MATH
21 B
Mathematics Math21b Spring 2018
Linear Algebra and Differential Equations
Linear algebra Math21b, Spring 2018
Course Head: Oliver Knill
Office: SciCtr 432

An important picture for coordinate change (last lecture this week)
  • In HW 12, you have to search for the unique 4-vector [a,b,c,d] with integer entries such that 1 < a < b < c < d < 10 and the length is an integer. Try to find it by treasure hunting. If you need help with a computer, here is a program
    n=9; Do[
        If[IntegerQ[Sqrt[a^2+b^2+c^2+d^2]],
          Print[{a,b,c,d},Sqrt[a^2+b^2+c^2+d^2]]],
    {a,1,n},{b,a+1,n},{c,b+1,n},{d,c+1,n}];
    
    By the way, Oliver currently can not find an example of 5 numbers 1 < a < b < c < d < e whose squares add up to a square. It would be a Pythagorean sextuple without repetition. Do they exist?
  • Here are some documents:

  • This week, we have looked at the concept of dimension, which is for us just the number of elements in a basis. The notion of dimension is fascinating: from a Scientific American Article written 10 years ago in 2008, where an approach to quantum gravity is discussed. It has been authored by Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll. Click on the picture to see the article.

    Please send questions and comments to knill@math.harvard.edu
    Math21b Harvard College Course ID:110989| Oliver Knill | Spring 2018 | Department of Mathematics | Faculty of Art and Sciences | Harvard University, [Canvas, for admin], Twitter