Introduction to Linear Algebra | Wild Linear Algebra A 1 | NJ Wildberger

This is the full first lecture of a course on Linear Algebra. Given by N J Wildberger of the School of Mathematics and Statistics at UNSW, the course gives a more geometric and natural approach to this important subject, with lots of interesting applications. Our orientation is that Linear Algebra is really ``Linear Algebraic Geometry'': so teaching the algebra without the geometry is depriving the student of the heart of the subject.

The first lecture discusses the affine grid plane and introduces vectors, along with the number one problem of linear algebra: how to invert a linear change of coordinates!

Intended audience: first year college or undergraduate students, motivated high school students, high school teachers, general public interested in mathematics. Enjoy!

Video Contents (thanks to Lucas Lofaro)

0:00 Intro
0:07 Course Overview
2:08 What is Linear Algebra
4:51 Two Dimensional Affine Grid Plane
9:26 Vectors and Coordinates
13:52 Refining the Grid Plane
17:33 Essential Vector Operations
22:32 Describing Vectors with Two Different Coordinate Systems
27:11 Generalizing Coordinate Transformations
30:46 Main problem of Linear Algebra
34:01 General Solution in One and Two Dimensions
40:30 Outstanding Questions
41:06 Exercises

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[ricetown]

Honestly I'm obsessed with these videos and can't believe they are free

[truscorpion]

Thanks!!! Norman for taking your valuable time to enlighten me and a host of

[alexclarosfernandez]

I just want to say thank you for such a superb explanation. It is reall inspiring your passion and concern to teach this subject in a logical and self contained way!!!

[Artur.Baranov]

wow! i've seen lots of lectures on math, yours are the clearest one! you're doing fantastic job! thank you very much :)

[gerarnation]

One of the finest teachers around! \o/

[pinklady]

You simplify everything and I understand you easily.
Thank you for your time in explaining well this tutorial. I have learned much, especially from Bob's grid and Rachel's.

[OrionConstellationHome]

Thank you! You always have another angle and a new approach to everything. I love that. Great simple visuals! Clarity first, building confidence as you go. Well done! I just finished teaching this course and am always looking for how to do it better and more interesting next time. 🙏

[theoriginalanomaly]

This is exactly what I needed. Perfect level (for me) and perfect pace (for me). I appreciate it a lot. Thank you for the time you have spent!

[MrGameengineer]

Really good teaching style, concise and easy to follow.  I wish you were around 30 years ago when I was first learning linear algebra.  Brushing up now.

[federicofresneda]

Thank You Professor Wildberger!! It´s great find a clear and methodic introduction to this subject. The text books i´ve consulted so far begin always with very complicated and unclear "definitions" in the set theory language.

[WaelAjam]

Thank you sir, This introduction ist extremly helpful

[joshryan]

I really enjoy these lectures. I'm a 3rd year student of Mathematics (Undergrad, USA). I look forward to learning more about your ideas concerning real numbers and algebraic hyperbolic geometry. I'm also very curious as to how calculus is defined over the rational numbers, and how/if transcendental functions can be replaced completely by some rational "function" (considering they are so powerful in describing many natural phenomenon).

[ascultarird]

thank you professor..you made an miracol..to learn mathematics for free..you've free our minds.

[sofianb]

Great in depth explanation. lecture was very well presented. Thank you professor Wildberger.

[RAULGUARISMA]

This is a very clear and wonderful explanation regarding a Linear Algebra introduction lesson

[johnbake]

i like math i am in high school, i am planning to study statistics is a good career in terms of job oppotunitties?

[RatanLal-kbsc]

It is a very nice introduction to affine geometry. Thanks for your efforts.

[georgelaing]

This is a wonderfully clear presentation!

[quantabot]

Found it, just what I need, I never liked real numbers anyways...Thank you Professor

[gepliprl]

wow thank you very much prof. I wish i could buy you a glass of coffee, I come from comp. science background, for image processing, your lecture help me a lot.