An introduction to linear algebra designed to provide some important mathematical tools that will be useful in a variety of fields. Systems of linear equations, vectors and matrices, determinants, vector spaces, linear transformations, inner and cross products, and eigenvalues and canonical forms are considered. Prerequisite: Mathematics 102.
Objectives of the course
This course should help students to
- demonstrate the ability to analyze and solve mathematical exercises in linear algebra with a style and precision appropriate to the second-year level of university;
- begin the transition from viewing mathematics as a largely computational activity to interacting with its logical structure of definitions and proofs;
- demonstrate a modest familiarity with the applications of a computer algebra system to problem-solving and mathematical modeling in linear algebra.
- relate theoretical aspects of linear algebra to its algorithmic components and to a number of its important applications;
- appreciate the pervasive influence and contributions of linear algebra to mathematics and statistics and to the natural and social sciences.
Linear Algebra and Its Applications, Fourth Edition,
by David C. Lay, Addison Wesley, 2012 (Required)
ISBN-13: 978-0-321-38517-8, ISBN-10 0-321-38517-9
Schedule for Spring 2012
- Math 210 MWF Spring 2012, Lay (pdf)
Course Notes and Related Materials - Lay
Mathematica v5.2 Notebooks
The following Mathematica notebooks are available in three formats. Download the Mathematica notebook (nb) to your machine and use Mathematica to interpret its contents, or click on the pdf link (pdf) or the web page link (html) to see a static image of the evaluated notebook.
The following two textbooks are particularly recommended for further study. The first is devoted to the theory of linear algebra and the second to its applications.
Linear Algebra Done Right, Second Edition,
by Sheldon Axler, Springer, ISBN 0-387-98258-2, 1997 (for reference only)
Applied Linear Algebra,
by Peter J. Olver and Chehrzad Shakiban, Pearson Prentice-Hall, ISBN 0-13-147382-4, 2006 (for reference only)
- There are extensive supporting materials for David Lay's text at the Lay Linear Algebra web site. In particular, there are data sets in machine readable format for many of the exercises in the text, so you don't have to type in so many vectors and matrices to your computer algebra system. Go to Lay's web site and click on the blue "Data Sets" button.
- The online textbook by Jenny Baglivo of Boston College supporting MT580 Mathematics for Statistics includes a crisp and lucid treatment of much of the linear algebra in our own course. See chapter 9 on Linear Algebra Concepts, beginning on page 189. This reference is especially recommended for reviewing and consolidating one's understanding of linear algebra for a final exam or comprehensive exam.
- The online textbook Applied Linear Algebra and Matrix Analysis by Thomas Shore of the University of Nebraska, and its accompanying Mathematica notebooks, relate well to our own course.
- The online textbook Linear Algebra by William Chen of Macquarie University presents an elegant treatment of our subject.
- MIT OpenCourseWare hosts streaming video lectures and other materials supporting Gilbert Strang's MIT course 18.06 Linear Algebra, Spring 2005. Gilbert Strang's video lectures can also be downloaded for free from Apple's iTunes U site. Launch iTunes on your computer and navigate to iTunes Store:iTunes U:MIT:Mathematics:MIT 18.06 - Video. There are 34 lectures altogether in Gilbert Strang's semester-long course. Each one runs for about 40 to 50 minutes, and they can be viewed at your convenience on your computer or iPod.
- David Smith's Connected Curriculum Project at Duke University contains an engaging and innovative interactive linear algebra component.
- Jim Hartman at The College of Wooster offers a timeline illustrating a brief history of linear algebra.
- A study group hosted by the Institute for Advanced Study at Princeton offers some thoughts on teaching linear algebra, including an application to the biology of loggerhead sea turtles which extends David Smith's treatment of Leslie matrices. [Click on "Technology" and scroll down to "sea turtles."]
- Routine matrix calculations are best left to machines. We will make extensive use of a computer algebra system in this course, but many students prefer to rely on their calculators for some of this work. Prof. Selwyn Hollis of Florida Atlantic University offers a variety of calculator programs and a very thorough manual for doing mathematics on TI-89/92 calculators.]
Office: Woods Laboratories 120
Location and Time
Monday-Wednesday-Friday, 11:00 - 11:50 a.m.
Final Examination: Friday, May 4, 2:00 - 4:00 pm
Woods Laboratories 121
Homework is due on Fridays!
- 3 review examinations 60 %
- homework 20 %
- final examination 20 %
The Honor Code applies to all examinations and written work produced in this course. Plagiarism is copying or imitating the language and thoughts of others, whatever the medium (written papers or computer programs). All work on the examinations must be done individually.
Attendance is required and is an important factor in doing well in the class. All assignments must be completed, and the student is responsible for making up any work missed due to absence. Late work will be accepted ONLY if appropriate arrangements have been made with the instructor PRIOR to the due date. The Dean's Office may be notified after