# 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.

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.