results. I also love his synoptic approach to ancient math so he can focus his pages (and my time) giving me a roadmap to follow in my studies.

⭐Try figuring out what projective geometry is from chapter 8, much less working any of the problems in the entire chapter. In addition, try working any of the problems in Section 9.2 from the exposition. Try understanding anything about the zeta function from Section 10.8, much less from Section 11.4 what rational right-angled triangles is all about, much less work any of the problems. Try understanding anything about elliptical functions, much less what they are, from Chapter 12. Try understanding anything about the inverse square law, much less work Problem 13.3.5 from the sketchy exposition. Try figuring out what the author is talking about in section 13.4, much less work the problem set, the same with the problems in section 13.5, especially when the author did not explain how to distinguish between a transcendental and an algebraic function, the same. Try to follow the exposition in section 13.6 and attempt to work the problems that follow, the same with section 15.2. Try understanding section 16.2 (conformal mapping) which contains no illustrations or demonstrations of the derivations of conformal mappings, making it impossible to work the problems. Try understanding anything about geodesics in section 17.5 or about Beltram’s projective or conformal models in sections 18.6 and 18.6, much less work the problems. These are only a few of the many drawbacks encountered in this volume, the third being the author’s tendency to shy away from direct presentations and the fourth being the absence of answers. In short, the author needs a remedial English 101 course. In short, don’t expect to learn too much from this volume, despite the lies told by the other posters on this thread.

⭐I like that the book seems to cover the origins of major branches of mathematics and also provides introductions to the subjects. I enjoyed Stillwell’s Four Pillars of Geometry and look forward to reading this book. He seems to be good at explaining things in bite-size pieces.

⭐great book, superb balance between the mathematics and the history Nice set of exercises also.

⭐Excellent guide thru History of Mathematics with a good depth on the subjects. This book will be my companion for a long time since Prof. Stillwell motivates us not only to learn the historical events but also to explore and understand the work of the brightest minds in the field.

⭐Stillwell presents a really lovely review of mathematics placed in its historical context. It will certainly increase your curiosity on a wide range of topics and does come up with some interesting and intriuging surprises. His style is very readable by anyone interested in mathematics placing the problems into context and how the solutions spurred and influenced others to develop mathematics into the state that we have today. I would recommend this book to anyone with an enquiring mind and certainly for students about to start a university course in the sciences and mathematics.

⭐I bought this book because it is the set textbook for a course, on the history of mathematics, presented by Dr Norman Wildberger of the University of NSW, Australia. So far it has proved to be very good and I have every reason to think it will continue to be so.PS: the lectures are available on you tube; that is how I found out about it.

⭐Excellent book, but take it at its word – you need to have undergraduate maths to appreciate it. It lost me many times.

⭐Das Buch ist ziemlich einzigartig, da der Autor versucht Mathematik zu lehren indem er der geschichtlichen Entwicklung folgt. Leider funktioniert das nicht wirklich, denn die Erklärungen sind dürftig und die gestellten Aufgaben wohl ohne Sekundärliteratur kaum lösbar. Ich könnte mir aber vorstellen, dass das Buch interessant ist für Mathematiklehrer and der Schule und Universität, die gerne ihren Unterricht und ihre Aufgaben mit historischem Fakten und Fragestellungen aufpeppen wollen.Leider hat das Buch auch einige gewichtige Lücken. So wird Statistik nicht behandelt (da der Autor meint, das läge außerhalb der Mainstream-Mathematik), außerdem habe ich Kapitel über die Entwicklung der Linearen Algebra (z.B. Vektor- und Matrizenschreibweise), Fouriertransformation, Differentialgleichungen und Numerik vermisst. Also eigentlich alle Themen, die man heute besonders in der Anwendung braucht. Aber das ist wohl der Orientierung am Undergraduate Curriculum der Mathematik geschuldet.Ich fände es daher ehrlicher, wenn der Titel des Buches “Undergraduate Mathematics and Its History” lauten würde und der Autor vielleicht noch einen zweiten Band nachschieben würde, der die genannten Lücken füllt. Dann hätte dieses zweibändige Werk das Potential zur Standardreferenz über die historische Entwicklung der Mathematik zu werden.I purchased this book back in January (January 6, 2014), and due to a lack of need I haven’t thoroughly skimmed through it until now (April 7, 2014). To my immense dismay, IT’S MISSING PAGES! The following is a list of pages that are LITERALLY JUST BLANK!101114282932129132133135136137138139140142143146243246247255256257258259260297298299300301302303304305306307308322323326340341344346347350363364365366367368370371374471472473474475476477478479480481482483484485486487488490491502503506For anyone who wants to know the math, that’s OVER 10% OF THE MAJOR CONTENT OF THE BOOK!Fortunately for me, Amazon was kind enough to give me a refund even though I was approximately two months past the refund date.Other than the missing pages, the book was great, very informative and in depth.

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