The basic goal of mine is not to teach you mathematics, rather to have you create mathematics from your understanding. As both a student and teacher, i have realized that mathematics has unfortunately fell into a realm of memorization and recreation. In this course i will give real life examples why you would actually care about linear algebra, problems will have applications just not a "produce a number" idea. I expect to do examples from chemistry, physics as well as engineering.
At the end of this class it is hoped you will be able to:
- Solve linear equations
- Understand that all problems can be simplified to have linear characteristics
- Answer the question "What is a basis, span, or even a kernel"
- What are matrices?,What are would operations with such creatures entail?
- What do vectors represent and what operations do they follow
- know about orthogonal vectors, dot products, cross products
- think about linear transformations and projections
- Solving differential equations with the use of matrices
- Why do i even care about any of this stuff
- Introduction Video
Just me talking about the class. Expect the first lesson very soon!
- Writing Equations of Lines
Looking at the simple guy y=mx+b
- Solving Two Equations At The Same Time
Finding intersections of lines
- Vectors: What are they
Vector notation, ect
- Vector Operations: Addition and Subtraction:
- Dot Products
Orthogonality, dot products, what it all means
- Cross Products
- Basis and R^n
- Basic Linear Transformations
It may seem confusing however, the purpose of doing such a thing is to simplify complex matrix multiplications into just a constant times a coulomb vector
- Linear Algebra and Calculus Explored (Generalized)
- Know how to solve simple linear systems I.E Know that if i wrote the equation 0 = 10-x. x=10
- Basic understanding of trigonometry and geometry
Im building from the bottom up, so there is no need for really in depth knowledge such as calculus. However it will come in hand when we get into differential equations with matrices !
Im guessing the class would start now? I suppose ill give my post on reddit a few more days to settle to see if we get something else. Here it is for those who are interested. Perhaps ill look towards getting this started the end of this week or start of next week? http://www.reddit.com/r/UniversityofReddit/comments/yjcjc/interestcheckofferlinearalgebra_other/
I expect to take a pretty LINEAR approach to this class :) Topics will be covered as followed
- What are linear equations and how do vectors relate
- Matrices, their operations, and linear transformations on vector spaces and vectors.
- Detriments and eigenvalues (eigenshifts and eigenspaces)
- Change of basis, how it relates to span of a matrix and its kernel
- Linear algebra and how its a big deal in calculus
For each video i do where i present concepts i will post problems via a website (im making it right now stand by!) Where there will be questions and answers in form of pdfs. They will be hand written by me. I will probably do 3-10 problems for each concept video i do. Problems by me will be done step by step, i wont just write down an answer and be like figure out the road to get here. I expect to give interesting problems that would actually care about. I will answer emails best i can, i dont know how many people want to jump on my bandwagon here, so i dont know if there are 2 of you or 2000. Its no difference to me, however i will try my best!
Do not be scared with what you are reading. At this moment im pretty sure you are making a chocolate fudge monkey in your pants. Dont fear future mathematician, you can do it, mathematics seems complex but its just a lot of small ideas that are crunched together in order to make something magnificent. In this course i hope to create alot of small ideas within you, that in the end will come together and you will not only have mastery over the material, but be able to think more abstractly and even create ideas on your own!
On a more personal note, i feel like mathematics is one of the most beautiful things ever created by humans as a species. It should be spread to everyone around the globe for FREE. Nothing pisses me off more, than people trying to get money out of people to teach them mathematics or the sciences. I believe that mathematics is intellectual property of all of us, and we all deserve to reap its benefits, not only the few who understand it and want money for that understanding. So i choose to share my knowledge to you all for free. The only thing i ask in return is you think about what i am presenting you and maybe one day how you could use this said knowledge to possibly change the world as we know it. I discovered this reddit university today and saw that compared to other topics there were only a few math classes,im gonna help change that. I feel like this is a good place i can reach a new audience of people who want a future in mathematics, or just see it as a hobby. I hope taking my "courses" you will gain a new level of math literacy you have not seen before. Perhaps even, dare i say it, want to learn more math gasps
I have a A.S in computer science/mathematics, currently im working towards my masters and phd in cs/math. I am by no bounds a MIT or Stanford Professor, however im sure i can give you a new perspective on mathematics, specifically linear algebra for the time being.