Pretty nice intro to algebraic number theory

Good mathematics art is so underrated.

Credit to the K-theory YouTube channel.

https://www.youtube.com/channel/UCRXC6M65qiFlHaXGDNC--VA

Model theory types are pretty clear. Composites of types are pretty easy to think about like:

const int a = 1;

It is possible to even extend them to Ada like:

subtype Capital_Letter is Character range 'A' .. 'Z';

The Model Theory wiki is great. Its definitions so far have been really clear.

philosophy of mathematics and logic book

https://link.springer.com/book/10.1007/978-3-030-84706-7

I am just so busy this week. I might pass the thousand page mark for math literature read this month.

First we do the math. Then we make the math do the math.

https://www.microsoft.com/en-us/research/wp-content/uploads/2016/12/popl10_synthesis.pdf

Yeah, you can make a whole ideology out of algebra. Whitehead was great.

Convex algebraic geometry is both pretty, and really easy.

Also it is one of those areas that is a mix of algorithm analysis and optimization. So, super useful.

I wonder how analysis made it into mathematics. Now there is just a schism in the doctrine in a lot of places.

I think it is a "does it 'solve' problems I care about?” kind of thing. I think it is the foundation for validating inferences in math. The choice axiom went from, being considered problematic, to being mostly accepted because new problems from it did not hurt old problems.

No idea why, but a lot of scientific books and journals are free to download right now through Springer.

Algorithms in Real Algebraic Geometry

https://link.springer.com/book/10.1007/3-540-33099-2

CoCoAlib (Computations in Commutative Algebra library)

This thing is actually nice. My tired-brain can understand C/C++. It is well documented and has tests and debugging procedures. Is that a Hilbert Algebra? I can has type PolyRing?

Generic distractions and initial ideals (We played with CoCoA, got paid)

- Background
- Logic, Mathematics, Electronics

- Hobbies
- Philosophy, Programming, Video Games

I am pretty curious about how to use automated reasoning systems to help discover new things, use and verify old ideas, and generally make my life easier.

Current events I try to keep up on

- Math Logic community (The Journal of Symbolic Logic)

- Statistics community (JASML, AoS)

- Algebra community (JoA, JoAG, JoPaAA, SIGSAM)

- Formal Methods community (CAV/TACAS)

Passing the learning curve up to current events

- Abstract Algebra (Dummit, Foote)

- Commutative Algebra (Eisenbud)

- Algebraic Geometry (Hartshorne)

- Mathematical Logic (Mendelson)

- Model Theory (Marker)

Joined Aug 2020