Result: 1. The A. property basically says that we can always force a > b 2. We define sup S = \infty for unbounded S so sup S and inf S always make sense

Result: Working on Ross

Result: Working on Ross. 1. Algebraic numbers 2. Rational root theorem gives very easy proofs of why \sqrt{stuff} are not rational

Result: Slow start

Result: 1. P(either), P(none), P(exactly one)

Result: Sub-group theorems (2)

Result: 1. General linear group 2. Quaternion group (i,j,k cycle) 3. Follow-ups: sub-group lattice? Normal sub-group? What is Z_{5} again?

Result: Fine

Result: Up to dual bases

Result: Done

Result: Very bad

Result: Done, email now

Result: Needs more

Result: Fine. Needs another session

Result: Bad. Trying to get clear on PDF

Result: CDF of choosing random real in [a,b] ... (Consider [x1,x2] \in [a,b])

Result: Discrete'done'. 1. i.i.d. := independent and identically distributed

Result: Variance not linear, Var(aX+b) = a^{2} Var(X)

Result: Variance, standard deviation

Result: Anki study done, 0 cards made

Result: cdf for discrete rv (step function). Expected value

Result: Bad

Result: Hypergeometric: b blue, r red, pick k, X is number of blues, P(X=x). X bounded min and max

Result: Anki done. Add cards from tutorial later

Result: 17 cards

Result: Self-adjoint and normal operators

Result: Hint for counter-example for f(A ∩ B): Consider A ∩ B = ∅

Result: Ok

Result: Ok. Try and complete later

Result: 1. Self-adjoint operator (or Hermitian) iff T = T* 2. Every eigenvalue of self-adjoint operator is real ( Schema: Show λ = conj.(λ) )

Result: Done. Good

Result: Pascal ( = generalized geometric ), hypergeometric (blue & red balls, pick k)

Result: Bernoulli, geometric, binomial

Result: 1. X : S --> R (be careful knowing what object you should be referring to) 2. Phrase "finite or countably infinite" 3. pmf must say "0 otherwise"

Result: 1. Venn for probability was useful 2. Disjoint event =/= independent: disjoint means only one can happen, they defo affect each other

Result: Horsemen of conditional prob.: Chain rule, law of total prob., Bayes’

Result: Little analysis proof. False-positive

Result: 1. Disjoint \neq independent (quick proof) 2. Law of total prob. 3. Bayes’ is P(A|B) in reverse (may req. law of total prob.)

Result: Fine. On independence

Result: Chain rule for conditional (not done). Working on m-h

Result: Sample space for “breaking stick of length 1 into 3 pieces, prob. of being able to form a triangle” (geometric prob.) Started conditional

Result: Ok. Do probability later

Result: Fine

Result: Re-learn span of empty set in EOD tonight

Result: About 60% done

Result: 1. Orthog. decomposition (write u in terms of v and a vector orthog. to v) 2. Orthog. projection (project v onto vector space U = closest vector in U to v)

Result: 3 pages

Result: Recalled

Result: Ok