linear algebra in uiversity

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Linear Algebra

David Cherney, Tom Denton and Andrew Waldron


Edited by Katrina Glaeser, Rohit Thomas and Travis Scrimshaw
First Edition. Davis California, 2013.
This work is licensed under a
Creative Commons Attribution-NonCommercialShareAlike 3.0 Unported License.



This “book” grew out of a series of twenty five lecture notes for a sophomore
linear algebra class taught at the University of California, Davis. The audience was primarily engineering students and students of pure sciences, some
of whom may go on to major in mathematics. It was motivated by the lack of
a book that taught students basic structures of linear algebra without overdoing mathematical rigor or becoming a mindless exercise in crunching recipes
at the cost of fundamental understanding. In particular we wanted a book
that was suitable for all students, not just math majors, that focussed on
concepts and developing the ability to think in terms of abstract structures
in order to address the dizzying array of seemingly disparate applications
that can all actually be addressed with linear algebra methods.
In addition we had practical concerns. We wanted to offer students a
online version of the book for free, both because we felt it our academic
duty to do so, but also because we could seamlessly link an online book to
a myriad of other resources–in particular WeBWorK exercises and videos.
We also wanted to make the LaTeX source available to other instructors
so they could easily customize the material to fit their own needs. Finally,
we wanted to restructure the way the course was taught, by getting the
students to direct most of their effort at more difficult problems where they
had to think through concepts, present well-thought out logical arguments
and learn to turn word problems into ones where the usual array of linear
algebra recipes could take over.

How to Use the Book
At the end of each chapter there is a set of review questions. Our students
found these very difficult, mostly because they did not know where to begin,
rather than needing a clever trick. We designed them this way to ensure that
students grappled with basic concepts. Our main aim was for students to
master these problems, so that we could ask similar high caliber problems
on midterm and final examinations. This meant that we did have to direct
resources to grading some of these problems. For this we used two tricks.
First we asked students to hand in more problems than we could grade, and
then ...
Linear Algebra
David Cherney, Tom Denton and Andrew Waldron
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