Vietnam has actively organized the National Competition in Mathematics and since 1962, the Vietnamese Mathematical Olympiad (VMO). On the global stage, Vietnam has also competed in the International Mathematical Olympiad (IMO) since 1974 and constantly emerged as one of the top ten.

To inspire and further challenge readers, we have gathered in this book selected problems of the VMO from 1962 to 2008. A number of Selection Test problems are also included to aid in the formation and training of a national team for IMO.

The book is highly useful for high school students and teachers, coaches and instructors preparing for mathematical olympiads, as well as non-experts simply interested in having the edge over their opponents in mathematical competitions.

This book considers the views of participants in the process of becoming a mathematician, that is, the students and the graduates. This book investigates the people who carry out mathematics rather than the topics of mathematics. Learning is about change in a person, the development of an identity and ways of interacting with the world. It investigates more generally the development of mathematical scientists for a variety of workplaces, and includes the experiences of those who were not successful in the transition to the workplace as mathematicians. The research presented is based on interviews, observations and surveys of students and graduates as they are finding their identity as a mathematician. The book contains material from the research carried out in South Africa, Northern Ireland, Canada and Brunei as well as Australia.

The Pythagorean theorem may be the best-known equation in mathematics. Its origins reach back to the beginnings of civilization, and today every student continues to study it. What most nonmathematicians don't understand or appreciate is why this simply stated theorem has fascinated countless generations. In this entertaining and informative book, a veteran math educator makes the importance of the Pythagorean theorem delightfully clear.
He begins with a brief history of Pythagoras and the early use of his theorem by the ancient Egyptians, Babylonians, Indians, and Chinese, who used it intuitively long before Pythagoras's name was attached to it. He then shows the many ingenious ways in which the theorem has been proved visually using highly imaginative diagrams. Some of these go back to ancient mathematicians; others are comparatively recent proofs, including one by the twentieth president of the United States, James A. Garfield.
After demonstrating some curious applications of the theorem, the author then explores the Pythagorean triples, pointing out the many hidden surprises of the three numbers that can represent the sides of the right triangle (e.g, 3, 4, 5 and 5, 12, 13). And many will truly amaze the reader. He then turns to the "Pythagorean means" (the arithmetic, geometric, and harmonic means). By comparing their magnitudes in a variety of ways, he gives the reader a true appreciation for these mathematical concepts.
The final two chapters view the Pythagorean theorem from an artistic point of view - namely, how Pythagoras's work manifests itself in music and how the Pythagorean theorem can influence fractals.
The author's lucid presentation and gift for conveying the significance of this key equation to those with little math background will inform, entertain, and inspire the reader, once again demonstrating the power and beauty of mathematics

This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented. The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.

This tenth volume in the Poincare Seminar Series describes recent developments at one of the most challenging frontiers in statistical physics - the deeply related fields of glassy dynamics, especially near the glass transition, and of the statics and dynamics of granular systems. These fields are marked by a vigorous interchange between experiment, theory, and numerical studies, all of which are well represented by the leading experts who have contributed articles to this volume. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a Galilean dialogue on the mean field and competing theories of the glass transition, a wide-ranging survey of colloidal glasses, and experimental as well as theoretical treatments of the relatively new field of dense granular flows. This book should be of broad general interest to both physicists and mathematicians.

What are fractals? Why are they such fun? How do you make one? Why is a dripping tap not as random as it seems? What is chaos? Is the Mandelbrot Set really the most complex object in mathematics? In this beautifully illustrated book, fractal-hunter Oliver Linton takes us on a fascinating journey into the mathematics of fractals and chaos, diving into many kinds of self- similar structures to reveal some of the most recently discovered and intriguing patterns in science and nature. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

This book is the "Study Book" of ICMI-Study no. 20, which was run in cooperation with the International Congress on Industry and Applied Mathematics (ICIAM). The editors were the co-chairs of the study (Damlamian, Straesser) and the organiser of the Study Conference (Rodrigues). The text contains a comprehensive report on the findings of the Study Conference, original plenary presentations of the Study Conference, reports on the Working Groups and selected papers from all over world. This content was selected by the editors as especially pertinent to the study each individual chapter represents a significant contribution to current research.

