Linear Algebra
Course Description
This collegelevel advanced mathematics course covers the
same topics as a collegelevel 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
TI83). Students are encouraged to have a CAS calculator (with at least the
capabilities of the TI89).
Student Evaluation and Grading Policies
CTD Grade Scale 





A+ 
10098% 
A 
9793% 
A 
9290% 
B+ 
8987% 
B 
8683% 
B 
8280% 
C+ 
7977% 
C 
7673% 
C 
7270% 
D+ 
6967% 
D 
6663% 
D 
6260% 
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 CatÃ³lica 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 AllStar Math
Teams.
Schedule
Date(s) 
Topic(s) 
Activities 
Assignments
and/or
Assessment 
Instructional
Strategies 
July 2022 
Matrices and Linear
Systems of Equations :
vectors and linear
equations, matrix
operations, row
reduction , matrix
inversion, LU
factorization 
Wholeclass
discussions,
individual and
small group tasks 
Individual problem
sets, collaborative
problem sets,
quizzes 
Tiered
assignments,
problembased
learning, flexible
grouping 
July 2325 
Vector Spaces: Linear
combination and linear
dependence, rank and
spaces of a matrix,
complete solution to
Ax =b 
Wholeclass
discussions,
individual and
small group tasks 
Individual problem
sets, collaborative
problem sets,
quizzes, exam 
Tiered
assignments,
problembased
learning, flexible
grouping 
July 2830 
Orthogonality:
Fundamental Theorem of
Linear Algebra, orthongal
projections, least squares ,
GramSchmidt 
Wholeclass
discussions,
individual and
small group tasks 
Individual problem
sets, collaborative
problem sets,
quizzes 
Tiered
assignments,
problembased
learning, flexible
grouping 
July 31 –
August 4 
Determinants and
Eigenvalues: properties of
determinants and
Cramer’s Rule,
diagonalization,
symmetric matrices,
positive definite matrices,
similarity 
Wholeclass
discussions,
individual and
small group tasks 
Individual problem
sets, collaborative
problem sets,
quizzes, exam 
Tiered
assignments,
problembased
learning, flexible
grouping 
August 56 
Linear Transformations:
transformation matrices,
change of basis 
Wholeclass
discussions,
individual and
small group tasks 
Individual problem
sets, collaborative
problem sets,
quizzes 
Tiered
assignments,
problembased
learning, flexible
grouping 
August 78 
Applications: graphs and
networks, Markov chains,
linear programming,
norms and condition
numbers 
Wholeclass
discussions,
individual and
small group tasks 
Individual problem
sets, collaborative
problem sets,
quizzes, exam 
Tiered
assignments,
problembased
learning, flexible
grouping 
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