Essentials of Mathematics: Introduction to Theory, Proof, and the Professional Culture (Mathematical Association of America Textbooks)

Книга Essentials of Mathematics: Introduction to Theory, Proof, and the... Essentials of Mathematics: Introduction to Theory, Proof, and the Professional Culture Книги Математика Автор: Margie Hale Год издания: 2003 Формат: djvu Издат.:The Mathematical Association of America Страниц: 186 Размер: 3,5 ISBN: 0883857294 Язык: Английский0 (голосов: 0) Оценка:Essentials of Mathematics is designed as both a textbook and outside reading for college students who want to prepare themselves for mathematics courses beyond the first-year level. The mathematical content includes logic, set theory and a theoretical development of the number systems, giving students practice at proving mathematical statements. There are no answers in the book, but a separate manual provides instructor support. The book makes an excellent reference for students beginning to take courses in which proofs play a major role. In addition to the course material, there are narratives on the nature of mathematics and the mathematics profession. These sections can be read without help or guidance. Every mathematician must make the transition from the calculations of high school to the structural and theoretical approaches of graduate school. Essentials of Mathematics provides the knowledge needed to move onto advanced mathematical work, and a glimpse of what being a mathematician might be like. No other book takes this particular holistic approach to the task. The content is of two types. There is material for a "Transitions" course at the sophomore level; introductions to logic and set theory, discussions of proof writing and proof discovery, and introductions to the number systems (natural, rational, real, and complex). The material is presented in a fashion suitable for a Moore Method course, although such an approach is not necessary. An accompanying Instructor's Manual provides support for all flavors of teaching styles. In addition to presenting the important results for student proof, each area provides warm-up and follow-up exercises to help students internalize the material. The second type of content is an introduction to the professional culture of mathematics. There are many things that mathematicians know but weren't exactly taught. To give college students a sense of the mathematical universe, the book includes narratives on this kind of information. There are sections on pure and applied mathematics, the philosophy of mathematics, ethics in mathematical work, professional (including student) organizations, famous theorems, famous unsolved problems, famous mathematicians, a discussions of the nature of mathematics research and more Every mathematician must make the transition from the calculations of high school to the structural and theoretical approaches of graduate school. Essentials of Mathematics provides the knowledge needed to move onto advanced mathematical work and a glimpse of what being a mathematician might be like. No other book takes this particular holistic approach to the task. Essentials of Mathematics is designed as both a textbook and outside reading for college students who want to prepare themselves for mathematics courses beyond the first-year level and take courses in which proofs play a major role. There are also narratives on the nature of mathematics and the mathematics profession. The field of mathematics is composed of many subfields, some of which you have studied, and others of which you may not even be aware. Textbook And Self-study Guide For Students Beginning To Study Mathematics Requiring Proof.