![]() ![]() So many of my favorite Mac app are part of WinterFest. ![]() WinterFest 2021 features 22 great tools for writers, thinkers, planners. This week’s sponsor, WinterFest 2021 is here for you. We have kids to raise, degrees to pursue, new jobs to find, care to give, and care to take. Many of us need to reimagine our workplaces and our workflows. Karl-Dieter Crisman teaches mathematics at Gordon College in Massachusetts, where he also gets to work on open source software, the mathematics of voting, and examining connections between all of these and issues of belief and faith.Winter is here. Perhaps it will encourage more people to join this growing field, where the author says specialists treat outsiders “very well” - which has been this reviewer’s experience as well. It includes direct references to using the open source software SINGULAR to actually compute invariants, and retains the informal feel of its origins as lecture notes. This book would be a good second text for someone with a strong background in algebraic geometry who learned their arrangements from Orlik/Terao. There are also copious exercises, which is always useful in a text at this level. Similarly, although there are many (many) occasions where proofs or even examples are only given by references to the literature, there are also plenty of places where very useful examples are given to explain the literature, or proof sketches supplied for what Dimca identifies as folklore never previously given full proofs (e.g. ![]() Naturally, given that over half of volume is devoted to Milnor fibers and related areas of cohomological research by the author and his students, that isn’t surprising but Huh’s very recent results on log-concavity are given a good treatment as well. On the other hand, it does succeed as a monograph introducing many results, including quite recent ones. If you don’t know a litany of results in many fields (particularly in algebraic geometry and homological algebra) and don’t have another ready reference for combinatorial results in the field, you won’t get very far starting from scratch here. On the one hand, it is more of an invitation to an interesting field than a comprehensive text. The book under review aims to fill this gap, but only partly succeeds. However, this means there is no truly comprehensive introductory work containing more recent developments, particularly in algebraic geometry. More recently, Stanley has released a combinatorial guide, and a consortium of leading researchers has been working on a comprehensive e-text in the complex case for a number of years now. It is pedagogically sound, covers a wide range of topics from very basic starting points, and covers most foundational results throughout. Directly related fields include algebraic geometry, topology, and combinatorics, among others.Ī standard entry point to this for graduate students has long been Orlik and Terao’s Arrangements of Hyperplanes. ![]() Yet defining (hyper)planes of polyhedra(topes) fit in here, as do configurations of points in the complex plane, matroids, and puzzles about pieces of cake cut with straight cuts. Hyperplane arrangements are fascinating objects which do not always fit well into the “traditional” curriculum, for various definitions of traditional. ![]()
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