Calculus: Early Transcendentals (3rd edition)
On Teaching Mathematics
I consider myself very lucky to have a career as a teacher and practitioner of mathematics. When I was young, I decided I wanted to be a writer. I loved tel ling stories. But I was also good at math, and. once in coUege, it didn’t take me long to become enamored with it. I loved the fact that success in mathematics does not depend on your presentation skills or your interpersonal relationships. You are either right or you are wrong and there is little subjective evaluation involved. And I loved the satisfaction of coming up with a solution. That intensified when I started solving problems that were open research questions that had previously remained unsolved. So, I became a professor of mathematics. And I soon realized that teaching mathe matics is about telling a story. The goaJ is to explain to students in an intriguing manner, at the right pace, and in as clear a way as possible, how mathematics works and what it can do for you. I find mathematics immensely beautiful. I want students to feel that way, too.
On Writing a Calculus Text
I had always thought I might write a calculus text. But that is a daunting task. These days, calculus books average over a thousand pages. And I would need to convince myself that I had something to offer that was different enough from what already appears in the existing books. Then, I was approached about writing the third edition of Jon Rogawski ‘s calculus book. Here was a book for which I already had great respect. Jon· s vision of what a calculus book should be fit very closely with my own. Jon believed that as math teachers, how we say it is as important as what we say. Although he insisted on rigor at all times. he also wanted a book that was written in plain English, a book that could be read and that would entice students to read further and learn more. Moreover, Jon suived to create a text in which exposition, graphics, and layout would work together to enhance all facets of a student ·s calculus experience.
In writing his book. Jon paid special attention to certain aspects of the text:
I. Clear, accessible exposition that anticipates and addresses student difficulties
2. Layout and figures that communicate the flow of ideas.
3. Highlighted features that emphasize concepts and mathematical reasoning: Conceptual Insight, Graphical Insight, Assumptions Matter, Reminder, and Historical Perspective.
4. A rich collection of examples and exercises of graduated difficulty that teach basic skills, problem-solving techniques, rein force conceptual understanding, and motivate calculus through interesting applications. Each section also contains exercises that develop additional insights and challenge students to further develop their skiUs.
Coming into the project of creating the third edition, I was somewhat apprehensive. Here was an already excellent book that had attained the goals set for it by its author. First and foremost, I wanted to be sure that I did it no harm. On the other hand, I have been teaching calculus now for 30 years, and in that time, I have come to some conclusions about what does and does not work well for students.
As a mathematician, I want to make sure that the theorems, proofs, arguments and development are correct. There is no place in mathematics for sloppiness of any kind. As a teacher, I want the material co be accessible. The book should not be written at the mathematical level of the instructor. Students should be able to use the book to learn the material, with the help of their instructor. Working from the high standard that Jon set, I have 11ied hard co maintain the level of quality of the previous edition while making the changes that I believe will bring the book to the next level.
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