Andrea Ferretti – författare

This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra. The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra.Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.

This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author's book, Commutative Algebra.The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, starting from categorical language up to the construction of derived functors and spectral sequences. A full proof of the celebrated Freyd-Mitchell theorem on the embeddings of small Abelian categories is included.The second part of the book is devoted to the application of these techniques in commutative algebra through the study of projective, injective, and flat modules, the construction of explicit resolutions via the Koszul complex, and the properties of regular sequences. The theory is then used to understand the properties of regular rings, Cohen-Macaulay rings and modules, Gorenstein rings and complete intersections.Overall, this book is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra. The clear and thorough presentation of the material, along with the many examples and exercises of varying difficulty, make it an excellent choice for self-study or as a reference for researchers.

This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra. The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra.Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.

This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author's book, Commutative Algebra.The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, starting from categorical language up to the construction of derived functors and spectral sequences. A full proof of the celebrated Freyd-Mitchell theorem on the embeddings of small Abelian categories is included.The second part of the book is devoted to the application of these techniques in commutative algebra through the study of projective, injective, and flat modules, the construction of explicit resolutions via the Koszul complex, and the properties of regular sequences. The theory is then used to understand the properties of regular rings, Cohen-Macaulay rings and modules, Gorenstein rings and complete intersections.Overall, this book is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra. The clear and thorough presentation of the material, along with the many examples and exercises of varying difficulty, make it an excellent choice for self-study or as a reference for researchers.

This book constitutes revised selected papers from two workshops held at the 18th European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2018, in Dublin, Ireland, in September 2018, namely:MIDAS 2018 – Third Workshop on Mining Data for Financial Applications andPAP 2018 – Second International Workshop on Personal Analytics and Privacy.The 12 papers presented in this volume were carefully reviewed and selected from a total of 17 submissions.

This book constitutes revised selected papers from the 4th Workshop on Mining Data for Financial Applications, MIDAS 2019, held in conjunction with ECML PKDD 2019, in Würzburg, Germany, in September 2019. The 8 full and 3 short papers presented in this volume were carefully reviewed and selected from 16 submissions.

This book constitutes revised selected papers from the 5th Workshop on Mining Data for Financial Applications, MIDAS 2020, held in conjunction with ECML PKDD 2020, in Ghent, Belgium, in September 2020.*The 8 full and 3 short papers presented in this volume were carefully reviewed and selected from 15 submissions.

This two-volume set constitutes the refereed proceedings of the workshops which complemented the 21th Joint European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD, held in September 2021. Due to the COVID-19 pandemic the conference and workshops were held online. The 104 papers were thoroughly reviewed and selected from 180 papers submited for the workshops. This two-volume set includes the proceedings of the following workshops:Workshop on Advances in Interpretable Machine Learning and Artificial Intelligence (AIMLAI 2021)Workshop on Parallel, Distributed and Federated Learning (PDFL 2021)Workshop on Graph Embedding and Mining  (GEM 2021)Workshop on Machine Learning for Irregular Time-series (ML4ITS 2021)Workshop on IoT, Edge, and Mobile for Embedded Machine Learning (ITEM 2021)Workshop on eXplainable Knowledge Discovery in Data Mining (XKDD 2021)Workshop on Bias and Fairness in AI (BIAS 2021)Workshop on Workshop on Active Inference (IWAI 2021)Workshop on Machine Learning for Cybersecurity (MLCS 2021)Workshop on Machine Learning in Software Engineering (MLiSE 2021)Workshop on MIning Data for financial applications (MIDAS 2021)Sixth Workshop on Data Science for Social Good (SoGood 2021)Workshop on Machine Learning for Pharma and Healthcare Applications (PharML 2021)Second Workshop on Evaluation and Experimental Design in Data Mining and Machine Learning (EDML 2020)Workshop on Machine Learning for Buildings Energy Management (MLBEM 2021)

This two-volume set constitutes the refereed proceedings of the workshops which complemented the 21th Joint European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD, held in September 2021. Due to the COVID-19 pandemic the conference and workshops were held online. The 104 papers were thoroughly reviewed and selected from 180 papers submited for the workshops. This two-volume set includes the proceedings of the following workshops:Workshop on Advances in Interpretable Machine Learning and Artificial Intelligence (AIMLAI 2021)Workshop on Parallel, Distributed and Federated Learning (PDFL 2021)Workshop on Graph Embedding and Mining  (GEM 2021)Workshop on Machine Learning for Irregular Time-series (ML4ITS 2021)Workshop on IoT, Edge, and Mobile for Embedded Machine Learning (ITEM 2021)Workshop on eXplainable Knowledge Discovery in Data Mining (XKDD 2021)Workshop on Bias and Fairness in AI (BIAS 2021)Workshop on Workshop on Active Inference (IWAI 2021)Workshop on Machine Learning for Cybersecurity (MLCS 2021)Workshop on Machine Learning in Software Engineering (MLiSE 2021)Workshop on MIning Data for financial applications (MIDAS 2021)Sixth Workshop on Data Science for Social Good (SoGood 2021)Workshop on Machine Learning for Pharma and Healthcare Applications (PharML 2021)Second Workshop on Evaluation and Experimental Design in Data Mining and Machine Learning (EDML 2020)Workshop on Machine Learning for Buildings Energy Management (MLBEM 2021)

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