A Journey Through Discrete Mathematics
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A Journey Through Discrete Mathematics
This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.
A Trek Beyond Complexity: A Journey Through Discrete Math for Computing
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-03-10
Embark on a transformative journey into the realm of discrete mathematics, where abstract concepts converge with practical applications, unveiling the foundations of computing and shaping the digital landscape. This comprehensive book invites you to explore the intricate world of sets, logic, functions, relations, and algorithms, providing a solid understanding of the fundamental principles that underpin the digital age. Delve into the depths of counting and probability, unraveling the secrets of quantifying uncertainty and exploring the vast expanse of possibilities. Discover the power of recursion and mathematical induction, uncovering a systematic approach to solving complex problems and proving mathematical statements with unwavering rigor. Navigate the intricate maze of algorithms and complexity, delving into the depths of algorithm design techniques, complexity classes, and approximation algorithms. Witness the elegance of trees and graph theory, unveiling the hidden structures that underpin networks, data structures, and a myriad of real-world phenomena. Unveil the mysteries of number theory and cryptography, where prime numbers hold the key to unlocking encrypted messages and the intricacies of modular arithmetic pave the way for secure communication. Explore the realm of formal specifications and Z-notation, discovering rigorous methods for capturing requirements and ensuring the correctness and reliability of software systems. Witness the inner workings of automata and formal languages, revealing the intricate dance of symbols and rules that govern the behavior of computers and communication systems. Engage in the art of logic and reasoning, empowering yourself with the tools to analyze arguments, draw conclusions, and navigate the complexities of human discourse. Finally, experience the transformative power of discrete mathematics in action, as you explore its diverse applications in computer science, engineering, business, life sciences, and social sciences. From optimizing algorithms to modeling biological systems, discrete mathematics proves to be an indispensable tool for understanding and shaping the world around us. With its blend of theoretical rigor and practical relevance, this book caters to students seeking to master the foundations of computer science and professionals seeking to expand their knowledge. Embark on this intellectual odyssey and discover the elegance and power of discrete mathematics, a discipline that continues to shape the modern world. If you like this book, write a review!
Tale Of Discrete Mathematics, A: A Journey Through Logic, Reasoning, Structures And Graph Theory
Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory.An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills.All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers.As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book.