Relations

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• Misc
  • Colloquium
    • Monday, April 20, 3:30 - 4:30
    • Newton 201
    • Silvia Saccon, University of Texas at Dallas
    • “Are Modules Unique?”
    • Motivating idea: naturals mod 4 = {0,1,2,3}
      • Multiplication doesn’t quite have the properties we expect
      • Some multiplications behave fine, e.g., 0 * 1 = 0, 1 * 1 = 1
      • But 2 * 3 = 2 (so 2 isn’t prime), 3 * 3 = 1 (can a whole number be its own reciprocal?), 2 * 2= 0 (non-0 multiplicands multiply to 0?)
  • GREAT Day
    • Tuesday (Apr. 21)
    • Extra credit similar to colloquia for summary/reaction to any one math talk or poster
  • Exam 2
    • Monday (Apr. 20)
    • Material since 1st hour exam (e.g., control structure: for, while, if, vectorization; algorithms: bisection, chroma key; etc.)
    • Rules & format similar to 1st exam
    • Sample exam available through “Exercises” page
• Questions?
• Relations
  • Video lecture re “Introduction to Relations”
    • Relation = action, comparison, between elements of set
      • x R y, x and y in set
    • Reflexive: x R x
    • Symmetric: if x R y then y R x
    • Transitive: if x R y and y R z then x R z
    • Equivalence relation: reflexive, symmetric & transitive
    • Representing relations
      • e.g., “less than” on naturals mod 4 = {0,1,2,3}
      • { (0,1), (0,2), (1,3), (1,2), (0,3), (2,3) }
      • A relation is a set of ordered pairs
  • Can relations have other than 2 members?
    • 1 + 1 = 2, 1 + 2 = 3, 6 + 5 = 11, ...
    • Suggests relation “sum to” = { (1,1,2), (1,2,3), (6,5,11), ..., (x,y,x+y), ... }
    • “n-ary” relations, contain “n-tuples”
  • Databases as relations
    • { ... (name, manuf., price, photo, description, ... ) ... }
• Next
  • (After exam)
  • Cell arrays
    • A way to represent relations (and many other things) in Matlab
    • Read section 8.1

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