In this course we will learn the basics of linear algebra, integrating three different perspectives. We will study the geometry of vectors and higher-dimensional spaces, the algebra of real vectors and matrices, and the formal systems of vector spaces and linear transformations. We will see how the three perspectives interrelate, and how each can be used to better understand the other two.
Mathematics is a fundamentally linguistic activity. In this course we will learn to speak and write the language of mathematics; understanding, writing, and communicating proofs will be a substantial portion of the course.
Topics will include: geometry and manipulation of vectors, lines, and planes; systems of linear equations; vector spaces and linear transformations; matrix arithmetic, inverses, and determinants; bases, spanning sets, and linear independence; and eigenvectors and eigenvalues.
The course syllabus is available here.
- Complete Notes
- Notation Index
- Section 1: Systems of Linear Equations
- Section 2: Vector Spaces
- Section 3: Bases
- Section 4: Linear Transformations
- Section 5: Isomorphisms
- Section 6: Inner Products and Geometry
- Section 7: Eigenvectors and Eigenvalues
- Homework 1, due on Thursday, January 30
- Homework 2, due on Thursday, February 6
- Homework 3, due on Thursday, February 13
Tentative midterm dates are February 20 and March 31.
The final exam will be held in our usual classroom according to the official schedule.
The official textbook for this course is Linear Algebra: A Modern Introduction, 4th edition, by David Poole. The ISBN is 978-1-285-46324-7.
I do not plan to rely heavily on this text during the course, since I plan to present the material from a different perspective. I will be posting my course notes on the course website as we go, and you can use those as a reference for the material.
You shouldn’t need to purchase the book to complete the course, but I will be using it as my primary reference as I put the course notes together.
If you would like more references or other perspectives, you may wish to check out:
- Linear Algebra: Ideas and Applications by Richard Penney, available online through the library
- Linear Algebra: Step by Step by Kuldeep Singh, available online through the library
- A First Course in Linear Algebra by Rob Beezer, available free online
- Linear Algebra by Jim Hefferon, available free online