Math 3400: Linear Algebra

Resources

Announcements: Probable date of first exam: September 17

Second exam will be October 8 and will cover standards 4, 6, and 8 (as well as 1-3)

The third exam will be held November 17 and/or 19

Standards 5 and 9 will be done via assignment: Standard 5 and Standard 9

The third exam will be held November 17 and will cover standards 7, 10, 11

Standard 15 will be done via assignment: Standard 15

Office Hours: Monday and Wednesday 12:30-2:30 in SAC 378

Virtual spaces: Gathertown or Zoom office hours in room 914 3056 6288

Lecture notes: Chapter 1 notes , Chapter 2 notes , Chapter 4 notes , Chapter 5 notes (notes on determinants so that the characteristic polynomial makes sense), Chapter 6 notes

Detailed list of standards: topics list

Syllabus: Section 001 Section 002

Textbooks:

  • Linear Algebra and its Applications by Lay/Lay-Lay-McDonald, any edition


Course Schedule

Book table of contents

Week 1 (August 23-27): 1.1-1.3. Systems of equations and their connection to matrices. Solving a system of equations. Row reduction and echelon forms. Vector and matrix equations

Week 2 (Aug 30 - Sept 3): 1.3-1.5. Vectors and vector equations, the matrix equation Ax=b, solution sets of linear systems

Week 3 (Sept 8-10): 1.5 and 1.7. Solution sets of linear systems , linear independence

Week 4 (Sept 13-17): homework review, 1.8 (Intro to linear transformations), first exam

Week 5 (Sept 20-24): 1.8, 1.9, 2.1: linear transformations, the matrix of a linear transformation and properties of functions, matrix operations

Week 6 (Sept 27-Oct 1): 1.9, 2.1, 2.2: Properties of matrices and functions, matrix operations, the inverse of a matrix

Week 7 (Oct 4-8): 2.2, 2.3, exam: Inverse of a matrix, characterizations of invertible matrices, exam 2

Fall Break!

Week 8 (Oct 18-22): 2.3, 2.8: recap of invertible matrices, elementary matrices, computing the inverse of a matrix, subspaces, basis

Week 9 (Oct 25-29): 2.8, 2.9: bases of column and null space, dimension and rank, the basis theorem

Week 10 (Nov 1-5): Chapter 4: introduction to vector spaces and subspaces, relationship to what we already know, Markov chains

Week 11 (Nov 8-12): 5.1 and 5.2: eigenvalues and the characteristic polynomial

Week 12 (Nov 15-19): The characteristic polynomial and diagonalization, Exam 3, Google's pagerank

Week 13 (Nov 22): Adjacency matrices of graphs, Thanksgiving break!

Week 14 (Nov 29-Dec 3): 6.1-6.3: Inner products and orthogonality, orthogonal sets, projections

Week 15 (Dec 6-10): 6.4, 6.5: Gram-Schmidt, least-squares

Homework

Homework 1 (due Friday Sept 3)

Homework 2 (due Friday Sept 10)

Homework 3 (due Friday Sept 24)

Homework 4 (due October 1)

Homework 5 (due October 22)

Homework 6 (due October 29)

Homework 7 (due November 10)

Homework 8 (due November 22)

Homework 9 (due reading day December 10)