Linear Algebra Math 2700.006 Spring 2013 (Cohen) Vague Course Outline.
Please note: This entire schedule, including test dates, is subject to revision at ANY time!!!
Attend class regularly to stay aware of schedule changes.
Week 1: 1/14, 1/16
Sets and Set Notation.
Vector spaces and examples. (Section 4.1)
Week 2: 1/21, 1/23
Vector subspaces and spanning sets. (Section 4.1)
Systems of linear equations (Section 1.1, briefly)
Matrix row reductions and echelon forms. (Sections 1.2, 1.3)
Week 3: 1/28, 1/30
Matrix row reductions and echelon forms, contd. (Sections 1.2, 1.3)
Matrices and matrix transformations. (Sections 1.4, 1.5)
Week 4: 2/4, 2/6
Linear transformations in Euclidean space (Section 1.8)
Matrix representations of linear transformations (Section 1.9)
Week 5: 2/11, 2/13
Functions and function notation.
General inear transformations and isomorphisms (Section 4.2)
The kernel/null subspace and the column subspace (Section 4.2, Section 2.8)
Week 6: 2/18, 2/20
The range space of a linear transformation and column space of a matrix (Section 4.2)
Applications of vector space theory (Sections 1.10, 2.6, 2.7, something else entirely? I will seek
the class’s input!)
Week 7: 2/25, 2/27
Applications and review for Test 1.
TEST 1 February 27
Week 8: 3/4, 3/6
Linear independence. (Section 4.3, Section 1.7)
Bases and coordinate systems. (Sections 4.3, 4.4)
Change of basis. (Section 4.7)
SPRING BREAK 3/9-3/17
Week 9: 3/18, 3/20
Dimension and rank (Sections 4.5, 4.6, Section 2.9)
The Steinitz Exchange Lemma.
Isomorphic spaces.
Week 10: 3/25, 3/27
Linear transformations as matrices (Section 1.9)
Matrix operations (Section 2.1)
Inverting matrices (Sections 2.2, 2.3)
Determinants and their properties (Sections 3.1, 3.2)
Week 11: 4/1, 4/3
Eigenvectors and eigenvalues. (Section 5.1)
The characteristic equation. (Section 5.2)
Week 12: 4/8, 4/10
Diagonalizing matrices. (Section 5.3)
Computing eigenvalues and eigenvectors.
Applications, if we have time. (Again, class input is desired!)
Week 13: 4/15, 4/17
Applications and review for Test 2.
TEST 2 April 17
Week 14: 4/22, 4/24 and Week 15: 4/29, 5/1
Catch up if we have fallen behind, or begin Chapter 6.
Review for Final Exam!
FINAL EXAM WEDNESDAY MAY 8 10:30-12:30pm in WH 319