David Aldous

Robin Pemantle

The articles in this volume present the state of the art in a variety of areas of discrete probability, including random walks on finite and infinite graphs, random trees, renewal sequences, Stein's method for normal approximation and Kohonen-type self-organizing maps. This volume also focuses on discrete probability and its connections with the theory of algorithms. Classical topics in discrete mathematics are represented as are expositions that condense and make readable some recent work on Markov chains, potential theory and the second moment method. This volume is suitable for mathematicians and students.

Random Discrete Structures

Fiona C. Chambers

Anna Bryant

This innovative and user-friendly book uses a design thinking approach to examine transformative learning and liminality in physical education. Covering theory and practice, it introduces the important idea of ‘threshold concepts’ for physical education, helping physical educators to introduce those concepts into curriculum, pedagogy and assessment. The book invites us to reflect on what is learned in, through and about physical education - to identify its core threshold concepts. Once identified, the book explains how the learning of threshold concepts can be planned using principles of pedagogical translation for all four learning domains (cognitive, psychomotor, affective and social). The book is arranged into three key sections which walk the reader through the underpinning concepts, use movement case studies to explore and generate threshold concepts in physical education using design thinking approach and, finally, provide a guiding Praxis Matrix for PE Threshold Concepts that can be used for physical educators across a range of school and physical activity learning contexts. Outlining fundamental theory and useful, practical teaching and coaching advice, this book is invaluable reading for all PE teacher educators, coach educators, and any advanced student, coach or teacher looking to enrich their knowledge and professional practice.

A Design Thinking Approach

Threshold Concepts in Physical Education

Persi Diaconis

J. Michael Steele

Joel Spencer

Discrete probability theory and the theory of algorithms have become close partners over the last ten years, though the roots of this partnership go back much longer. The papers in this volume address the latest developments in this active field. They are from the IMA Workshops "Probability and Algorithms" and "The Finite Markov Chain Renaissance." They represent the current thinking of many of the world's leading experts in the field. Researchers and graduate students in probability, computer science, combinatorics, and optimization theory will all be interested in this collection of articles. The techniques developed and surveyed in this volume are still undergoing rapid development, and many of the articles of the collection offer an expositionally pleasant entree into a research area of growing importance.

Discrete Probability and Algorithms

Many leisure activities involve the use of turf as a surface. Grass surfaces on golf courses, bowling clubs, cricket pitches, racetracks, and parks all require maintenance by trained personnel. International Turf Management Handbook is written by a team of international experts. It covers all aspects of turf management and in particular * the selection and establishment of grass varieties * soils, irrigation and drainage * performance testing and playing qualities * issues relating to specific playing surfaces In its depth of coverage and detailed practical advice from around the world this comprehensive handbook is destined to become the standard reference work on the subject.

International Turf Management

If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i. i. d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i. i. d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and true distributions? These questions cover a wide cross-section of theoretical and applied probability. The common theme is that they all deal with maxima or min ima, in some sense.

David Aldous

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