Dover Mathematics: Its Content, Methods and Meaning

“If you can't explain it to a six year old, you don't understand it yourself.”In this book, several of the best mathematicians of XX century explain their areas of research to high school graduates. That includes, for example, the genius Andrey Kolmogorov, who wrote the chapter on probability.For me, this book is a comprehensive overview of undergraduate math that I took (and parts that I didn't) in extremely short, accessible, yet rigorous form. The chapters include great real-life examples, history moments, critical definitions and proofs. Unlike university courses, which are pressured to include as much of important material, this book is written to be interesting and to explain key concepts - something that course textbooks often badly miss.Especially mind-blowing chapter is the one about analytic geometry. I never studied and never even seen anywhere a dedicated course on analytic geometry, its material was spread over various analysis, algebra, and differential equation courses, and never represented as a single consistent picture. However, from the chapter written by the genius Boris Delaunay it comes out as a fundamental math discipline, clear, intuitive and powerful, that explains many things done in other disciplines, which typically seem esoteric when taken out of geometric context.Besides super-strong math content, this book is also an intriguing historical document. Though the translator removed most of the unrelated communist propaganda content that these world-class scientists had to include to make the book printable in the USSR, the chapters still include some interesting materialist explanations of math principles. I think they did honestly believe in it in some ways, so most of the explanations make sense, and makes me think that maybe the view of mathematics as a pure abstract science, and not part of natural sciences, is incomplete, if not outright wrong.I can strongly recommend this book to young people considering choosing math or math-related major. I give the same recommendation to anyone who, like me, did study math but feels like misses something important.

Gostei do livro, porém achei a letra muito pequena.

Imagine a book on "mathematics", wherein the chapter on probability is written by Andrei Kolmogorov, the chapter on topology by Pavel Aleksandrov, the chapter on functional analysis by Israel Gelfand, and the chapter on partial differential equations by Sergei Sobolev and Olga Ladyzenskaja, to name just four of altogether 20 chapters, and just five of altogether 18 famous mathematicians, who are the authors of this work. Although written in an informal style, the book is worth being read not only by serious students and mathematically interested laypersons, but also by educators at the university level. E.g., everyone who lectures on probability and statistics will benefit from reading Kolmogorov's chapter on probability theory.Every mathematician as well as every mathematically interested non-mathematician will like this masterpiece of mathematical exposition. Moreover, this Dover edition (three volumes bound as one, more than 1100 pages) is really worth its price.

In this work of over one thousand pages the authors have attempted a broad survey of the fields of mathematics as they were in the mid twentieth century. The book is highly readable and should be accessible to advanced undergraduates in the mathematical sciences. The main branches of mathematics including algebra, analysis, geometry, differential equations, complex analysis, number theory, approximation, linear algebra, non-euclidean geometry, measure theory, topology, functional analysis and group theory are all given chapters. I would recommend this work to anyone seeking an overview of mathematics which also contains some of the meat of the subject. Very informative.

This is my favorite math book I've ever read. As an amateur mathematician, looking to find my roots, and just explore the field of mathematics, there is no better book. Translated from the direct writings of the mathematical Giants of the 20th century, this book delivers concise, illuminating explanations paired with challenging, but accomplishable, examples and proofs. (Challenging meaning that the logical steps are definitely accomplishable for those with intermediate experience reading 2-3 math texts.)This is essentially a "math encyclopedia." I wish I could have read this in elementary school–it's a zoological categorization of math topics, which fascinating applications and almost magical properties. This is a great book to peruse. The chapters are not necessarily linked in sequential order, but having a basic knowledge of calculus is quite useful for interpreting multidimensional topics and functional analysis. (But they even have an introduction to calculus in the book! I didn't like it too much though; there were no practice problems.)For those who are interested in math, but do not know what types of math are out there––this book is for you. For those who enjoy a historical perspective on contemporary fields of mathematics and have experience reading technical mathematics, this will be an enjoyable, intriguing read.My favorites include the explanation of the Euler-Lagrange Equation and the explanation of Fundamental Groups of Motion. For further reference on my experience, I am currently a high school senior, having read a book on abstract algebra, completed a course on linear algebra, and single variable calculus.