The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.

If you've been waiting for a book that will evoke the delight and intrigue that mathematics has to offer, this is the book for you.
What are the odds of finding two people who share the same birth date in a room of thirty-five? Most people would guess they're pretty low. In actuality, the probability is better than 80 percent. This is just one of many entertaining examples of mathematical curiosities presented. Two veteran math educators have created the perfect introduction to the wonders of mathematics for the general reader, requiring only a high school background in the subject.
Among the entertaining and useful tricks they teach are shortcuts in arithmetic, such as ways to determine at a glance the exact divisors of any given number. They also demonstrate how the properties of certain numbers can lead to infinite loops. What is particularly exciting is how many correct answers turn out to be counterintuitive. Exploring all these features will instill insights into the nature of numbers, improve your ability to manipulate them, and give you an appreciation for the inherent elegance of mathematics.
As you marvel at the many unusual relationships and novelties revealed in this ingenious and delightful presentation, you'll be learning more math than you ever thought possible - and will be relishing every moment of it

In the last 15 years we have seen a major transformation in the world of music. - sicians use inexpensive personal computers instead of expensive recording studios to record, mix and engineer music. Musicians use the Internet to distribute their - sic for free instead of spending large amounts of money creating CDs, hiring trucks and shipping them to hundreds of record stores. As the cost to create and distribute recorded music has dropped, the amount of available music has grown dramatically. Twenty years ago a typical record store would have music by less than ten thousand artists, while today online music stores have music catalogs by nearly a million artists. While the amount of new music has grown, some of the traditional ways of ?nding music have diminished. Thirty years ago, the local radio DJ was a music tastemaker, ?nding new and interesting music for the local radio audience. Now - dio shows are programmed by large corporations that create playlists drawn from a limited pool of tracks. Similarly, record stores have been replaced by big box reta- ers that have ever-shrinking music departments. In the past, you could always ask the owner of the record store for music recommendations. You would learn what was new, what was good and what was selling. Now, however, you can no longer expect that the teenager behind the cash register will be an expert in new music, or even be someone who listens to music at all.

This bestselling series is written by an experienced team of Scottish authors and examiners. This Student Book includes: Complete coverage of the higher course, whilst the Revision Book gives plenty of confidence-building practice. Multiple-choice questions to offer complete support for the new multiple-choice paper. Worked examples and exam questions help consolidate learning and provide thorough exam preparation. 'Test-yourself' questions presenting opportunities for self-assessment. Clear diagrams convey key teaching points and help students to learn. Answers to all the questions are supplied for all-round support.

Many of us trained mainly in the humanities and liberal arts may respect mathematics as an essential scientific discipline, but have done very little mathematics and often feel intimidated by its rigors. If you've ever wondered what mathematicians mean by the aesthetic elegance of their subject, here is your chance to experience firsthand mathematics' intellectual pleasures.
Martin Gardner, in his review of Jerry King's The Art of Mathematics, praised King:
"Creative mathematicians seldom write for outsiders, but when they do, they usually do it well. Jerry King, a professor at Lehigh University, is no exception."
For his new book, Jerry P. King has designed a grand tour of mathematics in ten essential lessons for the general reader who wants to know how mathematics is done. Almost no prior mathematical knowledge is assumed and through lively exposition and lucid explanations real mathematics is made not only palatable, but even enjoyable to the uninitiated.
Professor King begins by establishing two key points: first, all mathematics flows from a few fundamental principles. Second, aesthetic considerations provide both the motivation for mathematics research and the standards for evaluating that research. The book is structured so that the reader gradually builds up an ever-greater skill set as each lesson is mastered.
The essential concepts introduced include symbolic logic, infinity, rational numbers, number theory, real and imaginary numbers, function, probability, calculus, and the building of mathematical models in applied mathematics. Throughout his exposition, King provides brief historical digressions, which highlight key developments made by the giants in the field of mathematics.
Eloquently written and clearly presented, Mathematics in 10 Lessons will inspire the reader to go on to learn more and will instill a true appreciation for mathematics as both an art and a science.