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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. Techno logy 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 de terminants 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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