learn more mathematics

I’ve felt the need to learn more math for a quite long time now. The problem is that I have a hard time sticking with it. I start and then get frustrated when it’s proceeding too slow and end up quitting for a while. No more. Now I will stick with it. I will start from the basics by reading “Engineering Mathematics” by Stroud. I aim to study 1-2 hours every day and see how that goes.

I want to learn more about math than differential equations. Why? I don’t know!

Not useful anymore now that I’m not in a computer science PhD program

to learning more math. I will like to do more math, and may learn some more that way; there isn’t anything crucial left for me to learn in math.

There’s a lot I don’t know of course, but there always will be.

Now I can truly say I’m thankful for grad school and the immersion I experienced in math and the confidence and assurance I now have. Maybe it will become useful in a concrete way someday. Maybe it will just have been a juicy love affair, which brought me this far in life. Either way, it’s a lovely enough thing that I want to pass on that love and knowledge to someone else.

Anyway, farewell to this goal.

I’ve been (trying) to read “Model Theory” by C.C. Chang and H. Jerome Keisler.
Also dipping into “Mathematical Logic” by J. Donald Monk

...I read a good review of it. :-)

I’ll try to find one online; most important to me is reteaching myself algebra, calculus, and differentiation. It’s absurd that I don’t remember anything.

Thought i’d write down something about what i’ve been reading in this vein:
Started reading “Basic Set Theory” by Levy
Also “Proofs and Types” by taylor and girard.
It’s interesting to see how mathematicians think – how it is both like and unlike programming for instance.
Eg Levy talks about introducing proper classes into the language of set theory and how these could be eliminated at any time by re-translating them into talk about “real” sets – half way through it struck me that what he was doing was introducing a kind of macro language for classes. bizarre.

The taylor book is fascinating too – instead of talking about the reference (denotation) of expressions , you construct a formalism for talking about proofs of terms.

you dont initially say what proofs of atomic sentences are
: proof of A is whatever we think proofs are

but proofs of complex assertions are structures built out of these entities:

ie a proof of [A and B] ( call it Pr[A and B] is a pair (tuple) of the proof of A and the proof of B

Pr[A^B] is (Pr[A],Pr[B])

Pr[AvB] is either: (1,Pr[A]) or (2,Pr[B]) ( that is a tuple consisting of the number 1 and the proof of A or … etc) – i suppose the 1 and 2 are just markers

Pr[A implies B] = a function from a proof of A to a proof of B
etc etc

ie the proof of “A implies A” is just the Identity function

and so on
..
the upshot being you can translate this proof theory into a theory of types ( and back again)

this strikes me as something you could do in haskell using type classes

I’m currently watching the lectures for MIT’s 18.06 to re-learn Linear Algebra. After that, I want to learn more about probability and statistics. A goal of mine in doing this is to be able to understand everything in Motwani and Raghavan’s Randomized Algorithms.