This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers…
Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles a…
This book experimentally investigates the angular light scattering properties of three atmospherically relevant particles: ice crystals, dust particles and secondary organic aerosol particles. Key optical quantities under examination are the near-backscattering depolarisation properties and the angular light scattering function. The main question is how these parameters are related to the parti…
The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not a…
Hydrogels are the foundation of regenerative medicine as a supportive matrix for cell immobilization and growth factor delivery. The fate of implanted cells is mediated by cell-matrix interaction at multiple scales and timed-release of growth factors to guide the differentiation and maturation of cells. Recently, there has been great interest in hydrogels with a hierarchical structure that mimi…
Here are clear explanations of how to make superb astronomical deep-sky images using only a DSLR or webcam and an astronomical telescope – no expensive dedicated CCD cameras needed! The book is written for amateur astronomers interested in budget astrophotography – the deep sky, not just the Moon and planets – and for those who want to improve their imaging skills using DSLR and webcam…
This book deals at some length with the question: Since there are many more poor than rich, why don’t the poor just tax the rich heavily and reduce the inequality? In the 19th century and the first half of the 20th century, the topic of inequality was discussed widely. Ending or reducing inequality was a prime motivating factor in the emergence of communism and socialism. The book discusses w…
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Ma…
This textbook, or really a “coursebook” for a college freshman-level class, has been updated for Spring 2014 and provides an introduction to programming and problem solving using both Matlab and Mathcad. We provide a balanced selection of introductory exercises and real-world problems (i.e. no “contrived” problems). We include many examples and screenshots to guide the reader. We assume…
200 words; this text will present the book in all promotional forms (e.g. flyers). Please describe the book in straightforward and consumer-friendly terms. [Plants interact with microbes in many different ways and on many different levels. The most obvious interaction results in plant disease, which can be a severe threat to the global food supply. Therefore, research strives to uncover the mec…