This book constitutes the refereed proceedings of the 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021, held virtually in September 2021.The 16 full papers and 25 short papers presented together with 16 posters were carefully reviewed and selected from 94 submissions. The papers are organized in the following topical sections: design of concrete diagrams; theory of diagrams; diagrams and mathematics; diagrams and logic; new representation syste...

This book constitutes the refereed proceedings of the 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018, held in Edinburgh, UK, in June 2018.The 26 revised full papers and 28 short papers presented together with 32 posters were carefully reviewed and selected from 124 submissions. The papers are organized in the following topical sections: generating and drawing Euler diagrams; diagrams in mathematics; diagram design, principles and classificati...

This book constitutes the thoroughly refereed post-conference proceedings of the 5th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2017, held in Melbourne, VIC, Australia, in August 2017, associated with IJCAI 2017, the 26th International Joint Conference on Artificial Intelligence. The 7 revised full papers presented were reviewed and selected from 9 submissions. The contributions address various issues for knowledge representation and reasonin...

This book constitutes the proceedings of the 22th International Conference on Conceptual Structures, ICCS 2016, held in Annecy, France, in July 2016.The 14 full papers and 5 short papers presented in this volume were carefully reviewed and selected from 40 submissions. They are organized around the following topical sections: time representation; graphs and networks; formal concept analysis; ontologies and linked data.

This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2015, held in Buenos Aires, Argentina, in July 2015, associated with IJCAI 2015, the 24th International Joint Conference on Artificial Intelligence. The 9 revised full papers presented were carefully reviewed and selected from 10 submissions. The papers feature current research involved in the development and applica...

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.*The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections:Part I: AI verification; blockchain and Security; Concurrency; hardwa...

How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for t...

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018.The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical application...

Most designers know that yellow text presented against a blue background reads clearly and easily, but how many can explain why, and what really are the best ways to help others and ourselves clearly see key patterns in a bunch of data? When we use software, access a website, or view business or scientific graphics, our understanding is greatly enhanced or impeded by the way the information is presented. This book explores the art and science of why we see objects the way we do. Based on t...

This book is Open Access under a CC BY licence.The LNCS 11427 and 11428 proceedings set constitutes the proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019.The total of 42 full and 8 short tool demo papers presented in these volumes was carefully...

This book constitutes the proceedings of the 10th International Computer Science Symposium in Russia, CSR 2015, held in Listvyanka, Russia, in July 2015.The 25 full papers presented in this volume were carefully reviewed and selected from 61 submissions. In addition the book contains 4 invited lectures. The scope of the proposed topics is quite broad and covers a wide range of areas in theoretical computer science and its applications.

Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and hard to teach, are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 and also has implications for a wider range of students. These are the ideas that really matter, that students get stuck on, and that can be obstacles to future learning. It shows how students learn, why they sometimes get things wrong, and the stre...