Difference between revisions of "09240/Classnotes for Tuesday September 22"
From Drorbn
(→Examples) 
(→Food for thought) 

Line 73:  Line 73:  
# Unnecessary for a V.S.  # Unnecessary for a V.S.  
−  # This is useless  +  # This is useless, since it does not describe reality. For example, a mathematical theory with 46 dimensions can be perfect and mathematically elegant, but if the only solution to it is a universe in which life cannot form it is not reality, hence we have no use for it. 
Revision as of 22:44, 22 September 2009

Contents 
Some links
 The Complex Numbers by Computer.
 Dori Eldar's work on "mechanical computations": Machines as Calculating Devices and Computing the function the hard way.
 The "Dimensions" video on "Nombres complexes", is at http://dimensionsmath.org/Dim_reg_AM.htm (and then go to "Dimensions_5".
WARNING: The notes below, written for students and by students, are provided "as is", with absolutely no warranty. They can not be assumed to be complete, correct, reliable or relevant. If you don't like them, don't read them. It is a bad idea to stop taking your own notes thinking that these notes can be a total replacement  there's nothing like one's own handwriting!
Visit this pages' history tab to see who added what and when.
Class notes for today
Vectors:
 can be added
 can be multiplied by a number (not another vector)
Let be a field. A vector space over the field is a set (of vectors) with a special element , a binary operation , a binary operation .
Convention for today:

VS1
VS2
VS3
VS4
VS5
VS6
VS7
VS8
Proof of VS4
Take an arbitrary
Set and note
Examples

 ...

 ...
 Polynomials
Food for thought
What is wrong with setting
 Unnecessary for a V.S.
 This is useless, since it does not describe reality. For example, a mathematical theory with 46 dimensions can be perfect and mathematically elegant, but if the only solution to it is a universe in which life cannot form it is not reality, hence we have no use for it.