Exploratory examples for real analysis Joanne E. Snow, Kirk E. Weller.
Series Detalles de publicación: Washington, D.C. Mathematical Association of America c2003.Descripción: xv, 138 p. ill. 26 cmISBN:- 0883857340
- 9780883857342
- 515 S6741e 22
- QA331.5 .S63 2003
| Imagen de cubierta | Tipo de ítem | Biblioteca actual | Biblioteca de origen | Colección | Ubicación en estantería | Signatura topográfica | Materiales especificados | Info Vol | URL | Copia número | Estado | Notas | Fecha de vencimiento | Código de barras | Reserva de ítems | Prioridad de la cola de reserva de ejemplar | Reservas para cursos | |
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| Libro | Biblioteca Encarnación Valdés Colección General bev | 515 S6741e (Navegar estantería(Abre debajo)) | Disponible | 80000002345158 |
Descripciones mejoradas de Syndetics:
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, discussions of the nature of mathematics research, and more. The prerequisites for a course based on this book include the content of high school mathematics and a certain level of mathematical maturity. The student must be willing to think on an abstract level. Two semesters of calculus indicates a readiness for this material.
Includes index.
Boundedness of sets -- Introducing the "Epsilon definition" of least upper bound -- Introduction to the formal definition of convergence -- Experience with the definition of the limit of a sequence -- Experience with the negation of the definition of convergence -- Algebraic combinations of sequences -- Conditions related to convergence -- Understanding the limit superior and the limit inferior -- Continuity and sequences -- Another definition of continuity -- Experience with the "E-d" definitions of continuity and limit -- Uniform convergence of a sequence of functions.
Tabla de contenidos provista por Syndetics
- 1 Boundedness of sets
- 2 Introducing the +epsilon definition+ of least upper bound
- 3 Introduction to the formal definition of convergence
- 4 Experience with the definiton of the limit of a sequence
- 5 Experience with the negation of the definition of convergence
- 6 Algebraic combinations of sequences
- 7 Conditions related to convergence
- 8 Understanding the limit superior and the limit inferior
- 9 Continuity and sequences
- 10 Another definition of continuity
- 11 Experience with the e - d definitions of continuity and limit
- 12 Uniform and convergence of a sequence of functions
- Appendix
- Visual guides
- About the authors