Enhanced descriptions from Syndetics:

Sarah Flannery is a cryptographer and mathematician already with an international reputation. She is also a sport-loving Co. Cork teenager who takes her Leaving Certificate next year. In this remarkable book, written with her father, her first maths teacher, she writes about her life, mathematics and making codes - and this extraordinary year. That is just one of the scores of media comments from all over the world which followed Sarah's winning this January, at the age of 16, the Irish Young Scientist of the Year award with a highly innovative, speedy and secure system of encoding data on the Internet. Since then she has travelled the world and lectured, and had approaches from many computer companies and universities. Her system still needs full peer evaluation but what is not in doubt is the originality of her mathematical mind. Her book offers many different things: it is a fresh and modest self-portrait by a girl who is the reverse of a comic-strip swot; it is an inspiring account of a mathematical education; with many puzzles and examples it offers a mass of insights into cryptography and numeracy.

Table of contents provided by Syndetics

• Foreword (p. vii)
• Preface (p. ix)
• Part I Background (p. 1)
• 1 Early Influences (p. 3)
• 2 Early Challenges (p. 8)
• 3 Beginning My First Project (p. 32)
• Part II Mathematical Excursions (p. 41)
• 4 Dad's Evening Class (p. 43)
• 5 Of Prime Importance (p. 47)
• 6 The Arithmetic of Cryptography (p. 71)
• 7 Sums with a Difference (p. 113)
• 8 One Way Only (p. 149)
• 9 Public Key Cryptography (p. 164)
• Part III Exhibition Time (p. 187)
• 10 Young Scientist '98 (p. 189)
• 11 The Birth of a Project (p. 194)
• 12 Young Scientist '99 (p. 218)
• Part IV After-Math (p. 229)
• 13 Media Blitz (p. 231)
• 14 Around the World and Back (p. 254)
• About This Book (p. 269)
• Appendix A "Cryptography--A New Algorithm Versus the RSA" (p. 271)
• Appendix B Answers to Miscellaneous Questions (p. 297)
• Appendix C Euclid's Algorithm (p. 305)
• Appendix D The Euler [phi]-function and the Euler-Fermat Theorem (p. 315)
• Acknowledgments (p. 320)
• Bibliography (p. 323)
• Index (p. 325)

