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Communicating with Data: The Art of Writing for Data Science aims to help students and researchers write about their data insights in a way that is both compelling and faithful to the data. This book aims to be both a resource for students who want to learn how to write about scientific findings both formally and for broader audiences and a textbook for instructors who are teaching science communication. In addition, a researcher who is looking for help with writing can use this book to self-train. The book consists of five parts. Part I helps the novice learn to write by reading the work of others. Part II delves into the specifics of how to describe data at a level appropriate for publication, create informative and effective visualizations, and communicate an analysis pipeline through well-written, reproducible code. Part III demonstrates how to reduce a data analysis to a compelling story and organize and write the first draft of a technical paper. Part IV addresses revision; this includes advice on writing about statistical findings in a clear and accurate way, general writing advice, and strategies for proof-reading and revising. Finally, Part V gives advice about communication strategies beyond the witten page, which includes giving talks, building a professional network, and participating in online communities. This part also contains 22 “portfolio prompts” aimed at building upon the guidance and examples in the earlier parts of the book and building a writer’s portfolio of data communication.

The disc embedding theorem provides a detailed proof of the eponymous theorem in 4-manifold topology. The theorem, due to Michael Freedman, underpins virtually all of our understanding of 4-manifolds in the topological category. Most famously, this includes the 4-dimensional topological Poincaré conjecture. Combined with the concurrent work of Simon Donaldson, the theorem reveals a remarkable disparity between the topological and smooth categories for 4-manifolds. A thorough exposition of Freedman’s proof of the disc embedding theorem is given, with many new details. A self-contained account of decomposition space theory, a beautiful but outmoded branch of topology that produces non-differentiable homeomorphisms between manifolds, is provided. Techniques from decomposition space theory are used to show that an object produced by an infinite, iterative process, which we call a skyscraper, is homeomorphic to a thickened disc, relative to its boundary. A stand-alone interlude explains the disc embedding theorem’s key role in smoothing theory, the existence of exotic smooth structures on Euclidean space, and all known homeomorphism classifications of 4-manifolds via surgery theory and the s-cobordism theorem. The book is written to be accessible to graduate students working on 4-manifolds, as well as researchers in related areas. It contains over a hundred professionally rendered figures.

What are the Chances of That? discusses chance and the importance of understanding how it affects our lives in its various guises such as risk, luck, and coincidence. The book goes beyond a mathematical approach to the subject, showing how our thinking about chance and uncertainty has been shaped by history and culture, and only relatively recently by the mathematical theory of probability. In considering how we think about uncertainty, five ‘dualities’ are proposed that encapsulate many of the ambiguities that arise. The book starts by tackling probability (‘Pure Chance’) and in successive sections (‘Life Chances’, ‘Happy Accidents’, ‘Taking Charge of Chance’) addresses respectively the role of chance in life, the positive face of uncertainty, and the ways in which we are able to act to mitigate and exploit chance. This is not primarily a mathematical book, but it does introduce basic concepts from the theory of probability, and some statistics. Although this book tackles serious subjects, it is written in an accessible way and is aimed at an educated and curious lay reader, to be read for pleasure and general interest. It includes graphical representations of the effects of chance, brain teasers, anecdotes, and discussion of the words we use to talk about uncertainty.