Result: q. 12, 13

Result: q.11 was clean. Looking forward to the next 4

Result: 10 good. 11 bad, gave up too early. Re-try after ☕️

Result: Did ok, missed a lemma

Result: q7. Easy but take an arbitrary element q.8 Sum of subspaces does not have coefficients

Result: 5+6 done. Composition of injective maps is injective BUT you can’t take v, w because we might just have the zero vector.

Result: TRICK to show V = U + W —> ADD ZERO. Take some v \in V, then v = [ v + ( ) ] - ( ) where the parts are in U, W respectively

Result: 1. We wanted outputs from U so obviously we should start with a basis of U 2. The ‘arbitrary output’ thing is becoming more clear now

Result: Integral test. Alternating series test

Result: Converges —> terms go to zero, ratio test, comparison test

Result: Nope

Result: Done

Result: Slow

Result: Distracted by phone

Result: Slow, groggy. Problems next

Result: Done. Now reading Schaum’s ‘Linear mappings’

Result: Done

Result: Done. Idea: straddle the 2nd price out

Result: Done. Learning, Bf, quant, personal

Result: Nothing

Result: (i) done, not (ii)

Result: Tough. Not enjoying this

Result: Feeling better. Meaning of ‘determined by’

Result: 6/11 pages. Follow-up references

Result: Linear map is determined by bases, matrix of linear map, invertibility, isomorphic

Result: Done. Good night all

Result: My proof wasn’t valid because the limits a,b are not necessarily in the sequences a_{n}, b_{n}

Result: I took the “b_{n} is bounded” approach for division rule but they took a different one. Suggests I could try their new method on the a_{n}b_{n} —> ab proof?

Result: Recalled + 2/3 algebra of limits proofs

Result: Limit is unique, convergent ==> bounded

Result: If you’re massaging inequalities you might invoke the shift rule, then you need N = max{ , }. Trying to prove limit is unique

Result: 🎉🎉 100 timers WOOOOO!!! 🎉🎉 Comparison test often combined with ‘shift rule’ to massage the inequalities

Result: Not much. Definitions, convergent => bounded, comparison

Result: Done. Standard limits, subsequences, Cauchy’s criterion, triangle inequalities

Result: 18/37 pages. Sequence tends to infinity, comparison, squeeze, algebra of limits

Result: Almost done

Result: Done. Book list: Four Corners

Result: About 2/3 done

Result: Done! q's 10-18

Result: q's 6-9

Result: q's 1-6. Good problems. Slow :(

Result: Done! Arbitrary vector constant. Moved onto trig. + hyperbolic substitutions

Result: Done and moved to vector-valued functions. Defn. of vector-valued function

Result: q's 10-13. {10, 11, 12} were fantastic, I should be able to recall those examples from memory

Result: Done + hyperbolics q's 1-9

Result: q's 3-10. sin and cos either both even, both odd, or one even/one odd. Draw a map for the strategies

Result: Done + trig. integrals q's 1-2. Weierstrass sub for sin^{2}(2x) is a lot easier to remember if you just remember t = tan(x) is the general sub for even powers

Result: q's 6-9

Result: q's 2-5. Weierstrass sub for cos(x), cos(x/2), cos(2x) are all just scaled versions of each other

Result: Done