Excerpt provided by Syndetics

4 Dad's Evening Class God made the natural numbers, all the rest is the work of Man. -leopold kronecker These were the first words that my father wrote on the board-a bit alarmingly, in German-on the evening of my first class at the Cork Institute of Technology, where he lectures in mathematics. He explained that Kronecker was a German mathematician who lived in the nineteenth century. Little did I know the role that the natural numbers (1, 2, 3, and so on . . .) would play in my life over the next two years. Although, as I have already said, my father had often taught or helped with my school mathematics at home, this was the first time I had ever attended a formal lecture of his and seen him present work in an organized way to a group of people. This unusual evening class had come about as a result of a conversation he and I had the previous summer, which started something like, "Now that you have decided to do transition year, I must do some math with you." He continued, "I'd like to show you how some beautiful but reasonably elementary mathematics is applied, stuff that you wouldn't ordinarily come across in school." Not knowing exactly what he had in mind, but not wishing to be collared and dragged to the kitchen blackboard at random times, I replied, "Dad, whatever you do, do something structured!" He promised to think carefully about the most effective but gentle way to give me a realistic glimpse into the mathematical world. Conscious of how much he would have appreciated it had someone done this for him thirty years ago, he felt obliged now to offer me the benefit of his mathematical knowledge. "Of course, only if you are genuinely interested-I wouldn't force it on you." Of course he wouldn't! But I was interested. So this is how the evening class was conceived, and this is how I was to be introduced to many wonderful mathematical ideas-accessible ideas I might never otherwise have encountered unless I chose to pursue mathematics as a career. The title for the intended series of lectures, "Mathematical Excursions," was suggested by one of Dad's favorite books, Excursions in Calculus by Robert M. Young. Dad wanted not to present mathematics in a very rigorous fashion, but rather to explore "elementary" aspects of "higher" mathematics, and learn how these ideas find applications in different fields of study outside mathematics. The only prerequisite for these excursions-besides a thorough grounding in ordinary arithmetic and basic algebra-was interest. The primary aim of the course was that everybody take pleasure in sharing in the spirit of discovery. The class, which met Tuesday evenings from seven to ten, consisted of eight people and ran for twenty-five nights. At fifteen and a half I was the youngest, though there were a couple others nearly as young. The rest were adults of various backgrounds: one was a secondary school mathematics teacher, one a chemistry graduate working in a medical laboratory, and others were computer scientists. All were there either because they had loved math at school but hadn't continued with it, or because they felt they hadn't properly appreciated the subject the first time around. This noncredit class, which was not part of any major, led to no award or certification at its completion and demanded no homework or study, may have seemed an ideal way of "getting back into math" in an easygoing, informal manner. Dad told us at the outset that there would be no pressure to perform, and that we need not fear being asked questions but we could ask them at any time. We were to feel free to say "any crazy thing" we liked, and not to be in the least afraid of appearing to make fools of ourselves. In fact, he told us, the more you are prepared to make a fool of yourself the more you'll learn. These reassurances convinced me that I was going to enjoy the next few Tuesday nights, even if I was not completely comfortable with the fact that the lecturer was my father. (Students always pity those who have to endure classes given by their parents, though I'm sure the situation is worse for the parent who is the teacher.) The first excursions were to be in elementary number theory, with some aspects of cryptography as their final destination. Along the way we would see interesting sights, rich in their own right regardless of whether or not they had immediate application. Dad told us that when he was a student, number theory was regarded as the sole province of mathematicians, and those who devoted their lives to its study were considered the purest of the pure, so few were its perceived applications. It wasn't until the 1960s that engineers and scientists began to find applications of number theory, and by the end of the 1970s the discipline came of age, in the applied sense, with the advent of public key cryptography (very briefly, a modern form of cryptography which makes it possible to make public the method by which messages are enciphered, but-amazingly-without revealing how these enciphered messages are deciphered). Now the U.S. government was putting millions of dollars into the study of cryptography, a subject full of wonderful ideas about which, Dad said, he could hardly wait to tell us. Whereas many great number theorists had barely made a living in the past, their modern counterparts were now being actively sought out, so great was the demand for expertise in this emerging science of secrecy which relied so fundamentally on the branch of mathematics that the great mathematician Karl Friedrich Gauss (of whom more later) revered above all else. It was he who said: Mathematics is the queen of the sciences and number theory is the queen of mathematics. As you might imagine, hearing all this filled me with curiosity and interest. Mom said it was like the Sleeping Beauty fairy tale, and she was prompted to write: A princess was the Theory of Number, whom no practical use did encumber, 'til Cryptography the prince ('tis all secrecy since), did kiss her awake from her slumber. I thought about those who had toiled away through the centuries at unraveling the mysteries of this subject, motivated by nothing more than a passionate desire to know. They could have hardly dreamt of the applications that some of their results would one day find. I wondered what it was they had discovered, and what they would think if they could see how some of these discoveries are now being used. I was eager to learn the subject and surmise for myself whether they would be surprised or not. We were at once tantalized and put on our guard by the warning that number theory is notoriously deceptive. We were told that very soon we'd find ourselves asking simple questions, many of which others have asked before us through the ages, and some of which have still not been answered to this day. Excerpted from In Code: A Mathematical Journey - A Young Woman's Mathematical Journey by Sarah Flannery, David Flannery All rights reserved by the original copyright owners. Excerpts are provided for display purposes only and may not be reproduced, reprinted or distributed without the written permission of the publisher.

