Book Recommendations for Linear Algebra
+ some thoughts on falling in love with math
Linear algebra is the subject that made me fall in love with math.
There was a key moment in my first year of undergrad when I was sitting in a linear algebra lecture. The professor explained to the class what a "vector space" was.
And it was like seeing color for the first time!
When I learned linear algebra, I saw for the first time that many different systems (geometry, systems of equations, transformations) were secretly the same thing, just wearing different clothes.
In this issue, I want to share the learning resources that helped me learn linear algebra (and fall in love with it).
Why Linear Algebra?
Linear algebra is a perfect “first introduction” to advanced math.
On one hand, it’s very concrete and geometric. You can literally draw the concepts: vectors, planes, rotations.
On the other hand, it introduces you to abstraction and rigor. You learn what a proof is. You meet your first real mathematical structures: vector spaces, linear maps, dual spaces.
If you're just getting started, or if you're looking for a deeper understanding, here are some resources I recommend.
Learning Resources
Introduction to Linear Algebra by Gilbert Strang
Strang’s book is concrete, intuitive, and very well-motivated. You’ll get lots of geometry and plenty of examples.
Gilbert Strang’s MIT Open Courseware lectures
These are some of the most wonderful lectures on the internet! (See link here) They explain the core concepts of linear algebra very clearly with lots of visual and numerical examples.
More advanced linear algebra
Linear Algebra Done Right by Sheldon Axler
The cult classic. This is the book I used when first learning linear algebra. It’s not for the faint of heart, and it requires some familiarity with proofs. However, it is extremely thorough and has tons of practice exercises.
Short Videos by Sheldon Axler
If you’re more of a video-person, the author has a lovely YouTube playlist where he explains all the core concepts in the book, step-by-step.
Problem of the Week
Find all integer solutions to the equation
Got a solution to the challenge problem? Submit it here.
Solution from last week
See here for the solution to last week’s problem. (Shoutout to Ammar Ratnani from Stanford whose solution is being featured this week!)
Huge thanks to Rainer Nase (Germany), Anisur Rahaman (India), Ammar Ratnani (Stanford), and Jiayi Wang (Shanghai, CN) for submitting solutions for this challenge problem!
Thanks for reading and happy learning! See you next week,
Adithya