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Author: Abraham Berman Publisher: World Scientific ISBN: 9811234892 Category : Mathematics Languages : en Pages : 163
Book Description
The book is based on lecture notes of a course 'from elementary number theory to an introduction to matrix theory' given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.
Author: Abraham Berman Publisher: World Scientific ISBN: 9811234892 Category : Mathematics Languages : en Pages : 163
Book Description
The book is based on lecture notes of a course 'from elementary number theory to an introduction to matrix theory' given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.
Author: Hong-Bing Yu Publisher: World Scientific ISBN: 9814271144 Category : Mathematics Languages : en Pages : 115
Book Description
Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. Readers are encouraged to try to solve the problems by themselves before they read the given solutions of examples. Only in this way can they truly appreciate the tricks of problem-solving.
Author: Richard S. Millman Publisher: Springer ISBN: 3319144278 Category : Mathematics Languages : en Pages : 230
Book Description
Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.
Author: M. Ram Murty Publisher: American Mathematical Soc. ISBN: 1470443996 Category : Decidability (Mathematical logic) Languages : en Pages : 256
Book Description
Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists. This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems. Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.
Author: Giorgio Ausiello Publisher: Springer ISBN: 3319626809 Category : Computers Languages : en Pages : 295
Book Description
This book explains the development of theoretical computer science in its early stages, specifically from 1965 to 1990. The author is among the pioneers of theoretical computer science, and he guides the reader through the early stages of development of this new discipline. He explains the origins of the field, arising from disciplines such as logic, mathematics, and electronics, and he describes the evolution of the key principles of computing in strands such as computability, algorithms, and programming. But mainly it's a story about people – pioneers with diverse backgrounds and characters came together to overcome philosophical and institutional challenges and build a community. They collaborated on research efforts, they established schools and conferences, they developed the first related university courses, they taught generations of future researchers and practitioners, and they set up the key publications to communicate and archive their knowledge. The book is a fascinating insight into the field as it existed and evolved, it will be valuable reading for anyone interested in the history of computing.
Author: Howard Eves Publisher: Courier Corporation ISBN: 0486150275 Category : Mathematics Languages : en Pages : 356
Book Description
The usefulness of matrix theory as a tool in disciplines ranging from quantum mechanics to psychometrics is widely recognized, and courses in matrix theory are increasingly a standard part of the undergraduate curriculum. This outstanding text offers an unusual introduction to matrix theory at the undergraduate level. Unlike most texts dealing with the topic, which tend to remain on an abstract level, Dr. Eves' book employs a concrete elementary approach, avoiding abstraction until the final chapter. This practical method renders the text especially accessible to students of physics, engineering, business and the social sciences, as well as math majors. Although the treatment is fundamental — no previous courses in abstract algebra are required — it is also flexible: each chapter includes special material for advanced students interested in deeper study or application of the theory. The book begins with preliminary remarks that set the stage for the author's concrete approach to matrix theory and the consideration of matrices as hypercomplex numbers. Dr. Eves then goes on to cover fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, similarity and congruence. A final optional chapter considers matrix theory from a generalized or abstract viewpoint, extending it to arbitrary number rings and fields, vector spaces and linear transformations of vector spaces. The author's concluding remarks direct the interested student to possible avenues of further study in matrix theory, while an extensive bibliography rounds out the book. Students of matrix theory will especially appreciate the many excellent problems (solutions not provided) included in each chapter, which are not just routine calculation exercises, but involve proof and extension of the concepts and material of the text. Scientists, engineers, economists and others whose work involves this important area of mathematics, will welcome the variety of special types of matrices and determinants discussed, which make the book not only a comprehensive introduction to the field, but a valuable resource and reference work.
Author: Willi-Hans Steeb Publisher: World Scientific Publishing Company ISBN: 9813101733 Category : Science Languages : en Pages : 252
Book Description
As an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus, this self-contained book is ideal for both graduate and undergraduate mathematics students. The coverage includes systems of linear equations, linear differential equations, functions of matrices and the Kronecker product. Many of the problems are related to applications in areas such as group theory, Lie algebra theory and graph theory. Thus, physics and engineering students will also benefit from the book. Exercises for matrix-valued differential forms are also included.
Author: Joel N. Franklin Publisher: Prentice Hall ISBN: Category : Mathematics Languages : en Pages : 312
Book Description
Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.
Author: Abraham Berman
Author: Abraham Berman
Author: Hong-Bing Yu
Author: Richard S. Millman
Author: M. Ram Murty
Author: Giorgio Ausiello
Author: Howard Eves
Author: Willi-Hans Steeb
Author: Thomas Butts
Author: Joel N. Franklin
Author: