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Page 2

Tuesday January 4, 2011 6:10 am Lethbridge

This page last updated on: Monday, January 10, 2011 7:59 PM

B. Actual Learning Activities

7:00 am

I am having an emotional high!

I have just downloaded and installed APLX and tried the following:

I had no difficulty using the APL formatted keyboard and quickly ran two tests. 2 + 3 gave the result 5, which is what I expected. I then tried creating a 2 x 3 matrix consisting of the numbers from 1 to 6. This also worked as I expected.

Note: the Greek letter iota generates a vector of integers from 1 to whatever number is to the right of the iota symbol. The Greek letter rho rearranges the vector on the right of the symbol (the numbers 1 2 3 4 5 6) according to the values of the vector to the left of the symbol (2 3) which gives a matrix of 2 rows and 3 columns.

It has been a very long time since I last did this, but it comes back effortlessly. I continue to be amazed at the human mind.

My immediate reaction is to set up a pilot project with some elementary school students, and perhaps some high school students, and show them how to work within this environment. But first I will need to brush up a bit on the use of the interface.

12:20 PM

The linear algebra book that I ordered in November has arrived. It really looks good.

Introduction to Linear Algebra (2009)

Gilbert Strang

This book arrived this morning. A quick skim of the first chapter is exciting. I think I will enjoy this book.

Preface

Here are 3 important web sites for use with this textbook:

• http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
  • links to all the video lectures
    
    
• http://web.mit.edu/18.06/www/psets.html
  • problem sets and solutions (the first problem set used problems from chapter 2)
    
    
• http://math.mit.edu/linearalgebra/
  • keyed directly to sections from the textbook.

Chapter 1 Introduction to Vectors

First, I want to see the overall structure of the chapter.

1.1 Vectors and Linear Combinations

Vectors in Three Dimensions
The Important Questions
Review of the Key Ideas
Worked Examples
Problem Set 1.1

1.2 Lengths and Dot Products

Lengths and Unit Vectors
Notes on Computing
Review of the Key Ideas
Worked Examples
Problem Set 1.2

1.3 Matrices

Linear Equations
The Inverse Matrix
Cyclic Differences
Independence and Dependence
Review of the Key Ideas
Worked Examples
Problem Set 1.3

This chapter takes 30 pages. The overall layout seems excellent but the problem sets look to be challenging. Let's try the first section and see what happens. Time 1:00 PM

Introduction to Vectors

• "The heart of linear algebra is ... in the linear combination of 2 vectors." [p. 1]
  
  
• "Sometimes we want one particular combination, ... other times we want all the combinations" [p. 1]

1.1 Vectors and Linear Combinations

• there are 3 ways to describe a (two-dimensional) vector:
  • using 2 numbers
  • drawing an arrow from (0,0)
  • a point in the plane.
    
    
• A vector v in two-dimensional space has two components, v1 and v2.
• The sum of two vectors is found a component at a time
• Take all linear combinations of u, or u and v, or u, v, w. In three dimensions, these combinations typically fill a line, then a plane, and then the whole space R3.

Time 1:20 PM Now to tackle the problem set. I will do this by hand.

 

 

Summary

Description	Done
Technology: download preview copy of APLX	Yes
Mathematics: chap. 7 of "Linear Algebra for Dummies"
Mathematics: Chap. 1 of "Introduction to Linear Algebra" by Gilbert Strang	Yes
Work on settings for Ship It! software.
Continue reading "Room" by Emma Donoghue	Yes

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