This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

The botanist and mining engineer John Miers (1789 1879) published Travels in Chile and La Plata in 2 volumes in 1826. The work is an account of his travels and residence in Chile between 1818 and 1825 and his investigations into the cultural, political, geographical and botanical aspects of the country. Richly illustrated with maps and his own drawings, the work is most valuable for the data it contains from Miers' research into the plants and birds he found there, including drawings and descriptions of many species previously unknown to the West. Volume 2 also gives an account of Chile's political and economic history; its religion and culture; its trade, agriculture and mining; and contains an appendix listing the plants and animals he examined. The work is both a rich source for geographical and botanical information and offers an insight into Victorian perceptions of Chile.

The botanist and mining engineer John Miers (1789 1879) published Travels in Chile and La Plata in 2 volumes in 1826. The work is an account of his travels and residence in Chile between 1818 and 1825 and his investigations into the cultural, political, geographical and botanical aspects of the country. Richly illustrated with maps and his own drawings, the work is most valuable for the data it contains from Miers' research into the plants and birds he found there, including drawings and descriptions of many species previously unknown to the West. Volume 1 also contains the main travel account of his journey from England to Chile, geographical descriptions of the places he explored there, and an account of his plans and negotiations to build a copper-refining plant. The work is a rich source of botanical information and offers an insight into Victorian perceptions of Chile.

Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.

Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.

Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.