311 – HW1

January 15, 2015

Go through the first 28 propositions of Book 1 of Euclid’s Elements. Make a list of the unjustified inferences you observe in the proofs.

(Due January 20 at the beginning of lecture.)

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403/503 – HW1

January 15, 2015

Use the axioms of vector space to verify that if V is a vector space over a field \mathbb F, then:

  1. For any v\in V, we have (-1)v=-v,
  2. For any v\in V, we have 0v=\vec 0, and
  3. For any r\in\mathbb F, we have r\vec 0=\vec 0.

(Due January 20, at the beginning of lecture.)