https://doi.org/10.1142/11796 |
September 2020
Pages: 300
Problem Solving in Mathematics and Beyond: Volume 19
ISBN: 978-981-121-989-4 (hardcover)
ISBN: 978-981-121-925-2 (softcover)
This book is composed of the most interesting problems from a quarter century of regional mathematics competitions for students aged 11?14 in the province of Styria, Austria. The problems presented here range from pure puzzles to a more traditional mathematical type of question, but all are somehow special, posed with the intent of giving the reader something interesting to think about, with the promise of an entertaining moment of elucidation and enlightenment at the end.
Number Digits
A Little Bit of Algebra
Building with Bricks
Sports
Circles
Logic
Fractions
Percentages
Our 3D World
Money
Its About Time
Letter Puzzles and Digit Puzzles
How Frau, How Fast, How Long
Triangles
Quadrilaterals and Polygons
Divisibility
Cutting and Rearranging
Sequences
Counting Things
Students, Teachers, Adults interested in solving mathematical puzzles, Trainers for Math Competitions.
https://doi.org/10.1142/11795 | August 2020
Pages: 304
Problem Solving in Mathematics and Beyond: Volume 18
ISBN: 978-981-121-990-0 (hardcover)
ISBN: 978-981-121-928-3 (softcover)
This book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations.
The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level.
Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics ? to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics ? something most general readers will not initially find possible, but we hope will be an end product of this book.
About the Author
Introduction
Arithmetic Entertainments
The Fun of Logical Reasoning
Geometric Surprises
A Potpourri of Mathematical Entertainments
Final Thoughts
General public, mathematics teachers, mathematics enthusiasts.
https://doi.org/10.1142/11830 | October 2020
Pages: 200
ISBN: 978-981-122-040-1 (hardcover)
ISBN: 978-981-122-107-1 (softcover)
This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.
The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems.
Preface
Arithmetic of Matrices
Elementary Matrices; Determinants
Vector Geometry in R?
Vector Spaces
Subspaces
Linear Independence
Basis for a Vector Space
Linearity
Linear Maps between Euclidean Spaces
Projection Operators
Eigenvalues and Eigenvectors
Diagonalization of Matrices
Spectral Theorem for Vector Spaces
Some Applications of the Spectral Theorem
Every Operator is Diagonalizable Plus Nilpotent
Complex Arithmetic
Real and Complex Inner Product Spaces
Orthonormal Sets of Vectors
Quadratic Forms
Optimization
Adjoints and Transposes
The Four Fundamental Subspaces
Orthogonal Projections
Least Squares Approximation
Spectral Theorem for Real Inner Product Spaces
Spectral Theorem for Complex Inner Product Spaces
Students and teachers of linear algebra.
https://doi.org/10.1142/11849 | February 2021
Pages: 200
ISBN: 978-981-122-096-8 (hardcover)
We live in the age of technology where messages are transmitted in sequences of 0's and 1's through space. It is possible to make an error with noisy channels, so self-correcting codes become vital to eradicate all errors (as the number of errors is small). These self-correcting codes are widely used in the industry for a variety of applications including e-mail, telephone, remote sensing (e.g., photographs of Mars), amongst others.
We will present some essentials of the theory in this book. Using linear algebra, we have the salient Hamming codes. The next level of coding theory is through the usage of ring theory, especially polynomials, rational functions and power series, to produce BCH codes, Reed?Solomon codes and the classical Goppa codes. Then we progress to the geometric Goppa code using Algebraic Geometry.
Linear Codes
Rings
Ring Codes
Algebraic Geometry
Algebraic Geometric Code
Decoding the Geometric Goppa Codes
Advanced college students, graduate students, working coding theoreticians, working algebraic geometers.