{"product_id":"exploring-the-infinite","title":"Exploring the Infinite","description":"\u003cp\u003eExploring the Infinite addresses the trend toward \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ea combined transition course and introduction to analysis course. It\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eguides the reader through the processes of abstraction and log-\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eical argumentation, to make the transition from student of mathematics to\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003epractitioner of mathematics. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis requires more than knowledge of the definitions of mathematical structures, \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eelementary logic, and standard proof techniques. The student focused on only these \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ewill develop little more than the ability to identify a number of proof templates and \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eto apply them in predictable ways to standard problems. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book aims to do something more; it aims to help readers learn to explore \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003emathematical situations, to make conjectures, and only then to apply methods \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eof proof. Practitioners of mathematics must do all of these things.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe chapters of this text are divided into two parts. Part I serves as an introduction \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eto proof and abstract mathematics and aims to prepare the reader for advanced \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ecourse work in all areas of mathematics. It thus includes all the standard material \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003efrom a transition to proof\" course. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ePart II constitutes an introduction to the basic concepts of analysis, including limits\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eof sequences of real numbers and of functions, infinite series, the structure of the \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ereal line, and continuous functions.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eFeatures\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eTwo part text for the combined transition and analysis course\u003c\/li\u003e\n\u003cli\u003e\n\u003cbr\u003e\u003cbr\u003e \u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eNew approach focuses on exploration and creative thought\u003c\/li\u003e\n\u003cli\u003e\n\u003cbr\u003e\u003cbr\u003e \u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eEmphasizes the limit and sequences \u003c\/li\u003e\n\u003cli\u003e\n\u003cbr\u003e\u003cbr\u003e \u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eIntroduces programming skills to explore concepts in analysis\u003c\/li\u003e\n\u003cli\u003e\n\u003cbr\u003e\u003cbr\u003e \u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eEmphasis in on developing mathematical thought\u003c\/li\u003e\n\u003cli\u003e\n\u003cbr\u003e\u003cbr\u003e \u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eExploration problems expand more traditional exercise sets\u003c\/li\u003e\n\u003cli\u003e\n\u003cbr\u003e\u003cbr\u003e \u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":54230422126936,"sku":"9781032477046","price":62.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9781032477046.jpg?v=1777165222","url":"https:\/\/agendabookshop.com\/products\/exploring-the-infinite","provider":"Agenda Bookshop","version":"1.0","type":"link"}