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Complex Numbers from A to ...Z Paperback – January 1, 2005

by Titu Andreescu (Author), Dorin Andrica (Author)

5.0 19 ratings

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Complex Numbers from A to ... Z
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* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory

Print length

332 pages
Language

English
Publisher

Birkhäuser Boston
Publication date

January 1, 2005
Dimensions

6.1 x 0.76 x 9.25 inches
ISBN-10

9780817643263
ISBN-13

978-0817643263
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Titu Andreescu
11
Paperback
18 offers from $46.58

Product details

ASIN ‏ : ‎ 0817643265
Publisher ‏ : ‎ Birkhäuser Boston; 2005th edition (January 1, 2005)
Language ‏ : ‎ English
Paperback ‏ : ‎ 332 pages
ISBN-10 ‏ : ‎ 9780817643263
ISBN-13 ‏ : ‎ 978-0817643263
Item Weight ‏ : ‎ 1.05 pounds
Dimensions ‏ : ‎ 6.1 x 0.76 x 9.25 inches

Best Sellers Rank: #5,318,216 in Books (See Top 100 in Books)
- #59,883 in Mathematics (Books)

Customer Reviews:
5.0 19 ratings

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Titu Andreescu

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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 and up to 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/

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AE

Great book on complex numbers for the serious reader

Reviewed in the United States on June 5, 2012

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Good book, especially for introductory complex geometry. The theory of complex numbers is built up in black and white, no frills (i.e. don't expect to find any silly historical notes or color pictures typical of modern textbooks) and I have a feeling that the reader who even thinks about buying this book would prefer it this way. The mathematical exposition is generally concise, clear and rigorous.

The only problem with the book is the occasional error. But the only errors I have found are minor in the sense that 1)There are very few of them and 2)They are numeric (The process is correct but the answer is wrong because of some simple arithmetic mistake).

5 people found this helpful

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Vicentiu Radulescu

A very useful book on complex numbers

Reviewed in the United States on December 31, 2005

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.

The book is self-contained; no background in complex numbers is assumed and complete

solutions to routine problems and to olympiad-caliber problems are presented in the last chapter of the book.

The aim of the core part of each chapter is to develop key mathematical ideas and to place them in the context of novel, interesting, and unexpected applications to real-world problems.

The first chapter deals with complex numbers in algebraic form and leads up to the geometric interpretations of the modulus and of the algebraic operations. The second chapter deals with various applications to trigonometry,

starting with elementary facts on the polar representation of complex numbers

and going up to more sophisticated properties related to $n$th roots of unity and their applications in solving

binomial equations. Chapter 3 is devoted to the applications of complex numbers in solving problems in Plane and Analytic Geometry. This chapter includes a lot of interesting properties related to collinearity, orthogonality, concyclicity, similar triangles, as well as very useful analytic formulas for the geometry of a triangle and of a circle in the complex plane. Chapter 4 contains much more powerful results such as: the nine-point circle of Euler, some important distances in a triangle, barycentric coordinates, orthopolar triangles, Lagrange's theorem, geometric transformations in the complex plane. This chapter also includes a marvelous theorem known in the mathematical

folklore under the name of "Morley's Miracle" and which simply states that "the three points of intersection

of the adjacent trisectors of any triangle form an equilateral triangle". As stated in the book, this theorem

was mistakenly attributed to Napoleon Bonaparte. The proof of this theorem follows directly from Theorem 3 on page 155, a deep result which was obtained by the celebrated French mathematician Alain Connes (Fields Medal in

1982 and Clay Research Award in 2000),

in connection with his revolutionary results in Noncommutative Geometry. Chapter 5 illustrates the force of the

method of complex numbers in solving several Olympiad-caliber problems where this technique works very efficiently.

This very successful book is the fruit of the prodigious activity of two well-known creators of mathematics problems in various mathematical journals. The big experience of the authors in preparing students for various mathematical competitions allowed them to present a big collection of beautiful problems. This book continues the tradition making national and international mathematical competition problems available to a wider audience and is bound to appeal to anyone interested in mathematical problem solving.

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. Teachers would find this book to be a welcome resource, as will contest organizers.

This book is meant both to be read and to be used.

All in all, an excellent book for its intended audience!

36 people found this helpful

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brwar

I have to say that this book is really awesome

Reviewed in the United States on July 10, 2013

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.

4 people found this helpful

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science-buff

lots of unusual and challenging problems on complex numbers

Reviewed in the United States on March 12, 2006

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Comprehensive and yet concise enough to cover lots of material. Lots of wonderful questions to challenge any math problem lovers.

Highly recommended.

6 people found this helpful

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RENATO MADEIRA

Amazing book on complex numbers

Reviewed in the United States on December 7, 2007

This is a complete work about complex numbers. Perfect for Mathematical Olympiads. A lot of difficult problems.

6 people found this helpful

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malfalfa

I approve

Reviewed in the United States on August 1, 2011

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.

3 people found this helpful

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kakababu

awesome book for olympiad like competition

Reviewed in India on June 27, 2019

Verified Purchase

It is my first book by titu adresscu . i like this book so much . nice explanation of every topic , lot of example and solved problem. a good book to start journey into the complex number and complex no. geometry .

Moran Moueza

Géométrie des nombres complexes

Reviewed in France on March 24, 2016

Verified Purchase

Très bon livre sur la géométrie des nombres complexes. Peut servir à ceux qui visent les olympiades de mathématiques.
Je l'utilise avec "complex numbers et geometry de Liang Shin Hahn" qui est plus théorique et surprenant. Ces deux livres se complètent mutuellement. Par contre il ne faut pas s'attendre à y trouver la théorie des fonctions complexes qui est plus du domaine de l'analyse.
C'est un bon investissement. Mais les nombres complexes sont un domaine très vaste qui passe par les nombres de Gauss et les algèbres de Lie. Il y a du boulot...

One person found this helpful

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Biswajit Ghosh

As expected

Reviewed in India on November 5, 2019

Verified Purchase

Nice

Amar Aparajeet

Great

Reviewed in India on July 27, 2019