The French expression "dessins d'enfants'' means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number ......
This book presents nine variations on a classic and beloved puzzle type. Building upon the rules of Sudoku, the puzzles in this volume introduce new challenges by adding clues involving sums, differences, means, divisibility, and more. Each of the first eight chapters presents a rule system followed by a series of puzzles that progress in ......
A Constructive Approach Through Interval Arithmetic
Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly ......
Linear Algebra: Concepts and Applications is designed to be used in a first linear algebra course taken by mathematics and science majors. It provides a complete coverage of core linear algebra topics, including vectors and matrices, systems of linear equations, general vector spaces, linear transformations, eigenvalues, and eigenvectors. All ......
This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of ......
A Dingo Ate My Math Book presents ingenious, unusual, and beautiful nuggets of mathematics with a distinctly Australian flavor. It focuses, for example, on Australians' love of sports and gambling, and on Melbourne's iconic, mathematically inspired architecture. Written in a playful and humorous style, the book offers mathematical entertainment as ......
Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and curvature bounded below (CBB). Even though the definitions of the two classes of spaces are ......
This book is a translation from Russian of Part III of the book Mathematics Through 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 ......
This book is a concrete introduction to abstract algebra and number theory. Starting from the basics, it develops the rich parallels between the integers and polynomials, covering topics such as Unique Factorization, arithmetic over quadratic number fields, the RSA encryption scheme, and finite fields. In addition to introducing students to the ......
