## Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

**Approved:**2008-04-15, Naoki Saito, Roland Freund, Hong Xiao

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

Search by ISBN on Amazon: 978-0030105678

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1 |
From various sources (see note below) |
What is Applied Linear Algebra? Motivational introduction with examples |

2 |
Sec. 1.4-1.6 |
Systems of linear algebraic equations, LU factorization and its applications |

3 |
Sec.2.1-2.3, 2.6 |
Vector spaces, subspaces, bases, linear transformations |

4 |
Sec. 3.1, 3.2, 3.4 |
Orthogonality. QR factorization and Gram-Schmidt process I. |

5 |
Sec. 3.3; Midterm Exam |
Orthogonality. QR factorization and Gram-Schmidt process II. Applications to least squares problems |

6 |
Sec. 5.1-5.3 |
Eigenvalue decomposition and its applications I |

7 |
Sec.5.4-5.6 |
Eigenvalue decomposition and its applications II |

8 |
Sec. 6.3 with extra material |
Singular value decomposition and its applications I |

9 |
Sec. 6.3 with extra material |
Singular value decomposition and its applications II |

10 |
Some appropriate sections from the text as well as extra material, handouts |
Other applications (see notes below) |

**Additional Notes:**

- • Basic concepts of linear algebra (22A or 67) are assumed and will not be reviewed in the class. The instructor should explicitly inform the enrolled students of this requirement.
- • Knowledge of programming language is required. A certain number of programming projects will be assigned in the course. Applications of least squares, eigenvalue decomposition, singular value decomposition form good programming projects.
- • In the 1
^{st}Week, it is important to motivate the students using important examples to show how linear algebra is used in real world. Suggested examples are: image compression, web search engines, inverse problems (e.g., tomography), etc. - • In the 8
^{th}and 9^{th}Weeks, the instructor should supply some applications of SVD including web search engines, least squares problems, image approximations, inverse problems in a more details manner some of which were discussed in the 1^{st}Week. - • In the 10
^{th}Week, an instructor can freely choose various applications of interest. Examples are:Sec. 2.5 Graphs and Networks;Sec. 3.5 The Fast Fourier Transform;Sec. 6.1-6.2 Positive Definite MatricesSec. 8.2 The Simplex Method and Karmarkar's Method.

Other possible sources of material are:

- − Carl D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2000.
- − Lloyd. N. Trefethen and Davis Bau, III: Numerical Linear Algebra, SIAM, 1997.
- − Michael W. Berry and Murray Browne: Understanding Search Engines: Mathematical Modeling and Text Retrieval, 2
^{nd}Ed., SIAM, 2005.