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Elementary Linear Algebra

Math 1890-001

Syllabus for Spring 2012

Instructor
Charlie Odenthal
charles.odenthal@utoledo.edu
http://www.math.utoledo.edu/~codentha
Office
UH 3019
419.530.2297
Office Hours
11:00am - 11:50am MWF
2:00pm - 3:50pm M
Class Room
UH 4440
Class Time
12:00 - 12:50pm MWF
Text
Linear Algebra by Jim Hefferon
A free pdf of the text is available here: http://joshua.smcvt.edu/linearalgebra/
Exam Days
Midterm 1: F Feb 17 (Chapters One and Two)
Midterm 2: F Mar 30 (Chapter Three)
Final: M Apr 30 (12:30 - 2:30)
(Cumulative Final with emphasis on Chapters Four and Five)
Course Grading
homework (10%) due on Wednesdays
quizzes (10%) given on Wednesdays
midterms (50%)
final exam (30%)
Course Schedule
We'll cover approximately one section of the text each meeting. There are 44 sections in the text and 42 class meetings not counting exam days. Something will have to give.
Chapter One: Linear Systems
  1. Solving Linear Systems
    Week 1
    1. Gauss' Method
    2. Describing the Solution Set
    3. General = Particular + Homogeneous
      Week 2
  2. Linear Geometry of n-Space
    1. Vectors in Space
    2. Length and Angle Measures
      Week 3
  3. Reduced Echelon Form
    1. Gauss-Jordan Reduction
    2. Row Equivalence
Chapter Two: Vector Spaces
  1. Definition of Vector Spaces
    1. Definition and Examples
      Week 4
    2. Subspaces and Spanning Sets
  2. Linear Indepence
    1. Definition and Examples
  3. Basis and Dimension
    1. Basis
      Week 5
    2. Dimension
    3. Vector Spaces and Linear Systems
    4. Combining Subspaces
      Week 6 (Midterm)
Chapter Three: Maps Between Spaces
  1. Isomorphisms
    1. Definition and Examples
    2. Dimension Characterizes Isomorphism
      Week 7
  2. Homomorphisms
    1. Definition
    2. Rangespace and Nullspace
  3. Computing Linear Maps
    1. Representing Linear Maps with Matrices
    2. Any Matrix Represents a Linear Map
      Week 8
  4. Matrix Operations
    1. Sums and Scalar Products
    2. Matrix Multiplication
    3. Mechanics of Matrix Multiplication
      Week 9
    4. Inverses
  5. Change of Basis
    1. Changing Representations of Vectors
    2. Changing Map Representations
      Week 10
  6. Projection
    1. Orthogonal Projection Into a Line
    2. Gram-Schmidt Orthogonalization
    3. Projection Into a Subspace
      Week 11 (Midterm)
Chapter Four: Determinants
  1. Definition
    1. Exploration
    2. Properties of Determinants
    3. The Permutation Expansion
      Week 12
    4. Determinants Exist
  2. Geometry of Determinants
    1. Determinants as Size Functions
  3. Other Fomulas
    1. Laplace's Expansion
      Week 13
Chapter Five: Similarity
  1. Complex Vector Spaces
    1. Factoring and Complex Numbers: A Review
    2. Complex representations
  2. Similarity
    1. Definition and Examples
    2. Diagonlizability
      Week 14
    3. Eigenvalues and Eigenvectors
  3. Nilpotence
    1. Self-Composition
    2. Strings
      Week 15
  4. Jordan Form
    1. Polynomials of Maps and Matrices
    2. Jordan Canonical Form
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