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 |