Essence of linear algebra preview

Two quick things I can recommend without hesitation, which focus on an intuitive understanding of concepts: 1. Essence of Linear Algebra mini-series - ▶ this video 2. Better Explained website - link YouTube has a lot of high quality math content, it definitely helped through university. It's also worth mentioning the Stanford U courses. The main takeaway I have for you is learn the concepts intuitively first, then spend the time to play around with them on paper until they sink in. Some things will be easy, some will be frustrating, much like programming you will walk away from a frustrating problem and have an epiphany while doing something completely different. All the best and have fun!

If anyone's looking for a (high level) overview of linear algebra, I'd highly recommend 3blue1brown's video series: ▶ this video It's mostly graphical, and is really helpful in forming and cementing an intuition for linear algebra.

For linear algebra basics, I also especially recommend 3Blue1Brown's youtube channel and his "Essence of" series: ▶ this video I've never seen the material presented more clearly - it's completely visual and focused on building intuition first.

Fror a high-level overview of linear algebra, 3Blue1Brown's youtube series I cannot recommend highly enough. ▶ this video

Wow, this lecturer is great! I think this is the most intuitive explanation of Kalman filters I've seen yet. I've seen other lecturers try to quickly jump into state space and lose students with big matrices. I would have paid good money for this if I wasn't already familiar with the material. The clarity is up there with The Essence of Linear Algebra: ▶ this video Trading math videos on the Internet--definitely nerds.

+1 And definitely follow through his "pause and ponder" sections. If you want to build up your maths skills, it is crucial to learn how to think in the maths way. Like becoming a good programmer involves writing lots of code yourself, or to become a good dancer you need to practice your steps. For maths it's abstract thinking. Appreciation of maths is one thing, having the discipline to self-study a whole other. Edit. Regarding your 2nd Edit: His videos are made for the broadest audience possible. I'd recommend picking any video whose topic interests you the most at the moment. You will see what knowledge you lack (take notes of these!) and can expand from there. Be it to watch his maths fundamental ((1)) series [0],[1] or just rewatch. ((1)): As in any other things, knowing your fundamentals is significant to the understanding of a topic. It won't help you at all if you can apply (copy paste) some machine learning techniques if you don't know about linear algebra at all. [0]: ▶ this video [1]: link

So many things I could say about this, but I"ll let Alan Kay speak for me - link Alan talks about how ideas in Calculus could be manifested from an early age and a richness in understanding built up as they aged up: - at very young ages, kids really respond well through "doing" / the enactive channel. When asked to draw a circle, kids in Papert's group would first emulate what a LOGO turtle would do by rotating their body in a circle (making tiny increments in x and y). - as they got a bit older, the visual / iconic channel was more developed and they could understand the abstraction of a circle on pencil/paper and how the concepts carried over there - closer to early teens, symbols were much easier to grasp and relate to, etc. With this context in mind, there have been some cool efforts to mix the second and third channels I just mentioned to communicate advanced math concepts. Vi Hart and Grant Sanderson's youtube channels come to mind. Here are my favorite videos by Grant: - "What does it feel like to invent math": link - On the visual intuition behind a hard problem on the Putnam exam - "The hardest problem on the hardest test": link - From vectors to matrices to vector spaces to higher-level ideas like the link between linear algebra and calculus: "Essence of linear algebra" series: ▶ this video What I especially like about Grant's videos, is that he often walks through what a mathematician would do, the questions she would ask, etc.

For an article like this I find that static visualizations aren't anywhere near as effective as dynamic ones found in a similar explanation here (3Blue1Brown on Linear Algebra Transformations) ▶ this video

Ooooh, these are nice. Here are mine: Extra History: stories of historical incidents — link Real Engineering: mostly materials science — link - Wendover Productions — mostly transportation - link Tom Scott: a bit of everything — link - Jay foreman: Urban planning and maps — link The Engineer Guy: Manufacturing — link Practical Engineering: Mostly Civil Engineering — link 3Blue1Brown: Math, visualized to me more intuitive — ▶ this video

See the "Essence of Linear Algebra" (visualized) by the same author -- it should give you more intuition into the nature of the transformations: Essence of Linear Algebra ▶ this video

Have you seen the Essence of Linear Algebra video series posted to HN a few days ago? Seeing the geometric transformations animated gives you intuition hard to develop otherwise: Essence of Linear Algebra (visualized) ▶ this video

It at least cuts down on the amount of time you have to explain the mechanics of it. This is more intuitive to memorize than an algorithm composed of bullet-point instructions. For intuition, I highly recommend ▶ this video - I think both the intuition and practicing the details should be learned.