Exploring the Infinite addresses the trend towarda combined transition course and introduction to analysis course. Itguides the reader through the processes of abstraction and log-ical argumentation, to make the transition from student of mathematics topractitioner of mathematics. This requires more than knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques. The student focused on only thesewill develop little more than the ability to identify a number of proof templates andto apply them in predictable ways to standard problems. This book aims to do something more; it aims to help readers learn to exploremathematical situations, to make conjectures, and only then to apply methodsof proof. Practitioners of mathematics must do all of these things. The chapters of this text are divided into two parts. Part I serves as an introductionto proof and abstract mathematics and aims to prepare the reader for advancedcourse work in all areas of mathematics. It thus includes all the standard materialfrom a transition to proof" course. Part II constitutes an introduction to the basic concepts of analysis, including limitsof sequences of real numbers and of functions, infinite series, the structure of thereal line, and continuous functions. FeaturesTwo part text for the combined transition and analysis courseNew approach focuses on exploration and creative thoughtEmphasizes the limit and sequencesIntroduces programming skills to explore concepts in analysisEmphasis in on developing mathematical thoughtExploration problems expand more traditional exercise sets | Exploring The Infinite by Jennifer Brooks, Hardcover | Indigo Chapters