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Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.
From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996
Teacher Guide for Book 1 of the Principles of Mathematics - Biblical Worldview Curriculum for junior high! Math is a real-life tool that points us to God and helps us explore His creation, yet it often comes across as dry facts and meaningless rules. Here at last is a curriculum that has a biblical worldview integrated throughout the text and problems, not just added as an afterthought. The resources in the Teacher Guide will help students master and apply the skills learned in the Student Textbook. What does this Teacher Guide include? Worksheets, Quizzes, and Tests: These perforated, three-hole punched pages help provide practice on the principles taught in the main student textbook.Answer Keys: The answers are included for the worksheets, quizzes, and tests found in this Teacher Guide.Schedule: A suggested calendar schedule is provided for completing the material in one year, though this can be adapted to meet individual student needs. There is also an accelerated schedule for completing the material in one semester. Are there any prerequisites for this course? This curriculum is aimed at grades 6-8, fitting into most math approaches the year or two years prior to starting high school algebra. If following traditional grade levels, Book 1 should be completed in grade 6 or 7, and Book 2 in grade 7 or 8. In Book 1 students should have a basic knowledge of arithmetic (basic arithmetic will be reviewed, but at a fast pace and while teaching problem-solving skills and a biblical worldview of math) and sufficient mental development to think through the concepts and examples given. Typically, anyone in sixth grade or higher should be prepared to begin. The focus of the course is actually learning math for life, not simply preparing to pass a test.