This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them.
Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.
For twenty years, clinical pastoral educators, congregational caregivers, chaplains, pastoral psychotherapists, and pastoral theologians have turned to Pamela Cooper-White's Shared Wisdom to ground their teaching, training, and understandings of countertransference and how the use of the caregiver's self, in turn, impacts the relational dynamic between caregivers and care seekers. Now, Cooper-White updates her groundbreaking book to present new insights on how understanding one's own emotional reactions remains a core competency for ministry. With precision and depth, Cooper-White continues to innovate the theory and practice of spiritual care, counseling, and spiritual psychotherapy. This revised and expanded 20th anniversary edition explores current research on countertransference and intersubjectivity; mutual influence and unconscious relationships; and intercultural and interreligious dynamics in caring relationships. Cooper-White examines how the relational paradigm for pastoral assessment and theological reflection that she pioneered now has important implications for evolving types of care relationships. As she does so, she addresses emerging topics such as postcolonial theory, spiritual and religious fluidity, and gender diversity. CPE supervisors, pastoral care and counseling educators and practitioners, pastoral theology scholars, and psychotherapists looking for an in-depth understanding of relationality and intersubjectivity will find the 20th anniversary edition of Shared Wisdoma must-have resource to build and expand upon a core competency.
This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends with suggested projects for independent study. Students will follow Pólya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Pólya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.
Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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