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)
G. Strang, "Introduction to Linear Algebra," 5th Edition
Search by ISBN on Amazon: 9780980232776
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:
LectureChapterTopic
11.1Vectors and Linear Combinations
21.2Lengths and Dot Products
Lab 1Intro to Matlab
31.3Matrices
42.1Vectors and Linear Equations
52.2, 2.3Elimination
Lab 2Linear Algebra in Matlab
62.4Rules for Matrix Operations
72.5Inverse Matrices
Lab 3Enzyme Kinetics/Color Vision
83.1Spaces of Vectors
93.2The Nullspace of A
103.3The Complete Solution to Ax = b
Lab 4Lab 4: Colorblindness/Data Fitting
113.4Independence, Basis and Dimension
123.5Dimensions of the Four Subspaces
134.1Orthogonality of the Four Subspaces
LabCatch up/Exam prep
144.2Projections
154.4Orthonormal Bases and Gram-Schmidt
Lab 6Conserved Quantities and Nullspace
165.1Properties of Determinants
176.1Introduction to Eigenvalues
Lab 7Eigenvalues in Images and Populations
186.2Diagonalizing a Matrix
196.4Symmetric Matrices
206.5Positive Definite Matrices
LabCatch up/Exam prep
217.1Image Processing and Linear Algebra
227.2Bases and Matrices in the SVD
Lab 7PCA and "Big Data"
237.3Principal Component Analysis
247.4Geometry of the SVD
258.1Idea of a Linear Transformation
Lab 8Breeder's Equation, Dim. Reduction
268.2The Matrix of a Linear Transformation