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Zoekresultaten (5)

HBO/WO

MBO

1 april 2019

10 Supply and Demand: A mathematical approach

Get to know Basic Concepts: -- y=ax+b -- Demand=aP+b -- Supply=aP+b

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Ning Ding

1 april 2019

11 Application: Case of Cocoa Grind

Supply and demand explained in the case of cocoa grind

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Ning Ding

23 augustus 2023

Lecture: Introduction General Explainable AI

Understand, analyze and elaborate upon the importance of XAI in the modern world. Differentiate between transparent and opaque machine learning models. Categorize and discuss approaches to explainability XAI based on model scope, agnosticity, data types and explanation techniques. Discern, investigate and discuss the trade-off between accuracy and interpretability. Summarize and understand the working principles and mathematical modeling of XAI techniques like LIME, SHAP, DiCE, LRP, counterfactual and contrastive explanations. Expand on possible applications of XAI techniques like LIME, SHAP, DiCE, LRP to generate explanations for black-box models for tabular, textual, and image datasets.

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HCAIM Consortium

8 oktober 2021

Foundations of General Relativity: From Einstein to Black Holes

This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory. 4 October 2022: as of today the second edition has been published online and in print. Further research and a meeting with Roger Penrose prompted the author to expand the material about the Hole Argument, Penrose’s 1965 theorem, and Cosmic Censorship. This changed the preambles to Chapters 6 and 10, as well as §§1.5, 6.1, 7.5, 7.6, 10.4, 10.5. He also added new sections 5.11 & 7.8. Klaas Landsman (1963) has been a professor of mathematical physics since 2001, initially at the University of Amsterdam and since 2004 at Radboud University, where he is a founding member of the Institute for Mathematics, Astrophysics, and Particle Physics (IMAPP). He was a postdoc at the University of Cambridge from 1989-1997, and a research fellow of the Royal Netherlands Academy of Arts and Sciences (KNAW) from 1997—2002. He has been an elected member of the KNAW since 2019. His previous Open Access books include Foundations of Quantum Theory (2017) and The Challenge of Chance (2016). He also wrote two popular science books in Dutch. In 2020 he won the international FQXi essay contest on Undecidability, Uncomputability, and Unpredictability.

Open (Access) Tekst Boek

Klaas Landsman

27 maart 2023

Number Fields

Number Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory. Part I of the book contains topics in basic algebraic number theory as they may be presented in a beginning master course on algebraic number theory. It includes the classification of abelian number fields by groups of Dirichlet characters. Class field theory is treated in Part II: the more advanced theory of abelian extensions of number fields in general. Full proofs of its main theorems are given using a ‘classical’ approach to class field theory, which is in a sense a natural continuation of the basic theory as presented in Part I. The classification is formulated in terms of generalized Dirichlet characters. This ‘ideal-theoretic’ version of class field theory dates from the first half of the twentieth century. In this book, it is described in modern mathematical language. Another approach, the ‘idèlic version’, uses topological algebra and group cohomology and originated halfway the last century. The last two chapters provide the connection to this more advanced idèlic version of class field theory. The book focuses on the abstract theory and contains many examples and exercises. For quadratic number fields algorithms are given for their class groups and, in the real case, for the fundamental unit. New concepts are introduced at the moment it makes a real difference to have them available.

Open (Access) Tekst Boek

Frans Keune