Ciro Santilli @cirosantilli 37

This section is about the definition of the dot product over ${\mathbb{C}}^n$, which extends the definition of the dot product over ${\mathbb{R}}^n$.

Some motivation is discussed at: math.stackexchange.com/questions/2459814/what-is-the-dot-product-of-complex-vectors/4300169#4300169

The complex dot product is defined as:

E.g. in ${\mathbb{C}}^1$:

We can see therefore that this is a form, and a positive definite because:

Just like the usual dot product, this will be a positive definite symmetric bilinear form by definition.

A:

math.stackexchange.com/questions/2382011/computational-complexity-of-modular-exponentiation-from-rosens-discrete-mathem mentions:can be calculated in:Remember that $log(m)$ and $log(n)$ are the lengths in bits of $m$ and $n$, so in terms of the length in bits $M$ and $N$ we'd get:

The intersection of two beautiful arts: coding and physics!

Computational physics is a good way to get valuable intuition about the key equations of physics, and train your numerical analysis skills:

Other child sections:

Programming is hard. To Ciro Santilli, it's almost masochistic.

What makes Ciro especially mad when programming is not the hard things.

It is the things that should be easy, but aren't, and which take up a lot of your programming time.

Especially when you are already a few levels of "simple problems" down from your original goal, and another one of them shows up.

This is basically the cause of Hofstadter's law.

But of course, it is because it is hard that it feels amazing when you achieve your goal.

Putting a complex and useful program together is like composing a symphony, or reaching the summit of a hard rock climbing proble.

Programming can be an art form. There can be great beauty in code and what it does. It is a shame that this is hard to see from within the walls of most companies, where you are stuck doing a small specific task as fast as possible.

Static case of Maxwell's law for electricity only.

Is implied by Gauss' law if Maxwell's equations: physics.stackexchange.com/questions/44418/are-the-maxwells-equations-enough-to-derive-the-law-of-coulomb

The "static" part is important: if this law were true for moving charges, we would be able to transmit information instantly at infinite distances. This is basically where the idea of field comes in.

Public landing page: www.ox.ac.uk/admissions/undergraduate/courses/course-listing/computer-science-and-philosophy

A mixed cross department course with the philosophy department. Its corresponding masters is known as Oxford MCompSciPhil. The handbook is together with the computer science one: Section "Computer science course of the University of Oxford".

Public landing page: www.ox.ac.uk/admissions/undergraduate/courses/course-listing/computer-science-and-philosophy

Corresponding undergrad: Computer Science and Philosophy course of the University of Oxford.

As mentioned at Section "Computer security researcher", Ciro Santilli really tends to like people from this area.

Also, the type of programming Ciro used to do, systems programming, is particularly useful to security researchers, e.g. Linux Kernel Module Cheat.

The reason he does not go into this is that Ciro would rather fight against the more eternal laws of physics rather than with some typo some dude at Apple did last week and which will be patched in a month.