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Introduction to Algebra
This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters,new material on axiom of Choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics.
Combinatorics
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
Introduction to Algebra
This book is an undergraduate textbook on abstract algebra, beginning with the theories of rings and groups. As this is the first really abstract material students need, the pace here is gentle, and the basic concepts of subring, homomorphism, ideal, etc are developed in detail. Later, asstudents gain confidence with abstractions, they are led to further developments in group and ring theory (simple groups and extensions, Noetherian rings, and outline of universal algebra, lattices and categories) and to applications such as Galois theory and coding theory. There is also a chapteroutlining the construction of the number systems from scratch and proving in three different ways that trascendental numbers exist.
Sets, Logic and Categories
Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.
Permutation Groups
This book summarizes recent developments in the study of permutation groups for beginning graduate students.
The Mindful Day
Combining contemplative traditions, modern neuroscience, and psychology, this engaging, relatable book is the ultimate how-to guide for overscheduled adults looking to bring peace and focus to their daily lives at home, in the workplace, and beyond. At the pinnacle of the digital age, it's hard to imagine packing one more thing into our overwhelmed lives. But new research shows that simple daily exercises can change the way our brain works, improve focus, lift our mood, create stronger connections, and help us develop greater resilience. In this enriching book, noted teacher and mindfulness expert Laurie Cameron provides an everyday road map to cultivate inner peace and navigate any situation with control and clarity. Timeless teachings and straightforward practices designed for busy schedules--from the morning commute to back-to-back meetings to family dinners--show how mindfulness can transform life at home, in the workplace, and beyond. A personal guide for women who have leaned in, men who want to be more effective, and professionals looking to optimize their lives, this book will help readers lead their lives with intention and purpose.
Designs, Graphs, Codes and their Links
This book stresses the connection between, and the applications of, design theory to graphs and codes. Beginning with a brief introduction to design theory and the necessary background, the book also provides relevant topics for discussion from the theory of graphs and codes.
Planning Law and Practice
The Law related to Town and Country Planning has a major impact on the physical environment and the lives of individuals, whether they be developers or private citizens. The main aim of this book is to provide a text for students, practitioners and members of the public who are engaged in the study, practice or personal involvement in the planning system of England and Wales.
The Mathematics of Paul Erdős II
This is the most comprehensive survey of the mathematical life of the legendary Paul Erdős (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdős' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles as well as key articles that survey some of the cornerstones of Erdős' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdős complement this striking collectio...
Resistance at the Edge of Empires
From 1985 to 2001, the collaborative research initiative known as the Bannu Archaeological Project conducted archaeological explorations and excavations in the Bannu region, in what was then the North West Frontier Province (NWFP) of Pakistan, now Khyber-Pakhtunkhwa. This Project involves scholars from the Pakistan Heritage Society, the British Museum, the Institute of Archaeology (UCL), Bryn Mawr College and the University of Cambridge. This is the third in a series of volumes that present the final reports of the exploration and excavations carried out by the Bannu Archaeological Project. This volume presents the first synthesis of the archaeology of the historic periods in the Bannu region, spanning the period when the first large scale empires expanded to the borders of South Asia up until the arrival of Islam in the subcontinent at the end of the first and beginning of the second millennium BC. The Bannu region provides specific insight into early imperialism in South Asia, as throughout this protracted period, it was able to maintain a distinctive regional identity in the face of recurring phases of imperial expansion and integration.
