# 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 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 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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