More Fallacies, Flaws, and Flimflam is the second volume of selections drawn mostly from the College Mathematics Journal column “Fallacies, Flaws, and Flimflam” from 2000 through 2008. The MAA published the first collection, Mathematical Flaws, Fallacies, and Flimflam, in 2000. As in the first volume, More Fallacies, Flaws, and Flimflam contains items ranging from howlers (outlandish procedures that nonetheless lead to a correct answer) to deep or subtle errors often made by strong students. Although some are provided for entertainment, others challenge the reader to determine exactly where things go wrong. Items are sorted by subject matter. Elementary teachers will find chapter 1 of most use, while middle and high schoolteachers will find chapters 1, 2, 3, 7, and 8 applicable to their levels. College instructors can delve for material in every part of the book. There are frequent references to the College Mathematics Journal; these are denoted by CMJ.
Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition can often be misleading. This book collects and analyses a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves.
Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students, as well as some talented and motivated high school students, to a better appreciation of the power of mathematical technique. Even at the specific level of quadratic diophantine equations, there are unsolved problems, and the higher degree analogues of Pell's equation, particularly beyond the third, do not appear to have been well studied. In this focused exercise book, the topic is motivated and developed through sections of exercises which will allow the readers to recreate known theory and provide a focus for their algebraic practice. There are several explorations that encourage the reader to embark on their own research. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have (or have forgotten) a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.
This text records the problems given for the first 15 annual undergraduate mathematics competitions, held in March each year since 2001 at the University of Toronto. Problems cover areas of single-variable differential and integral calculus, linear algebra, advanced algebra, analytic geometry, combinatorics, basic group theory, and number theory. The problems of the competitions are given in chronological order as presented to the students. The solutions appear in subsequent chapters according to subject matter. Appendices recall some background material and list the names of students who did well. The University of Toronto Undergraduate Competition was founded to provide additional competition experience for undergraduates preparing for the Putnam competition, and is particularly useful for the freshman or sophomore undergraduate. Lecturers, instructors, and coaches for mathematics competitions will find this presentation useful. Many of the problems are of intermediate difficulty and relate to the first two years of the undergraduate curriculum. The problems presented may be particularly useful for regular class assignments. Moreover, this text contains problems that lie outside the regular syllabus and may interest students who are eager to learn beyond the classroom.
This book contains 500 problems that range over a wide spectrum of areas of high school mathematics and levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained and taught by the book. For many problems, more than one solution is supplied so that students can see how different approaches can be taken to a problem and compare the elegance and efficiency of different tools that might be applied. Teachers at both the college and secondary levels will find the book useful, both for encouraging their students and for their own pleasure. Some of the problems can be used to provide a little spice in the regular curriculum by demonstrating the power of very basic techniques. This collection provides a solid base for students who wish to enter competitions at the Olympiad level. They can begin with easy problems and progress to more demanding ones. A special mathematical tool chest summarizes the results and techniques needed by competition-level students.
In the mid 1980s, the International Commission on Mathematical Instruction (ICMI) inaugurated a series of studies in mathematics education by comm- sioning one on the influence of technology and informatics on mathematics and its teaching. These studies are designed to thoroughly explore topics of c- temporary interest, by gathering together a group of experts who prepare a Study Volume that provides a considered assessment of the current state and a guide to further developments. Studies have embraced a range of issues, some central, such as the teaching of algebra, some closely related, such as the impact of history and psychology, and some looking at mathematics education from a particular perspective, such as cultural differences between East and West. These studies have been commissioned at the rate of about one per year. Once the ICMI Executive decides on the topic, one or two chairs are selected and then, in consultation with them, an International Program Committee (IPC) of about 12 experts is formed. The IPC then meets and prepares a Discussion Document that sets forth the issues and invites interested parties to submit papers. These papers are the basis for invitations to a Study Conference, at which the various dimensions of the topic are explored and a book, the Study Volume, is sketched out. The book is then put together in collaboration, mainly using electronic communication. The entire process typically takes about six years.
Originally published in 1967. The nationalistic sentiment of French Canada was starkly dramatized by the Montreal terrorist bombings in the spring of 1963. Admittedly the work of extremists, that eruption of violence was an offshoot of the profound social, political, economic, and cultural transformation—an accelerated evolution rather than a revolution—that Quebec has undergone since the end of World War II. This revolution tranquille is characterized by a new sense of self-confidence among French Canadians, an eagerness to reject what they regard as any hint of second-class citizenship, and a determination to take full share in all aspects of Canadian life—without, however, sacrificing their French culture and heritage. A threat to the Canadian Confederation is implicit in the growing reluctance of modern French-speaking Canadians to abide the "tyranny of the majority," however enlightened or well-intentioned it may be. This first book-length study in English of the conflict between French and English Canadians provides a thorough treatment of French-Canadian complaints against English Canada, and of their implications for Canadian unity. Dr. Corbett devotes the first part of his study to an analysis of the ferment within the French-speaking population of Quebec during the postwar period. He discusses the relation between French-Canadian nationalism and other nationalisms and the roles played by the language barrier, the church, and the separatist movement. In the second part of the study he considers the political, economic, and social implications of separatism, with particular regard to the proposals for adapting the Constitution to Quebecois demands. After tracing the evolution of the ambivalent English-Canadian concept of Canada's national identity, he concludes that the future of the Confederation will depend on how far the English majority is willing to go in meeting French demands.
This is the first introductory text that focuses on social anthropological research using Canadian examples and perspectives. In this groundbreaking new book, Edward Hedican provides undergraduate students with a solid background on the theoretical and applied aspects of anthropology, while exploring the rich history of the discipline in a Canadian context. In ten concise chapters, readers are introduced to the basic conceptual building blocks of introductory anthropology in a refreshingly succinct and engaging way. With a strong focus on Canadian theory, this book includes discussion of evolutionism, feminist anthropology, marriage and the family, and political economy.
Anthropologists are often reluctant to present their work relating to matters of a broad social context to the wider public even though many have much to say about a range of contemporary issues. In this second edition of a classic work in the field, Edward J. Hedican takes stock of Anthroplogy's research on current indigenous affairs and offers an up-to-date assessment of Aboriginal issues in Canada from the perspective of applied Anthropology. In his central thesis, Hedican underlines Anthropology's opportunity to make a significant impact on the way Aboriginal issues are studied, perceived, and interpreted in Canada. He contends that anthropologists must quit lingering on the periphery of debates concerning land claims and race relations and become more actively committed to the public good. His study ranges over such challenging topics as advocacy roles in Aboriginal studies, the ethics of applied research, policy issues in community development, the political context of the self-government debate, and the dilemma of Aboriginal status and identity in Canada. Applied Anthropology in Canada is an impassioned call for a revitalized Anthropology - one more directly attuned to the practical problems faced by First Nations peoples. Hedican's focus on Aboriginal issues gives his work a strong contemporary relevance that bridges the gap between scholarly and public spheres.
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