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Complex Numbers from A to ...Z Paperback – November 22, 2005

ISBN-13: 978-0817643263 ISBN-10: 0817643265 Edition: 2005th

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Product Details

  • Paperback: 322 pages
  • Publisher: Birkhäuser; 2005 edition (November 22, 2005)
  • Language: English
  • ISBN-10: 0817643265
  • ISBN-13: 978-0817643263
  • Product Dimensions: 9.1 x 6.3 x 0.8 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #1,188,595 in Books (See Top 100 in Books)

Editorial Reviews

Review

From the reviews:

"The book is a real treasure trove of nontrivial elementary key concepts and applications of complex numbers developed in a systematic manner with a focus on problem-solving techniques. Much of the book goes to geometric applications, of course, but there are also sections on polynomial equations, trigonometry, combinatorics.... Problems constitute an integral part of the book alongside theorems, lemmas and examples. The problems are embedded in the text throughout the book, partly as illustrations to the discussed concepts, partly as the testing grounds for the techniques just studied, but mostly I believe to emphasize the centrality of problem solving in the authors' world view.... The book is really about solving problems and developing tools that exploit properties of complex numbers.... The reader will find a good deal of elegant and simple sample problems and even a greater quantity of technically taxing ones. The book supplies many great tools to help solve those problems. As the techniques go, the book is truly From 'A to Z'."   —MAA

“It is for the readers who seek to harness new techniques and to polish their mastery of the old ones. It is for somebody who made it their business to be solving problems on a regular basis. These readers will appreciate the scope of the methodological detail the authors of the book bring to their attention, they will appreciate the power of the methods and theintricacy of the problems.”(MAA REVIEWS)

"This book is devoted to key concepts and elementary results concerning complex numbers. … It contains numerous exercises with hints and solutions. … The book will serve as a useful source for exercises for an introductory course on complex analysis." (F. Haslinger, Monatshefte für Mathematik, Vol. 149 (3), 2006)

"Both of the authors are well-known for their capacity of an integral point of view about mathematics: from the level of the school, through the university level, to the scientific results. The theory appears strictly connected with the problems, the hardest world contest included. Both of them have a very rich experience in preparing Olympic teams in Romania and in the United States.

"… A significant list of references and two indexes complete the book. I strongly recommend the book for pupils, students and teachers." —Dan Brânzei, Analele Stiintifice

"The main purpose of this book is to stimulate young people to become interested in mathematics … . This book is a very well written introduction to the theory of complex numbers and it contains a fine collection of excellent exercises … . the targeted audience is not standard and it ‘includes high school students and their teachers, undergraduates, mathematics contestants such as those training for Olympiads or the William Lowell Putnam Mathematical Competition, their coaches, and any person interested in essential mathematics." (Vicentiu D. Radulescu, Zentralblatt MATH, Vol. 1127 (4), 2008)

From the Back Cover

It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.

The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them.

The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented.

The book reflects the unique experience of the authors. It distills a vast mathematical literature, most of which is unknown to the western public, and captures the essence of an abundant problem culture. The target audience includes undergraduates, high school students and their teachers, mathematical contestants (such as those training for Olympiads or the W. L. Putnam Mathematical Competition) and their coaches, as well as anyone interested in essential mathematics.


More About the Author

Dr. Titu Andreescu is an associate professor of mathematics in the Science and Mathematics Education department at the University of Texas at Dallas (UTD). Much of his career has been devoted to competition math, an efficient medium for teaching creative problem-solving for a wide-range of math topics. With over 30 years of experience teaching, coaching, and mentoring the brightest mathematical minds of our age, Dr. Andreescu's books are essential for every math enthusiast's library. Here are just a few highlights from his distinguished career:

-Authored, co-authored, and edited more than 40 math books and publications
-Head coach and leader of the USA International Mathematical Olympiad (IMO) for 8 years
-Director of the Mathematical Association of American (MAA) American Mathematics -Competitions for 5 years
-Has contributed hundreds of problems to various math competitions including up to and including the IMO
-Co-founder of the Purple Comet! Math Meet, the first international team based math competition, http://www.purplecomet.org/
-Founder and Director of AwesomeMath, an organization that provides enriching experiences in mathematics to intellectually curious learners, https://www.awesomemath.org/

Customer Reviews

4.8 out of 5 stars
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See all 6 customer reviews
As a Math major, I really love the way this book is written.
brwar
I very strongly recommend this book to all students curious about elementary mathematics, especially those who are bored at school and ready for a challenge.
Vicentiu Radulescu
Comprehensive and yet concise enough to cover lots of material.
science-buff

Most Helpful Customer Reviews

33 of 38 people found the following review helpful By Vicentiu Radulescu on December 31, 2005
Format: Paperback
Mathematics is amazing not only in its power and beauty, but also in the way that it has applications in so many areas. The aim of this book is to stimulate young people to become interested in mathematics, to enthuse, inspire, and challenge them, their parents and their teachers with the wonder, excitement, power, and relevance of mathematics.

This book is a very well written introduction to the fascinating theory of complex numbers and it

contains a fine collection of excellent exercises ranging in difficulty from the fairly easy, if calculational, to the more challenging. As stated

by the authors, the targeted audience is not standard and it "includes high school students and their teachers,

undergraduates, mathematics contestants such as those training for Olympiads or the William Lowell Putnam Mathematical Competition, their coaches, and any person interested in essential mathematics."

The book is mainly devoted to complex numbers and to their wide applications in various fields, such as geometry, trigonometry or algebraic operations. An important feature of this marvelous book is that

it presents a wide range of problems of all degrees of difficulties, but also

that it includes easy proofs and natural generalizations of many theorems in elementary geometry.

The authors show how to approach the solution of such problems, emphasizing the use of methods rather than the mere use of formulas. Of course, the more sophisticated the problems become, the more specific this approach has to be chosen.
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2 of 2 people found the following review helpful By malfalfa on August 1, 2011
Format: Paperback
Goes over the basics of complex numbers from A to Z and is absolutely loaded with examples and practice problems. I wish it was more proofs and less practice problems, but that's just a personal preference.
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1 of 1 people found the following review helpful By brwar on July 9, 2013
Format: Paperback
Actually I didn't buy this book but just download it from Stanford's library's website. Hopefully it's legal. I mean, it's Stanford's website, right? But I have to thank the author for writing such a great book. I didn't learn much about complex numbers in my high school, and don't feel comfortable with my college complex analysis textbook, so I got this book to build a firm foundation for my complex analysis class. As a Math major, I really love the way this book is written. It's so well-ordered (well, I didn't mean that well-ordered in Mathematics, you get the idea-_-), so clear and every step is backed by reasons. IT MAKES SENSES! Anyway, I would recommend this book to anyone who wants to take complex analysis because a lot of us don't have enough knowledge about complex numbers but the complex analysis class is based on the assumption that we are already masters of it.
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