# 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.

## MAT 27A: Linear Algebra with Applications to Biology

**Approved:**2018-03-01, S. Walcott, M. Goldman

**ATTENTION:**

Also known as BIS 027A.

**Units/Lecture:**

Lecture—3 hour; Laboratory—2 hours.

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

**Prerequisites:**

MAT 017C C- or better or MAT 021C C- or better or MAT 021CH C- or better.

**Course Description:**

Introduction to linear algebra with biological, medical, and bioengineering applications.

**Suggested Schedule:**

Lecture | Chapter | Topic |
---|---|---|

1 | 1.1 | Vectors and Linear Combinations |

2 | 1.2 | Lengths and Dot Products |

Lab 1 | Intro to Matlab | |

3 | 1.3 | Matrices |

4 | 2.1 | Vectors and Linear Equations |

5 | 2.2, 2.3 | Elimination |

Lab 2 | Linear Algebra in Matlab | |

6 | 2.4 | Rules for Matrix Operations |

7 | 2.5 | Inverse Matrices |

Lab 3 | Enzyme Kinetics/Color Vision | |

8 | 3.1 | Spaces of Vectors |

9 | 3.2 | The Nullspace of A |

10 | 3.3 | The Complete Solution to Ax = b |

Lab 4 | Lab 4: Colorblindness/Data Fitting | |

11 | 3.4 | Independence, Basis and Dimension |

12 | 3.5 | Dimensions of the Four Subspaces |

13 | 4.1 | Orthogonality of the Four Subspaces |

Lab | Catch up/Exam prep | |

14 | 4.2 | Projections |

15 | 4.4 | Orthonormal Bases and Gram-Schmidt |

Lab 6 | Conserved Quantities and Nullspace | |

16 | 5.1 | Properties of Determinants |

17 | 6.1 | Introduction to Eigenvalues |

Lab 7 | Eigenvalues in Images and Populations | |

18 | 6.2 | Diagonalizing a Matrix |

19 | 6.4 | Symmetric Matrices |

20 | 6.5 | Positive Definite Matrices |

Lab | Catch up/Exam prep | |

21 | 7.1 | Image Processing and Linear Algebra |

22 | 7.2 | Bases and Matrices in the SVD |

Lab 7 | PCA and "Big Data" | |

23 | 7.3 | Principal Component Analysis |

24 | 7.4 | Geometry of the SVD |

25 | 8.1 | Idea of a Linear Transformation |

Lab 8 | Breeder's Equation, Dim. Reduction | |

26 | 8.2 | The Matrix of a Linear Transformation |