Proofs And Confirmations

This is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While apparent that the conjecture must be true, the proof was elusive. Researchers became drawn to this problem, making connections to aspects of invariant theory, to symmetric functions, to hypergeometric and basic hypergeometric series, and, finally, to the six-vertex model of statistical mechanics. All these threads are brought together in Zeilberger's 1996 proof of the original conjecture. The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something new here.

The terms forensic investigator and forensic investigation are part of our cultural identity. They can be found in the news, on television, and in film. They are invoked, generally, to imply that highly trained personnel will be collecting some form of physical evidence with eventual scientific results that cannot be questioned or bargained with. In other words, they are invoked to imply the reliability, certainty, and authority of a scientific inquiry. Using cases from the authors’ extensive files, Forensic Investigations: An Introduction provides an overview of major subjects related to forensic inquiry and evidence examination. It will prepare Criminal Justice and Criminology students in forensic programs for more specialized courses and provide a valuable resource to newly employed forensic practitioners. Written by practicing and testifying forensic professionals from law enforcement, academia, mental health and the forensic sciences, this work offers a balanced scientific approach, based on the established literature, for broad appeal. The purpose of this book is to help students and professionals rid themselves of the myths and misconceptions they have accumulated regarding forensic investigators and the subsequent forensic investigations they help to conduct. It will help the reader understand the role of the forensic investigator; the nature and variety of forensic investigations that take place in the justice system; and the mechanisms by which such investigations become worthy as evidence in court. Its goals are no loftier than that. However, they could not be more necessary to our understanding of what justice is, how it is most reliably achieved, and how it can be corrupted by those who are burdened with apathy and alternative motives. A primary text for instructors teaching forensic courses related to criminal and forensic investigation Written by forensic professionals, currently in practice and testifying in court Offers applied protocols for a broad range of forensic investigations Augments theoretical constructs with recent, and relevant case studies and forensic reports Based on the most recent scientific research, practice, and protocols related to forensic inquiry

The most recalcitrant problem of philosophy, free will, laid out and taken beyond unsatisfactory standard solutions by Britain's foremost working philosopher.Determinism comes in many forms, some confused, some inconsistent, some incomplete. Some philosophers maintain that determinism is incompatible with true freedom. And others, that determinism is no threat to our freedom. But are these philosophers really assigning an 'unfreedom' to us and merely pretending that we are responsible for our choices and acts of love and violence?Ted Honderich argues that there are strong reasons to think both positions wrong. Developing from where his earlier work left off, he considers there is a new and more difficult problem of determinism. It too can lead to the thought that we are unfree but morally responsible. As he demonstrates, the hardest and deepest question in philosophy needs a really different answer.

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.