Lectures And Problems A Gift To Young Mathematicians

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Lectures and Problems: A Gift to Young Mathematicians

Author : V. I. Arnold
Publisher : American Mathematical Soc.
ISBN 13 : 147042259X
Total Pages : 176 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures and Problems: A Gift to Young Mathematicians by : V. I. Arnold

Download or read book Lectures and Problems: A Gift to Young Mathematicians written by V. I. Arnold and published by American Mathematical Soc.. This book was released on 2015-11-30 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Arnold (1937-2010) was one of the great mathematical minds of the late 20th century. He did significant work in many areas of the field. On another level, he was keeping with a strong tradition in Russian mathematics to write for and to directly teach younger students interested in mathematics. This book contains some examples of Arnold's contributions to the genre. "Continued Fractions" takes a common enrichment topic in high school math and pulls it in directions that only a master of mathematics could envision. "Euler Groups" treats a similar enrichment topic, but it is rarely treated with the depth and imagination lavished on it in Arnold's text. He sets it in a mathematical context, bringing to bear numerous tools of the trade and expanding the topic way beyond its usual treatment. In "Complex Numbers" the context is physics, yet Arnold artfully extracts the mathematical aspects of the discussion in a way that students can understand long before they master the field of quantum mechanics. "Problems for Children 5 to 15 Years Old" must be read as a collection of the author's favorite intellectual morsels. Many are not original, but all are worth thinking about, and each requires the solver to think out of his or her box. Dmitry Fuchs, a long-term friend and collaborator of Arnold, provided solutions to some of the problems. Readers are of course invited to select their own favorites and construct their own favorite solutions. In reading these essays, one has the sensation of walking along a path that is found to ascend a mountain peak and then being shown a vista whose existence one could never suspect from the ground. Arnold's style of exposition is unforgiving. The reader--even a professional mathematician--will find paragraphs that require hours of thought to unscramble, and he or she must have patience with the ellipses of thought and the leaps of reason. These are all part of Arnold's intent. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Mathematical Methods of Classical Mechanics

Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
ISBN 13 : 1475720637
Total Pages : 530 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Mathematical Methods of Classical Mechanics by : V.I. Arnol'd

Download or read book Mathematical Methods of Classical Mechanics written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

The Survival of a Mathematician

Author : Steven George Krantz
Publisher : American Mathematical Soc.
ISBN 13 : 0821846299
Total Pages : 310 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Survival of a Mathematician by : Steven George Krantz

Download or read book The Survival of a Mathematician written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 2009-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: "One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."--BOOK JACKET.

Experimental Mathematics

Author : V. I. Arnold
Publisher : American Mathematical Soc.
ISBN 13 : 0821894161
Total Pages : 158 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Experimental Mathematics by : V. I. Arnold

Download or read book Experimental Mathematics written by V. I. Arnold and published by American Mathematical Soc.. This book was released on 2015-07-14 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Mathematics via Problems

Author : Arkadiy Skopenkov
Publisher : American Mathematical Society, Mathematical Sciences Research Institute
ISBN 13 : 1470448785
Total Pages : 196 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematics via Problems by : Arkadiy Skopenkov

Download or read book Mathematics via Problems written by Arkadiy Skopenkov and published by American Mathematical Society, Mathematical Sciences Research Institute. This book was released on 2021-02-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation from Russian of Part I of the book Mathematics Through Problems: From Olympiads and Math Circles to Profession. The other two parts, Geometry and Combinatorics, will be published soon. The main goal of this book is to develop important parts of mathematics through problems. The author tries to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover and recreate much of elementary mathematics and start edging into the sophisticated world of topics such as group theory, Galois theory, and so on, thus building a bridge (by showing that there is no gap) between standard high school exercises and more intricate and abstract concepts in mathematics. Definitions and/or references for material that is not standard in the school curriculum are included. However, many topics in the book are difficult when you start learning them from scratch. To help with this, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions The book is based on classes taught by the author at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Mathematical Understanding of Nature

Author : Vladimir Igorevich Arnolʹd
Publisher : American Mathematical Soc.
ISBN 13 : 1470418894
Total Pages : 167 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematical Understanding of Nature by : Vladimir Igorevich Arnolʹd

Download or read book Mathematical Understanding of Nature written by Vladimir Igorevich Arnolʹd and published by American Mathematical Soc.. This book was released on 2014-09-04 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between mathematics and science."--

Lectures on the Mathematics of Finance

Author : Ioannis Karatzas
Publisher : American Mathematical Soc.
ISBN 13 : 0821809091
Total Pages : 163 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lectures on the Mathematics of Finance by : Ioannis Karatzas

Download or read book Lectures on the Mathematics of Finance written by Ioannis Karatzas and published by American Mathematical Soc.. This book was released on 1997 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the author discusses the main aspects of mathematical finance. These include, arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems.

