Linear Algebra
Course Description
This college-level advanced mathematics course covers the
same topics as a college-level introductory
course in Linear Algebra – matrices, vector spaces, and their characteristics.
Technology will be used as a
tool to assist with computations once those computations are well understood.
Emphasis is placed on
understanding of concepts and problem solving , including proofs of important
theorems and building
connections between key concepts.
Outcomes
Upon successful completion of the course:
• Students will be able to perform matrix operations including addition,
multiplication, inversion, and
various kinds of factorization.
• Students will understand the concepts associated with vector spaces,
including linear dependence , basis,
dimension, orthogonality and projections.
• Students will be able to compute determinants and how they relate to
many concepts in Linear Algebra
• Students will understand the concepts associated with symmetric
matrices, the Spectral Theorem, and
singular value decomposition .
Resources and Materials
• Textbook: Introduction to Linear Algebra (Strang),
Wellesley- Cambridge Press .
• Calculator: All students are expected to have a graphing calculator
(with at least the capabilities of the
TI-83). Students are encouraged to have a CAS calculator (with at least the
capabilities of the TI-89).
Student Evaluation and Grading Policies
| CTD Grade Scale |
|
|
|
|
|
| A+ |
100-98% |
A |
97-93% |
A- |
92-90% |
| B+ |
89-87% |
B |
86-83% |
B- |
82-80% |
| C+ |
79-77% |
C |
76-73% |
C- |
72-70% |
| D+ |
69-67% |
D |
66-63% |
D- |
62-60% |
| F |
below 60% |
|
|
|
|
| Breakdown of final grade |
|
|
|
|
|
| Homework |
15% |
Test 1 |
20% |
|
|
| Quizzes |
15% |
Test 2 |
20% |
|
|
| Final Exam |
30% |
|
|
|
|
Instructor Biography
Abel Castillo earned a B.S. in Industrial Engineering from
Universidad Católica Boliviana and a Master’s
degree in Education from Framingham State College. He has taught Algebra,
Geometry, and AP Calculus
at an American school in Santa Cruz, Bolivia, as well as Calculus at the
university level. Abel is currently a
teacher and Math Team coach at Evanston Township High School (less than two
miles away from
Northwestern’s campus), as well as a coach for the Chicago Area All-Star Math
Teams.
Schedule
| Date(s) |
Topic(s) |
Activities |
Assignments
and/or
Assessment |
Instructional
Strategies |
| July 20-22 |
Matrices and Linear
Systems of Equations :
vectors and linear
equations , matrix
operations, row
reduction , matrix
inversion, LU
factorization |
Whole-class
discussions,
individual and
small group tasks |
Individual problem
sets, collaborative
problem sets,
quizzes |
Tiered
assignments,
problem-based
learning, flexible
grouping |
| July 23-25 |
Vector Spaces: Linear
combination and linear
dependence, rank and
spaces of a matrix,
complete solution to
Ax =b |
Whole-class
discussions,
individual and
small group tasks |
Individual problem
sets, collaborative
problem sets,
quizzes, exam |
Tiered
assignments,
problem-based
learning, flexible
grouping |
| July 28-30 |
Orthogonality:
Fundamental Theorem of
Linear Algebra, orthongal
projections, least squares ,
Gram-Schmidt |
Whole-class
discussions,
individual and
small group tasks |
Individual problem
sets, collaborative
problem sets,
quizzes |
Tiered
assignments,
problem-based
learning, flexible
grouping |
July 31 –
August 4 |
Determinants and
Eigenvalues: properties of
determinants and
Cramer’ s Rule ,
diagonalization,
symmetric matrices,
positive definite matrices,
similarity |
Whole-class
discussions,
individual and
small group tasks |
Individual problem
sets, collaborative
problem sets,
quizzes, exam |
Tiered
assignments,
problem-based
learning, flexible
grouping |
| August 5-6 |
Linear Transformations:
transformation matrices,
change of basis |
Whole-class
discussions,
individual and
small group tasks |
Individual problem
sets, collaborative
problem sets,
quizzes |
Tiered
assignments,
problem-based
learning, flexible
grouping |
| August 7-8 |
Applications: graphs and
networks, Markov chains,
linear programming,
norms and condition
numbers |
Whole-class
discussions,
individual and
small group tasks |
Individual problem
sets, collaborative
problem sets,
quizzes, exam |
Tiered
assignments,
problem-based
learning, flexible
grouping |
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