Exploring the Infinite

<p>Exploring the Infinite addresses the trend toward </p><p></p><p>a combined transition course and introduction to analysis course. It</p><p></p><p>guides the reader through the processes of abstraction and log-</p><p></p><p>ical argumentation to make the transition from student of mathematics to</p><p></p><p>practitioner of mathematics. </p><p></p><p>This requires more than knowledge of the definitions of mathematical structures </p><p></p><p>elementary logic and standard proof techniques. The student focused on only these </p><p></p><p>will develop little more than the ability to identify a number of proof templates and </p><p></p><p>to apply them in predictable ways to standard problems. </p><p></p><p>This book aims to do something more; it aims to help readers learn to explore </p><p></p><p>mathematical situations to make conjectures and only then to apply methods </p><p></p><p>of proof. Practitioners of mathematics must do all of these things.</p><p></p><p>The chapters of this text are divided into two parts. Part I serves as an introduction </p><p></p><p>to proof and abstract mathematics and aims to prepare the reader for advanced </p><p></p><p>course work in all areas of mathematics. It thus includes all the standard material </p><p></p><p>from a transition to proof course. </p><p></p><p>Part II constitutes an introduction to the basic concepts of analysis including limits</p><p></p><p>of sequences of real numbers and of functions infinite series the structure of the </p><p></p><p>real line and continuous functions.</p><p></p><p>Features</p><p></p><ul> <br><br><p></p> <li>Two part text for the combined transition and analysis course</li> <br><br> <br><br><p></p> <li>New approach focuses on exploration and creative thought</li> <br><br> <br><br><p></p> <li>Emphasizes the limit and sequences </li> <br><br> <br><br><p></p> <li>Introduces programming skills to explore concepts in analysis</li> <br><br> <br><br><p></p> <li>Emphasis in on developing mathematical thought</li> <br><br> <br><br><p></p> <li>Exploration problems expand more traditional exercise sets</li> <br><br> </ul><p></p>