Day 1, Mat234: Linear Algebra

Today:

Welcome!
- Introductions (3x5 cards)
  1. Name
  2. Where are you from?
  3. Year (Sophomore, etc.)
  4. Major
  5. Something special about yourself.
  6. The name of your invisible friend.
- Some course details:
  - The course website may be useful: http://www.nku.edu/~longa/classes/mat234
  - Syllabus (logistics, etc.)
  - Our text is free, available as a pdf:
    - Linear Algebra, along with
    - the answers to exercises.
    Note: save the two files in the same directory (without changing file names), so that clicking on an exercise will send you to its answer and clicking on an answer will send you to its exercise.
  - You should do the reading in advance of our discussion of each section in class.
  - Because the text is virtual, you will be allowed to use an electronic reader in class. That includes a laptop, but I'm concerned that it not be used for doing your emails, etc. We'll see how this works, but please don't abuse the system. Ordinarily I forbid the use of electronic devices in class (especially cell phones).
  - The plan of attack (we're using the author's suggestion on page v, first timetable - slightly modified to include an additional test, as well as the padding that an extra week provides).
- 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 -- if it exists! Ah, an important issue that arises immediately....
- 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 practicing. You may use any calculator, but the more powerful, the better.
  - Other software will be used (e.g. Mathematica, Octave)
  - 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: Read Section One.I.1

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