## Mathematics 210## Linear Algebra |

- 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.

- Math 210 MWF Spring 2012, Lay (pdf)

- Chapter 1: Linear Equations in Linear Algebra
- Chapter 2: Matrix Algebra
- Chapter 3: Determinants
- Chapter 4: Vector Spaces
- Chapter 5: Eigenvalues and Eigenvectors
- Chapter 6: Orthogonality and Least Squares
- Chapter 7: Symmetric Matrices and Quadratic Forms

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.

- Linear Equations (nb pdf html)
- Elementary Row Operations (nb pdf html)
- Matrix Algebra (nb pdf html)
- Implementing Gaussian Elimination (nb pdf html)
- LU Decomposition (nb pdf html)
- 2D-Graphics (nb pdf html)
- 3D-Graphics (nb pdf html)
- Determinants (nb pdf html)
- Arrows and Polygons (nb pdf html)
- Vector Spaces (nb pdf html)
- Difference Equations (nb pdf html)
- Eigenvalues (nb pdf html)
- Iterative Estimates for Eigenvalues (nb pdf html)
- Orthogonality and Least Squares (nb pdf html)
- Fitting Data (nb pdf html)
- Gram-Schmidt (nb pdf html)
- Implementing Gram-Schmidt (nb pdf html)
- Representation of a Linear Functional (nb pdf html)
- Spectral Decomposition (nb pdf html)
- Quadratic Forms (nb pdf html)
- Singular Value Decomposition (nb pdf html)
- Principal Component Analysis (nb pdf html)

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.

- 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.]

Homework is due on Fridays!

- 3 review examinations 60 %
- homework 20 %
- final examination 20 %