Susquehanna Township High School
Linear Algebra Syllabus
Ms. Mary Beth Nied, Room 312
Email:
Teacher Page: http://www.hannasd.org/Domain/584
Duration: Semester 1 of the 2014-2015 School Year
Class time: Period 8,9
Text: Introduction to Linear Algebra, Gilbert Strang
Course Description: Linear Algebra introduces students to abstract mathematical concepts by way of matrix theory and vector spaces. This course focuses on matrices and their applications, vector spaces, inner products, linear transformations and eigenvalues and eigenvectors.
Prerequisite: Successful completion of AP Calculus BC or equivalent course and a 90 or better in Differential Equations.
Possible Topics:
1. Introduction to Vectors
a. Vectors
b. Lengths and Dot Products
c. Planes
2. Matrices and Systems of Linear Equations
a. Matrices and Linear Equations
b. The Idea of Elimination
c. Elimination Using Matrices
d. Rules for Matrix Operations
e. Inverse Matrices
f. Elimination = Factorization: A=LU
g. Transposes and Permutations
3. Introduction to Vector Spaces
a. Spaces of Vectors
b. The Nullspace of A: Solving Ax = b
c. Independence, Basis, and Dimension
d. Dimension of the Four Subspaces
4. Matrix Determinants
a. The Properties of Determinants
b. Permutations and Cofactors
c. Cramer’s Rule, Inverse and Volumes
5. Orthogonality
a. Orthogonality of the Four Subspace
b. Projections
c. Lease Squares Approximations
d. Orthogonal bases and Gram-Schmidt
6. Eigenvalues and Eigenvectors
a. Introduction to Eigenvalues
b. Diagonalizing a Matrix
c. Application to Differential Equations
d. Symmetric Matrices
e. Positive Definite Matrices
f. Similar Matrices
7. Linear Transformations
a. The Idea of a Linear Transformation
b. The Matriz of a Linear Transformation
c. Choice of Basis: Similarity and Diagonalization
8. Applications of Linear Algebra
a. Graphs and Networks
b. Markov Matrices and Economic Models
c. Linear Programming
d. Fourier Series: Linear Algebra for Functions
e. Computer Graphics
9. Introduction to Mathematical Logic
a. Connectives and Sentential Logic
b. Tautologies, Satisfiability, Truth Tables
c. Logical Consequence
d. Inverse, Converse, Composite, Contrapositive
e. Proof by Induction
f. Proof by Deduction
g. Axiom Systems
Expectations:
1. Students must maintain a notebook, binder or folder containing all class notes and homework assignments.
2. Students must bring a notebook or folder, textbook, and pencil to class each day. All work must be done in pencil.
3. Students must participate appropriately in class.
4. Students must fully complete homework in order to receive credit for the assignment.
5. Students must complete all exams, quizzes, projects, and the final exam.
6. Students must assume responsibility for their make-up work and grades using their Schoolwires account.
7. Students must conduct themselves in a professional manner (courteous and mature behavior) and follow the policies and guidelines of the Susquehanna Township School District.
8. The Susquehanna Township School District tardy policy and electronic device policy will be followed.
Evaluation:
Students will be graded using a total points system. Categories for grading include homework, quizzes, exams, projects and a final exam. Students must complete all assigned work. Students must make up homework and class work when absent. Students who do not complete exams or project will be given an incomplete for the marking period and will have 2 weeks to hand in all missing work.
Make-up Policy:
It is the student’s responsibility to make-up all required notes, homework, quizzes, assignments, projects, and tests. Homework should be made up within two weeks upon return to school. Tests and quizzes should be made up within 5 days of return, if new material was presented during the absence. If no new material was presented, quizzes and tests should be completed during class upon the student’s return to school. If a student is absent on the review day prior to a chapter exam, the student will be required to take the exam on the day of the return. Students may not be permitted to make up any work assigned during an unexcused absence.