In the verge of the almost start of the next semester, I would like to mention a few words for the lectures on multilinear algebra calendar 2009B at CUCEI. It has to see with the overall plan to be developed along the weeks comprising from august to december, for a 16 weeks period.
It would be extremely good if you already know such theories like linear algebra and vector calculus.
But because this can not be taken for granted, we will spend almost the two initial weeks to flashback such concepts like vectors, vector spaces, linear transformations and matrices, in algebra and in the calculus of several variables, we are going to review concepts like partial derivatives, directional derivative, chain’s rule, Taylor series in one and more variables, line and surface integrals and the formula of change of variables for integrals.
If you were not already taken those subjects before and you think that those can be learned meanwhile you are attending multilinear-algebra, you are going to feel that you will understand nothing after the third or fourth week, and so, you only will gain despair.
But do not worry to much, if you feel like you have a lot of questions, do not hesitate to ask me or someone else, no fear, no shame, thru this website or any other channel.
These are only preliminary advices to help you to decide what or when to study. In a next post I will explain more details about the guiding philosophy and method for our course. Remember that the main objective is to learn enough on tensors with the aid of differential geometry to really appreciate and grasp the modern concepts that pervade the today’s scientific ideas.
Now let me explain the mechanics we will follow the semester. The class consists in the exposition of themes which conform the program. Usually the order in the blackboard (indeed whiteboard) in not the usual that every teacher like to do. Always you will have the version alive and the reprises by online resources. When the theme is a flashback (i.e. a remembering of some material already seen) I will order the best I could trying to use the maximum of math symbols. But in new themes, those you do not know yet, the explaining will be a little bit disorganized and this is on purpose. The aim is to bring the new knowledge to you with the natural first time confusion arising when something new is grasping. Do not expect that I dictate lesson direct from a material aid, like a printed page or a book or photocopies: all the material that is about for you to learn, will come from my memory, that is, in the whiteboard will begin to arise and evolve in symbols, diagrams and schemes the easy notions of the subject. I will ask to you to bring a white notebook, pencil and eraser as a tools to learn. I have the opinion that notebooks with pages with lines or grid (rayas o cuadrícula) interfere the reasonings because these patterns block your visual perceptions. Annotate everything that surge in the whiteboard for you to re-read in a posterior time, and if questions come write it down there where you are readining. If you do not assist to the class for XYZ reasons, try to put youself the soonest possible into the thread of the class. It is important to be puntual: missing minutes are enough to loose the ideas. Ask for everything you want to know, it is my duty to explain and re-explain till everyone is satisfied. Do not hesitate to ask. In the cucei moodle resources called álgebra multilineal y geometría diferencial you can find samples of lessons of past semesters even examinations. A few words about the english: as you know english is a confortable mean to communicate science because all academic and scientific people use it, so there is not a reason to not custom. And if you already read it and write it, tell me if mine is adecuate to tell all these things I am talking.