Pawel Pralat – författare

This accessible book helps readers to see the bigger picture of advanced mathematics. The book contains carefully selected, challenging problems in an easy-to-follow, step-by-step process. Neither prior preparation nor any mathematical sophistication is required.

The authors guide the reader to “train their brain” to think and express themselves in a rigorous, mathematical way, and to extract facts, analyze the problem, and identify main challenges. A firm foundation in a diverse range of topics is presented. Moreover, the authors show how to draw appropriate, true conclusions. Computer support is used to better intuition into discussed problems. The book is designed for self-study. It can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. The reader will develop a deeper understanding in preparation to succeed in more advanced course work.

Features•The authors employ a six-step process: 1.SOURCE2.PROBLEM3.THEORY4.SOLUTION5.REMARK6.EXERCISES

•An Appendix introduces programming in Julia

This book is also suitable for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions.

This accessible book helps readers to see the bigger picture of advanced mathematics. The book contains carefully selected, challenging problems in an easy-to-follow, step-by-step process. Neither prior preparation nor any mathematical sophistication is required.

The authors guide the reader to “train their brain” to think and express themselves in a rigorous, mathematical way, and to extract facts, analyze the problem, and identify main challenges. A firm foundation in a diverse range of topics is presented. Moreover, the authors show how to draw appropriate, true conclusions. Computer support is used to better intuition into discussed problems. The book is designed for self-study. It can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. The reader will develop a deeper understanding in preparation to succeed in more advanced course work.

Features•The authors employ a six-step process: 1.SOURCE2.PROBLEM3.THEORY4.SOLUTION5.REMARK6.EXERCISES

•An Appendix introduces programming in Julia

This book is also suitable for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions.

Graph Searching Games and Probabilistic Methods is the first book that focuses on the intersection of graph searching games and probabilistic methods. The book explores various applications of these powerful mathematical tools to games and processes such as Cops and Robbers, Zombie and Survivors, and Firefighting.

Written in an engaging style, the book is accessible to a wide audience including mathematicians and computer scientists. Readers will find that the book provides state-of-the-art results, techniques, and directions in graph searching games, especially from the point of view of probabilistic methods.

The authors describe three directions while providing numerous examples, which include:

• Playing a deterministic game on a random board.

• Players making random moves.

• Probabilistic methods used to analyze a deterministic game.

Graph Searching Games and Probabilistic Methods is the first book that focuses on the intersection of graph searching games and probabilistic methods. The book explores various applications of these powerful mathematical tools to games and processes such as Cops and Robbers, Zombie and Survivors, and Firefighting.

Written in an engaging style, the book is accessible to a wide audience including mathematicians and computer scientists. Readers will find that the book provides state-of-the-art results, techniques, and directions in graph searching games, especially from the point of view of probabilistic methods.

The authors describe three directions while providing numerous examples, which include:

• Playing a deterministic game on a random board.

• Players making random moves.

• Probabilistic methods used to analyze a deterministic game.

This book constitutes the proceedings of the 16th International Workshop on Algorithms and Models for the Web Graph, WAW 2019, held in Brisbane, QLD, Australia, in July 2019. The 9 full papers presented in this volume were carefully reviewed  and selected from 13 submissions. The papers cover topics of all aspects of algorithmic and mathematical research in the areas pertaining to the World Wide Web, espousing the view of complex data as networks.

This book constitutes the proceedings of the 17th International Workshop on Algorithms and Models for the Web Graph, WAW 2020, held in Warsaw, Poland, in September 2020. The 12 full papers presented in this volume were carefully reviewed and selected from 19 submissions. The aim of the workshop was to further the understanding of graphs that arise from the Web and various user activities on the Web, and stimulate the development of high-performance algorithms and applications that exploit these graphs.

Due to the corona pandemic the conference was postponed from June 2020 to September 2020.

This book provides a broad overview of the state of the art of the research in generative methods for the analysis of social media data. It especially includes two important aspects that currently gain importance in mining and modelling social media: dynamics and networks.

The book is divided into five chapters and provides an extensive bibliography consisting of more than 250 papers. After a quick introduction and survey of the book in the first chapter, chapter 2 is devoted to the discussion of data models and ontologies for social network analysis. Next, chapter 3 deals with text generation and generative text models and the dangers they pose to social media and society at large. Chapter 4 then focuses on topic modelling and sentiment analysis in the context of social networks. Finally, Chapter 5 presents graph theory tools and approaches to mine and model social networks. Throughout the book, open problems, highlighting potential future directions, are clearly identified.

The book aims at researchers and graduate students in social media analysis, information retrieval, and machine learning applications.

This book constitutes the refereed proceedings of the 19th International Workshop on Modelling and Mining Networks, WAW 2024, held in Warsaw, Poland, during June 3–6, 2024.

The 12 full papers presented in this book were carefully reviewed and selected from 19 submissions. The aim of this workshop was to further the understanding of networks that arise in theoretical as well as applied domains. The goal was also to stimulate the development of high-performance and scalable algorithms that exploit these networks. 

This book constitutes the refereed proceedings of the 20th International Workshop on Modelling and Mining Networks, WAW 2025, held in Vilnius, Lithuania, during June 30–July 3, 2025.The 13 full papers presented in this book were carefully reviewed and selected from 20 submissions.The aim of the 20th Workshop on Modelling and Mining Networks was to further the understanding of networks that arise in theoretical as well as applied domains. The goal was also to stimulate the development of high performance and scalable algorithms that exploit these networks.