Day 1, Mat225: Linear Algebra

Today:

Welcome!
- Introductions (4x6 cards)
  1. Name
  2. Where are you from?
  3. Working? If so, where, and how many hours?
  4. Year (Sophomore, etc.)
  5. Major
  6. Why are you taking linear algebra?
  7. What is your height (feet/inches)?
  8. Something special about yourself.
- Welcome to David Freeman, especially....
Some course details:
- The course website may be useful: http://www.nku.edu/~longa/classes/mat225
- You should do the reading in advance of our discussion of each section in class.
- Syllabus (logistics, etc.)
- The plan of attack
- I may use blackboard, but only in a limited way. You may certainly find it useful for discussion. I will monitor it only loosely, but please notify me if there is something that I should see or address.
Questions?
A brief overview:
- What is linear algebra?
  - Fun and powerful
  - almost universal
  - well-behaved (by comparison with life in the non-linear lane...)
- Linear equations:
  - ax+by=c
    no sweat, right? Geometrically, a line.
  - Systems of linear equations:
    - a₁x+b₁y = c₁
    - a₂x+b₂y = c₂
    More troublesome? Geometrically, the intersection of two lines....
- Vectors - 2-d, 3-d, ..., n-d:
  - Computer scientists, graphics, physicists, mathematicians: manipulation and transformation (e.g. rotation, scaling, projection)
  - Physicists and chemists:
    - Positions of points (say stars, or molecules)
- Matrices:
  - Urban Planners (and everyone!): spreadsheets
  - Computer Scientists: images, and image compression (for example)
  - Applications
    - e.g. averages (see image compression, for example)
    - Mathematicians, CS: encryption
    - Everyone: Least Squares solutions to over-determined systems of equations
    - decompositions:
      - Statisticians: statistical techniques
      - and again, for image processing (e.g. the SVD -- fundamental theorem of linear algebra).
- Software/technology:
  - I'll be making (limited) use of the TI-92/89, but you'll be able to use it on the exams, so it's worth using.
  - MATLAB will be available: I'll be working out the details....
  - I'll use my octave interface, to access octave, a MATLAB clone. This is useful in class, and for you (so that you can work at home).
Next time: Section 1.1 (First assignment: pp. 11-13, #1, 4, 5, 10, 11, 16, 17, 22, 23, 24, 29, 33; due next Wednesday)

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