Math 231 Linear Algebra

Spring 2020

Instructor: Enrique Treviño
Lectures: MWF 2:30 - 3:50 pm in Young Hall 207
Office Hours: MWF between 11:00am to 12pm. You can also arrange a meeting by appointment.
Office: Young Hall 105
Email:
Phone Ext.: #6187

Announcements

Announcements will be posted here

All the homework assignments will appear here:
Homework

Course Description

Vector spaces, linear independence, linear transformations, matrices, determinants, and applications to geometry. Prerequisite: Mathematics 230 or permission of the instructor. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

Textbook

A First Course in Linear Algebra by Robert A. Beezer

The textbook is an open-source book, you can download it free at the textbook's website. If you prefer a hardcover version of the book, the book can be ordered online at Amazon or at Barnes and Noble for around $30. For example here.

Topics we will cover

A tentative list of topics is:

Chapter 1: Systems of Linear Equations

Solving Systems of Linear Equations
Reduced Row-Echelon Form
Homogeneous Systems of Equations
Nonsingular Matrices

Chapter 2: Vectors

Vector Operations
Linear Combinations
Spanning Sets
Linear Independence
Linear Dependence and Spans
Orthogonality

Chapter 3: Matrices

Matrix Operations
Matrix Multiplication
Matrix Inverses and Systems of Linear Equations
Matrix Inverses and Nonsingular Matrices
Column and Row Spaces

Chapter 4: Vector Spaces

Vector Spaces
Subspaces
Linear Independence and Spanning Sets
Bases
Dimension
Properties of Dimension

Chapter 5: Determinants

Determinant of a Matrix
Properties of Determinants of Matrices

Chapter 6: Eigenvalues

Eigenvalues and Eigenvectors
Properties of Eigenvalues and Eigenvectors
Similarity and Diagonalization

Student Learning Outcomes

Main Goals:

Learn how to solve systems of equations.
Learn what matrices are, how to manipulate them.
Learn how to invert matrices and why it is useful to do so.
Learn about vector spaces, linear combinations, spanning sets and dimension.
Learn what a determinant is and what it helps us classify.
Learn what eigenvalues are and their applications to real-world problems.
Learn how to do "simple" proofs regading objects from linear algebra, such as linear combinations.

Grading

The course grade will be based on:
Homework 10%,
Midterms 60% (20% each),
Final Exam 30%.

Homework

There will be written homework roughly every week. The homework will be posted here. Collaboration in the homework is permitted, however it must be your own.

Exams

There will be three midterms and one final exam. On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams.

The tentative dates for the exams:

The first midterm will be on Wednesday February 19.
The second midterm will be on Wednesday April 1.
The third midterm will be on Wednesday April 29.
The final exam will be on Saturday May 2 from 1:30pm to 4:30pm.

Attendance

Students are expected to come to every lecture and every exam.

If the dates of the exams conflict with Lake Forest approved events, inform me as soon as possible.

Description of instructional time and expectations:

This course meets 3 times per week for 4.5 hours per week. The course carries 1.0 course credit (equivalent to four semester credit hours). Students are expected to devote a minimum of 12 hours of total work per week (in-class time plus out-of-class work) to this course.

Academic Honesty

Please read the College's information on Academic Honesty. If a student cheats in an exam, quiz or homework assignment, I will proceed with charging the student with the Academic Honesty Judicial Board. The usual (first) penalty is a 0 in the assignment on which the cheating occured plus some ethics lectures the student would take. The second penalty is usually suspension.

Accommodations Statement

If you are a student who needs an accommodation because of a disability or medical or psychological condition that limits your ability to fully participate in this course, please contact Kara Fifield, Director of Disability Services, to document your disability with the College and with the professor of this course. Academic accommodations should be reasonable and not alter the fundamental nature of this course. Because it can take a week or more to arrange requested accommodations, you are encouraged to establish your semester accommodations as early in the semester as possible. Contact Kara Fifield by email or phone: kfifield@lakeforest.edu or 847-735-5167. For more information about services for students with disabilities at Lake Forest College, see: http://www.lakeforest.edu/academics/resources/disability/

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Kara Fifield.

Last modified on January 12, 2020.