Conjecture and Proof (Classroom Resource Materials) by Miklós Laczkovich | (PDF) Free Download

Description

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on ‘Conjecture and Proof’. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of e, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.

User’s Reviews

Editorial Reviews: Review I love this book! It’s a very well designed problem driven course done in the splendid Hungarian tradition. — Michael Bert, MAA OnlineMichael Berg, MAA Online Book Description How to prove interesting and deep mathematical results from first principles, with exercises. Book Description The Budapest semesters in mathematics aim to convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course ‘Conjecture and Proof’. Prerequisites are kept to a minimum and exercises are included. This book should prove fascinating for any mathematically literate reader. About the Author Miklos Laczkovich was born in Budapest, Hungary. He graduated from the Eotvos Lorand University (Budapest) and has been teaching at the same University since then, but also had several visiting positions at various universities in Canada, England, Italy and in the United States. His main field of interest is real analysis. He was an invited speaker at the First European Congress of Mathematics held in Paris, France in 1992. In 1993 he won the Ostrowski prize for the solution of Tarski’s ‘circle-squaring’ problem. Member of the Hungarian Academy of Sciences. Read more

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

⭐”Conjecture and Proof” is a collection of the lecture notes designed for a one-semester course in Hungary for American and Canadian students. The course was intended for creative problem solving and for conveying the tradition of Hungarian mathematics. Other purpose of the book includes showing the spirit of mathematics. Hungary is a country well-known for inventions. Her inventions include Rubik cube, fuel injector, helicopter, stereo, television, transformer, generator, ball pen, telephone switch, neutron bomb, and contact lens. Her scientists have been awarded for Nobel prizes at the least 11 times. With knowing the history of Hungary, the expectation of the book is logical. Even though the book is intended for undergraduate students, it exposure the readers on many deep, interesting, and important theorems with completed proofs but easily accessible methods on1. the irrationality of the number of the square root of 2, of the number e, and of the number pi,2. the three classical geometric construction problems,3. constructible regular polygons (Gauss Theorem),4. e is transcendental,5. Banach-Tarski Paradox. The book also comes with a sketch of the proof of Hilbert’s third problem, which states that the regular tetrahedron is not equidecomposable to the cube nor to any rectangular box of the same volume. The proof is based on an additive and invariant function. The value of the function at a regular tetrahedron is nonzero, but the value of the function at the cube is zero. The first time I read the book while I was an undergraduate. Most of the material covers on the book were new to me other than the irrationality of square root of 2, the pigeonhole principle, countable and uncountable sets. The chapters 2, 3, 6, 7, 11, 13, 15, 16 impressed me the most. They were geometry related, especially the proofs on the three classical geometric construction problems (doubling the cube, trisection of angles, and squaring the circle). Banach-Tarski Paradox was another shock. If a solid ball can be broken down into infinite points and “then be put back together in a different way,” two identical copies of the original ball can be yield. Anyway, I own the book now for the provided proofs.

⭐Purchased for my son who has been doing independent research in mathematics in college. A great book for introducing the ideas and techniques of proof writing.

⭐I have recently acquired a copy of the Hungarian edition (apparently a translation of this English edition) and I can tell you, these guys have selected some of the best and most representative problems in Mathematics. The proofs are very concise and you really do not need much more than high school/early college math to follow them. There are a number of exercises for each chapter (topic) and some of them also come with hints. I would also consider these exercises to tease brighter high school math wizards. For those who have already seen them during their studies, it is surely worth another look. I have not seen the English edition, but reading the Hungarian version, I assume it must also be very well written.

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