|
Showing 1 - 4 of
4 matches in All Departments
Intended for juniors and seniors majoring in mathematics, as well
as anyone pursuing independent study, this book traces the
historical development of four different mathematical concepts by
presenting readers with the original sources. Each chapter
showcases a masterpiece of mathematical achievement, anchored to a
sequence of selected primary sources. The authors examine the
interplay between the discrete and continuous, with a focus on sums
of powers. They then delineate the development of algorithms by
Newton, Simpson and Smale. Next they explore our modern
understanding of curvature, and finally they look at the properties
of prime numbers. The book includes exercises, numerous
photographs, and an annotated bibliography.
The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve -- or attempt to solve -- a great problem, this book helps readers discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.
Number Theory Through the Eyes of Sophie Germain: An Inquiry Course
is an innovative textbook for an introductory number theory course.
Sophie Germain (1776-1831) was largely self-taught in mathematics
and, two centuries ago, in solitude, devised and implemented a plan
to prove Fermat's Last Theorem. We have only recently completely
understood this work from her unpublished letters and manuscripts.
David Pengelley has been a driving force in unraveling this mystery
and here he masterfully guides his readers along a path of
discovery. Germain, because of her circumstances as the first woman
to do important original mathematical research, was forced to learn
most of what we now include in an undergraduate number theory
course for herself. Pengelley has taken excerpts of her writings
(and those of others) and, by asking his readers to decipher them,
skillfully leads us through an inquiry-based course in elementary
number theory. It is a detective story on multiple levels. What is
Sophie Germain thinking? What do her mathematical writings mean?
How do we understand what she knew and what she was trying to do,
where she succeeded and where she didn't?
Changing the way students learn calculus at New Mexico State
University. In the Spring of 1988, Marcus Cohen, Edward D. Gaughan,
Arthur Knoebel, Douglas S. Kurtz, and David Penegelley began work
on a student project approach to calculus. For the next two years,
most of their waking hours (and some of their dreams) would be
devoted to writing projects for their students and discovering how
to make the use of projects in calculus classes not only
successful, but practical as well. A grant from the National
Science Foundation made it possible for this experiment to go
forward on a large scale. The enthusiasm of the original group of
five faculty was contagious, and soon other members of the
department were also writing and using projects in their calculus
classes. At the present time, about 80% of the calculus students at
New Mexico State University are doing projects in their Calculus
courses. Teachers can use their methods in teaching their own
calculus courses. Student Research Projects in Calculus provides
teachers with over 100 projects ready to assign to students in
single and multivariable calculus. The authors have designed these
projects with one goal in mind: to get students to think for
themselves. Each project is a multistep, take-home problem,
allowing students to work both individually and in groups. The
projects resemble mini-research problems. Most of them require
creative thought, and all of them engage the student's analytic and
intuitive faculties. the projects often build from a specific
example to the general case, and weave together ideas from many
parts of the calculus. Project statements are clearly stated and
contain a minimum of mathematical symbols. Students must draw their
own diagrams, decide for themselves what the problem is about, and
what toolsfrom the calculus they will use to solve it. This
approach elicits from students an amazing level of sincere
questioning, energetic research, dogged persistence, and
conscientious communication. Each project has accompanying notes to
the instructor, reporting students' experiences. The notes contain
helpful information on prerequisites, list the main topics the
project explores, and suggests helpful hints. The authors have also
provided several introductory chapters to help instructors use
projects successfully in their classes and begin to create their
own.
|
|