{"product_id":"exploring-the-infinite-jennifer-brooks-9781032477046","title":"Exploring the Infinite: An Introduction to Proof and Analysis","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 \u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e \u003cli\u003eTwo part text for the combined transition and analysis course\u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e \u003cli\u003eNew approach focuses on exploration and creative thought\u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e \u003cli\u003eEmphasizes the limit and sequences \u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e \u003cli\u003eIntroduces programming skills to explore concepts in analysis\u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e \u003cli\u003eEmphasis in on developing mathematical thought\u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e \u003cli\u003eExploration problems expand more traditional exercise sets\u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e \u003c\/ul\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Jennifer Brooks\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1032477040\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781032477046\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e CRC Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 01\/21\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 300\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback","brand":"Jennifer Brooks","offers":[{"title":"Paperback","offer_id":44302026834175,"sku":"9781032477046","price":58.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_e6bae283-da63-41c7-a3b6-01814c33166a.jpg?v=1695159096","url":"https:\/\/www.whiterainbookhouse.com\/products\/exploring-the-infinite-jennifer-brooks-9781032477046","provider":"WR Book House","version":"1.0","type":"link"}