Mathematics and programming are two foundational pillars in the digital era we live in today. This book, From Equations to Algorithms: Mathematics Essentials with Julia, is designed to help you understand the essence of mathematics in the world of programming and explore how mathematical concepts can be translated into effective algorithms. The aim is to build a strong foundation in mathematics while offering practical guidance on applying these concepts through Julia programming. This book merges core mathematical principles with modern programming techniques. Each chapter delves into one or more key mathematical concepts frequently used in data analysis, machine learning, and optimization algorithms—from basic equations and set theory to linear algebra and optimization. Using Julia, readers will learn how these concepts can be translated into functional code, ultimately providing real-world utility for various technology-driven projects. This practical approach makes the book suitable not only for beginners looking to build a fundamental understanding of mathematics and programming but also for professionals eager to deepen their skills. Throughout, readers will discover how Julia simplifies computation and visualization processes, helps identify patterns, and offers deeper insights into solving complex problems. I extend my gratitude to everyone who supported the creation of this book, especially those who championed the integration of mathematics and programming into everyday life. I hope this book will serve as a valuable learning resource and open new avenues for understanding mathematics through a modern, algorithmic approach. Happy reading, and may your journey toward mastering mathematics and programming be enjoyable and inspiring!

In its fourth edition, this book focuses on real-world examples and practical applications and encourages students to develop a "big-picture" understanding of how essential organization and architecture concepts are applied in the computing world. In addition to direct correlation with the ACM/IEEE CS2013 guidelines for computer organization and architecture, the text exposes readers to the inner workings of a modern digital computer through an integrated presentation of fundamental concepts and principles. It includes the most up-to-the-minute data and resources available and reflects current technologies, including tablets and cloud computing. All-new exercises, expanded discussions, and feature boxes in every chapter implement even more real-world applications and current data, and many chapters include all-new examples. --

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

Contains research articles on linear algebra with emphasis on applications and numerical procedures. These applications include such areas as Markov chains, networks, signal processing, systems and control theory, mathematical programming, economic and biological modeling, and statistics and operations research.