Reviews provided by Syndetics

Library Journal Review

"I have no doubt that I am not a genius," writes Sarah Flannery, the 16-year-old Irish girl who won first place in the 1999 European Union Contest for Young Scientists. Nonetheless, her project about public key cryptography, the method used to transmit secure data over the Internet, created a media sensation. Until a security hole was discovered, some believed that Sarah's encryption algorithm could be worth millions, and she became an instant celebrity. Though her mathematician father helped write this book, Sarah's own heartfelt enthusiasm is obvious. She is breathlessly excited to get a phone call from a mathematician whose papers she has read, frustrated by the difficult math in research journals, flattered by media attention, and genuinely intrigued by the mathematics of encryption, which she valiantly explains. A particularly touching moment comes when Sarah is overjoyed to see her dad because she finally has somebody who will talk with her about mathematics. The prize-winning contest paper is included as an appendix. Despite the advanced math discussed here, this will appeal to high school and college students because the author is a very young mathematician and does a commendable job of explaining how she got interested in such an intense science project. For public and college libraries. Amy Brunvand, Univ. of Utah Lib., Salt Lake City (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.

Publishers Weekly Review

At 16, Flannery made worldwide headlines as Ireland's 1999 Young Scientist of the Year for her discovery and presentation of the Cayley-Purser algorithm, an innovative encryption system roughly 22 times faster than the worldwide standard RSA algorithm. She declines the "genius" label, and a method for cracking her algorithm has since been discovered, but this only makes the book more interesting and unpredictable. It's more about the journey's adventure than the destination and less about Sarah's specialness than her spirit. The mix is part memoir, part puzzle book and part mathematical exploration, with scattered bits of mathematical lore. (The heaviest math is concentrated into two chapters and the appendices, leaving the remainder easy going for the fainthearted.) The puzzle-solving approach to math cultivated by her father (and coauthor) encourages exploration, an adventurous attitude, attention to concepts more than calculations and sheer enjoyment of taking on a challenge. It's also more egalitarian than proof-based approaches, giving newcomers a more equal footing with old pros, emphasizing the process of discovery and making connections, which is more fundamental than finished proofs. All this is wonderfully illustrated by Flannery's own story of her rapidly developing interest and proficiency in cryptography, as well as by the puzzles she uses to get readers thinking and introduce some basic concepts. Other threads, running from brief descriptions of her grandparents to her father's teaching methods and her relationship to family in the face of a media frenzy, give her story added depth, warmth and humor. 8 pages of b&w photos. (June) Forecast: Workman is hoping to, and should, attract budding young mathematicians with a first printing of 35,000, a $65,000 marketing budget and an eight-city author tour. (c) Copyright PWxyz, LLC. All rights reserved

Kirkus Book Review

A young Irishwoman’s account of the mathematical studies that made her Young Scientist of the Year. Flannery, now a first-year student at Cambridge, grew up solving logic puzzles posed by her father, a math teacher (and her collaborator here). In the beginning chapters, she offers the reader a selection of those brainteasers, many of which depend on mathematical reasoning. So when her high school science teacher recruited her to enter Ireland’s Young Scientist competition, Sarah’s father steered her toward a project with a strong math basis: cryptography, the encoding and decoding of messages. This once-cumbersome process is now handled by sophisticated computer programs based on number theory—especially the factoring of very large numbers. Sarah decided to concentrate on the programming aspect, to give herself hands-on experience with the computer work. But first she had to learn the relevant mathematics. To bring the reader up to speed, the authors step back from Sarah’s story to present the mathematical foundations of modern cryptology: prime numbers, factoring, and other arcana of number theory. This section is in many ways the meat of the story, accessible to anyone not totally allergic to equations. As Sarah learned the math, she spotted an alternative to the standard RSA algorithm on which modern cryptology is based, and soon her project turned into an exposition of her new method—which in time won her honors as Young Scientist of the Year not only in Ireland, but in all of Europe. The latter chapters tell of the competitions, her preparation and her bouts of nerves, her genuine surprise at winning, and the sometimes-exasperating aftermath as the media discovered her and turned her (for a while, at least) into a celebrity. A charming story, well worth slogging through the heavy loads of math. First printing of 35,000; $65,000 ad/promo; author tour

Author notes provided by Syndetics

Sarah Flannery is now a student at Cambridge University
David Flannery, Sarah's father, lectures on mathematics at Ireland's Cork Institute of Technology