Mathematics via Problems: Part 2: Geometry

Author : Alexey A. Zaslavsky
Publisher : American Mathematical Soc.
ISBN 13 : 1470448793
Total Pages : 177 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematics via Problems: Part 2: Geometry by : Alexey A. Zaslavsky

Download or read book Mathematics via Problems: Part 2: Geometry written by Alexey A. Zaslavsky and published by American Mathematical Soc.. This book was released on 2021-08-24 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation from Russian of Part II of the book Mathematics Through Problems: From Olympiads and Math Circles to Profession. Part I, Algebra, was recently published in the same series. Part III, Combinatorics, will be published soon. The main goal of this book is to develop important parts of mathematics through problems. The authors tried to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover and recreate much of elementary mathematics and start edging into more sophisticated topics such as projective and affine geometry, solid geometry, and so on, thus building a bridge between standard high school exercises and more intricate notions in geometry. Definitions and/or references for material that is not standard in the school curriculum are included. To help students that might be unfamiliar with new material, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions. The book is based on classes taught by the authors at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Inspiring Mathematics: Lessons from the Navajo Nation Math Circles

Author : Dave Auckly
Publisher : American Mathematical Soc.
ISBN 13 : 1470453878
Total Pages : 281 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Inspiring Mathematics: Lessons from the Navajo Nation Math Circles by : Dave Auckly

Download or read book Inspiring Mathematics: Lessons from the Navajo Nation Math Circles written by Dave Auckly and published by American Mathematical Soc.. This book was released on 2019-12-05 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The people of the Navajo Nation know mathematics education for their children is essential. They were joined by mathematicians familiar with ways to deliver problems and a pedagogy that, through exploration, shows the art, joy and beauty in mathematics. This combined effort produced a series of Navajo Math Circles—interactive mathematical explorations—across the Navajo Reservation. This book contains the mathematical details of that effort. Between its covers is a thematic rainbow of problem sets that were used in Math Circle sessions on the Reservation. The problem sets are good for puzzling over and exploring the mathematical ideas within. They will help nurture curiosity and confidence in students. The problems come with suggestions for pacing, for adjusting the problems to be more or less challenging, and for different approaches to solving them. This book is a wonderful resource for any teacher wanting to enrich the mathematical lives of students and for anyone curious about mathematical thinking outside the box. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

What to Solve?

Author : Judita Cofman
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (285 download)

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Book Synopsis What to Solve? by : Judita Cofman

Download or read book What to Solve? written by Judita Cofman and published by . This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics via Problems

Author : Mikhail B. Skopenkov
Publisher : American Mathematical Society, Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI)
ISBN 13 : 1470460106
Total Pages : 222 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematics via Problems by : Mikhail B. Skopenkov

Download or read book Mathematics via Problems written by Mikhail B. Skopenkov and published by American Mathematical Society, Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI). This book was released on 2023-11-17 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation from Russian of Part III of the book Mathematics via Problems: From Olympiads and Math Circles to Profession. Part I, Algebra, and Part II, Geometry, have been published in the same series. The main goal of this book is to develop important parts of mathematics through problems. The authors tried to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover such topics in combinatorics as counting, graphs, constructions and invariants in combinatorics, games and algorithms, probabilistic aspects of combinatorics, and combinatorial geometry. Definitions and/or references for material that is not standard in the school curriculum are included. To help students that might be unfamiliar with new material, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions. The book is based on classes taught by the authors at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, SLMath (formerly MSRI) and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

What to Solve?

