Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.
The authors, who have attended the BMO several times as leaders and/or deputy leaders, present a complete description of the evolution of the BMO from its creation until the present. All problems are presented with complete solutions. Many problems have alternative solutions or extensions. A preparatory addendum, containing additional concepts and useful classical results, has been incorporated at the end of the book.
Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.
This book presents 10 specific actions to be undertaken in order to provide results of practical relevance in seismology. From the statistical analysis of earthquakes, we can estimate the earthquake mean recurrence time and the probability of occurrence of the next earthquake. In addition, through statistical analysis, we can identify correlated foreshocks and estimate the occurrence time of the main shock. As the book shows, the general state of seismicity of a given seismic region can be assessed by statistical means, in particular the earthquake entropy. From measurements of the seismic waves on the Earth’s surface, we can deduce the tensor of the seismic moment, the earthquake’s energy and magnitude, as well as the orientation of the fault, the fault slip, the focal volume and the duration of the seismic activity.
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