Syllabus (PDF File)
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NOTE:
In Linear Algebra, we will be proving theorems and statements (both in
class and for homework). Since you may
not be familiar with some of the ideas of mathematical proofs, I have collected
a few internet resources to help you.
These resources discuss the general ideas and techniques of mathematical
proof and give examples. I encourage you
to read one or more of these during the first two weeks of the semester. The links are below.
·
A Few Words About
Proofs (PDF File)
·
Writing Proofs
(PDF File)
·
Conventions
for Writing Mathematical Proofs (PDF File)
·
Writing Proofs
(PDF File)
TEST I – Take-Home Part (PDF
File)
Study Guide for TEST I – In-Class
Portion (PDF File)
Study Guide for TEST II – In-Class
Portion (PDF File)
Study Guide for TEST III – In-Class
Portion (PDF File)
Study Guide for Final Exam (PDF
File)
POWER POINT PRESENTATIONS
NOTE: These Power
Point Presentations are saved as PDF files.
Chapter 1:
Systems of Linear Equations and Matrices
Section
1.1: Introduction to Systems of
Linear Equations
Section
1.2: Gaussian Elimination
Section
1.3: Matrices and Matrix Operations
Section
1.4: Inverses; Algebraic Properties
of Matrices
Section
1.5: Elementary Matrices and a
Method for Finding A−1
Section
1.6: More on Linear Systems and
Invertible Matrices
Section
1.7: Diagonal, Triangular, and
Symmetric Matrices
Chapter 2:
Determinants
Section
2.1: Determinants by Cofactor
Expansion
Section
2.2: Evaluating Determinants by Row
Reduction
Section
2.3: Properties of the Determinants;
Cramer’s Rule
Chapter 3:
Euclidean Vector Spaces
Section
3.1: Vectors in 2-Space, 3-Space,
and n-Space
Section
3.2: Norm, Dot Product, and Distance
in Rn
Section
3.3: Orthogonality
Section
3.4: The Geometry of Linear Systems
Section
3.5: Cross Product
Chapter 4:
General Vector Spaces
Section
4.1: Real Vector Spaces
Section
4.2: Subspaces
Section
4.3: Linear Independence
Section
4.4: Coordinates and Basis
Section
4.5: Dimension
Section
4.6: Change of Basis
Section
4.7: Row Space, Column Space, and
Null Space
Section
4.8: Rank, Nullity, and the
Fundamental Matrix Spaces
Section
4.9: Matrix Transformations from Rn to Rm
Section 4.10:
Properties of Matrix Transformations
Chapter 5:
Eigenvalues and Eigenvectors
Section
5.1: Eigenvalues and Eigenvectors
Section
5.2: Diagonalization
Chapter 6:
Inner Product Spaces
Section
6.1: Inner Products
Section
6.2: Angles and Orthogonality
in Inner Product Spaces
Section
6.3: Orthonomral
Bases; Gram-Schmidt Process; QR-Decomposistion
Chapter 7:
Diagonalization and Quadratic Forms
Section 7.1: Orthogonal Matrices
Section
7.2: Orthogonal Diagonalization