Author : Judita Cofman
Publisher :
ISBN 13 : 9780198532941
Total Pages : 0 pages
Book Rating : 4.5/5 (329 download)

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Book Synopsis What to Solve? by : Judita Cofman

Download or read book What to Solve? written by Judita Cofman and published by . This book was released on 1990 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arnold's Problems

Author : Vladimir I. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 9783540206149
Total Pages : 664 pages
Book Rating : 4.2/5 (61 download)

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Book Synopsis Arnold's Problems by : Vladimir I. Arnold

Download or read book Arnold's Problems written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2004-06-24 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research

Methods of Solving Number Theory Problems

Author : Ellina Grigorieva
Publisher : Birkhäuser
ISBN 13 : 3319909150
Total Pages : 391 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Methods of Solving Number Theory Problems by : Ellina Grigorieva

Download or read book Methods of Solving Number Theory Problems written by Ellina Grigorieva and published by Birkhäuser. This book was released on 2018-07-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter starts with simple topics like even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite complex, Olympiad-type problems right away. It also covers properties of the perfect, amicable, and figurate numbers and introduces congruence. The next chapter begins with the Euclidean algorithm, explores the representations of integer numbers in different bases, and examines continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to solving Diophantine linear and nonlinear equations and includes different methods of solving Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of solving challenging problems involving exponent and factorials. Chapter Four reviews the Pythagorean triple and quadruple and emphasizes their connection with geometry, trigonometry, algebraic geometry, and stereographic projection. A special case of Waring’s problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers. Appendices provide a historic overview of number theory and its main developments from the ancient cultures in Greece, Babylon, and Egypt to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.

A Festival of Mathematics

Author : Alice Peters
Publisher : American Mathematical Society, Mathematical Sciences Research Institute
ISBN 13 : 147045338X
Total Pages : 232 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Festival of Mathematics by : Alice Peters

Download or read book A Festival of Mathematics written by Alice Peters and published by American Mathematical Society, Mathematical Sciences Research Institute. This book was released on 2022-04-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, inspired by the Julia Robinson Mathematics Festival, aims to engage students in mathematical discovery through fun and approachable problems that reveal deeper mathematical ideas. Each chapter starts with a gentle on-ramp, such as a game or puzzle requiring no more than simple arithmetic or intuitive concepts of symmetry. Follow-up problems and activities require intuitive logic and reveal more sophisticated notions of strategy and algorithms. Projects are designed so that progress is more important than any end goal, ensuring that students will learn something significant no matter how far they get. The process of understanding the questions and how they build on one another becomes an exhilarating ride, revealing serious mathematics before the reader is aware of the transition. This book can be used in classrooms, math clubs, after school activities, homeschooling, and parent/student gatherings and is appropriate for students of age 8 to 18, as well as for teachers wanting to hone their skills. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

How Round Is a Cube?: And Other Curious Mathematical Ponderings

Author : James Tanton
Publisher : American Mathematical Soc.
ISBN 13 : 1470451158
Total Pages : 262 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis How Round Is a Cube?: And Other Curious Mathematical Ponderings by : James Tanton

Download or read book How Round Is a Cube?: And Other Curious Mathematical Ponderings written by James Tanton and published by American Mathematical Soc.. This book was released on 2019-07-12 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of 34 curiosities, each a quirky and delightful gem of mathematics and each a shining example of the joy and surprise that mathematics can bring. Intended for the general math enthusiast, each essay begins with an intriguing puzzle, which either springboards into or unravels to become a wondrous piece of thinking. The essays are self-contained and rely only on tools from high-school mathematics (with only a few pieces that ever-so-briefly brush up against high-school calculus). The gist of each essay is easy to pick up with a cursory glance—the reader should feel free to simply skim through some essays and dive deep into others. This book is an invitation to play with mathematics and to explore its wonders. Much joy awaits! In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Math Out Loud: An Oral Olympiad Handbook

Author : Steven Klee
Publisher : American Mathematical Soc.
ISBN 13 : 1470466937
Total Pages : 243 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Math Out Loud: An Oral Olympiad Handbook by : Steven Klee

Download or read book Math Out Loud: An Oral Olympiad Handbook written by Steven Klee and published by American Mathematical Soc.. This book was released on 2021-09-30 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math Hour Olympiads is a non-standard method of training middle- and high-school students interested in mathematics where students spend several hours thinking about a few difficult and unusual problems. When a student solves a problem, the solution is presented orally to a pair of friendly judges. Discussing the solutions with the judges creates a personal and engaging mathematical experience for the students and introduces them to the true nature of mathematical proof and problem solving. This book recounts the authors' experiences from the first ten years of running a Math Hour Olympiad at the University of Washington in Seattle. The major part of the book is devoted to problem sets and detailed solutions, complemented by a practical guide for anyone who would like to organize an oral olympiad for students in their community. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.