Martin Anthony

Accessible, concise, and interactive, this book introduces the mathematical methods that are indispensable in economics and finance. Fully updated to be as student friendly as possible, this edition contains extensive problems, worked examples and exercises (with full solutions at the end of the book). Two brand new chapters cover coupled systems of recurrence/differential equations, and matrix diagonalisation. All topics are motivated by problems from economics and finance, demonstrating to students how they can apply the mathematical techniques covered. For undergraduate students of economics, mathematics, or both, this book will be welcomed for its clarity and breadth and the many opportunities it provides for readers to practise and test their understanding.

Accessible, concise, and interactive, this book introduces the mathematical methods that are indispensable in economics and finance. Fully updated to be as student friendly as possible, this edition contains extensive problems, worked examples and exercises (with full solutions at the end of the book). Two brand new chapters cover coupled systems of recurrence/differential equations, and matrix diagonalisation. All topics are motivated by problems from economics and finance, demonstrating to students how they can apply the mathematical techniques covered. For undergraduate students of economics, mathematics, or both, this book will be welcomed for its clarity and breadth and the many opportunities it provides for readers to practise and test their understanding.

My name is Martin Anthony. I'm a young man living the dream of being a Metalhead. In 2010 I left home for six weeks to take a solo trip of a lifetime to visit the United States and Canada. For those six weeks, I was on my own, achieving a lifelong goal to visit North America. For six weeks I went across North America to visit eight great cities. In these six weeks I was able to see the sights I had wanted to visit, watch the Hard Rock and Heavy Metal bands I wanted to see and understand what being alone with only $5000 on tour is like. I survived a bomb threat in Times Square, walked through freeways to get to a Winger gig, dodged a jaywalking fine by a NYPD officer, shook hands with Ann and Nancy Wilson, walked the streets and avenues of Manhattan, crawled on my hands and feet to visit Lady Liberty and had a brush with Pornstar Carol Cox in Montreal. This is my Journal.

Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.

This book describes theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Research on pattern classification with binary-output networks is surveyed, including a discussion of the relevance of the Vapnik–Chervonenkis dimension, and calculating estimates of the dimension for several neural network models. A model of classification by real-output networks is developed, and the usefulness of classification with a 'large margin' is demonstrated. The authors explain the role of scale-sensitive versions of the Vapnik–Chervonenkis dimension in large margin classification, and in real prediction. They also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient constructive learning algorithms. The book is self-contained and is intended to be accessible to researchers and graduate students in computer science, engineering, and mathematics.

This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. The author discusses interesting connections between special types of Boolean functions and the simplest types of neural networks. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.

This book describes recent theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Research on pattern classification with binary-output networks is surveyed, including a discussion of the relevance of the Vapnik-Chervonenkis dimension, and calculating estimates of the dimension for several neural network models. A model of classification by real-output networks is developed, and the usefulness of classification with a ‘large margin’ is demonstrated. The authors explain the role of scale-sensitive versions of the Vapnik-Chervonenkis dimension in large margin classification, and in real prediction. They also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient constructive learning algorithms. The book is self-contained and is intended to be accessible to researchers and graduate students in computer science, engineering, and mathematics.