Thread 16835273

Exact sequence edition.
ITT: Discussion of math

Previous thread: >>16803023

>>16835273 (OP)
>/mg/ - math general
>picrel
More like "/~mg/ - not-maths general", amirite.

>>16835273 (OP)
does Mathchan still exist?

>>16835273 (OP)
>Mathchan
it's still down btw.

Math is gay.

Q.E.D.

>>16835273 (OP)
I'm a retard, when I was in university and school I could do Trigonometry, matrix and Inequation of second grade with no problem at all and now after 10 years of doing nothing I forgot everything, I took my old notebooks I wrote a lot, I took all mines from start to finish and re reading and re learning from what I wrote down.
Now I'm learning from first grade equations with fractions, because I noticed that after I took a job in Engineering I noticed that since I use software for calculation and many stuff I wanted to go back to the roots of when I needed to really know this stuff and calculate like that on the top of your head.
So I'm relearning and reloving math even if I feel like a retard but I noticing that is just like riding a bicycle but maybe slower, I noticed I even forgot binary and exadecimal calculus and I notice how everything makes so fucking much sense of life and logic and even programming that I started as an hobby last month, it's like rediscovering my own brain.
ESL sorry.
So how are you math anons?
Me I'm both sad but happy, sad because I turned off my brain after I took a job and happy because I'm rediscovering my brain.

>>16836318
keep at it anon. Doing math every day for over a year genuinely transforms your brain. I was also basically a retard at math before going to uni. Always make sure to challenge yourself, though. If a book is challenging to you, see that as a sign that you have a lot to learn from it, don't let that discourage you from reading it

>>16836378
>I was also basically a retard at math
How did you change that? Where did you start from? I’m solving linear algebraic equations, reading Elements by Euclid, books of propositional logic, Frege’s concept script, Logic gates , Thermodynamics , Quantum Mechanics and on set theory.

>>16836559
reading difficult books, analyzing proofs carefully until I've fully internalized the reasoning and could call them my own, and spending a lot of time on my own proofs (exercises, etc.).
When I first started out, these notes on Linear Algebra (technically also Algebra, maybe combine it with something like Shilov or Gorodentsev to get a full course) helped me a lot
https://www.ams.org/open-math-notes/omn-view-listing?listingId=110700
https://www.ams.org/open-math-notes/omn-view-listing?listingId=110701
If you want something on naive set theory that constructs the real numbers, I'd recommend the first chapter of Amann Escher's analysis series. Don't spend too much time on foundations
For physics, I always liked Landau Lifshitz. Volumes 1-3 and 5 are must reads imo, 4 is subsumed by later QFT books like Weinberg. Also check out these lectures https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

what IQ do you have to stand a chance in doing a bachelors/Master/PhD degree in mathematics? im working on linear algebra at the moment and analysis I but its not my main subject. i just booked the course for fun but Lina is doing something to my mind i cant explain. the past 4 months i worked 5-6 times a week net 4-5 hours a day without a break. i jumpstarted from 0 to 100 workload. sometimes i get deep encoding fatigue but damn i love algebra.

>>16833126
>>16832694
use deepseek, you can compile code with shadertoy to visualize it (at least it tries to anyway)

does anyone know a good, quick resource to learn the basics about modules, tensor products, and fibred products? i'm going through the rising sea of algebraic geometry right now and the category section is whopping my ass, mostly because it's using these things that i have never worked with before

>>16836854
Roman's Advanced Linear Algebra has a ton of material on modules and a decent amount on tensors (if im remembering correctly, I'm sure about the modules but it's been a couple years since I've opened that book).

>>16836854
since other anon mentioned Rotman I'll point out that Introduction to Homological Algebra Chapter 2 has a great explanation of tensor products, as well as a QRD rundown on modules in general

>>16836854
>>16837205
Roman is pretty good. Lang's Algebra also touches on modules and the tensor product, it's worth checking out.

>>16835326
What happened to Mathchan?

>>16837205
>>16837212
>>16837427
thanks anons

>>16837680
I heard the guy running it wanted to do an entire redesign of the chan. Seems to have been procrastinating for months now though

Any Geometric Langlandsfag here who can explain how you cope with this insane notation? shit's giving me an aneurysm

>>16836378
>Doing math every day for over a year genuinely transforms your brain.
Yeah I'm advancing a lot (i'm the OP you answered)
>reading difficult books, analyzing proofs carefully until I've fully internalized the reasoning and could call them my own, and spending a lot of time on my own proofs (exercises, etc.)
i'm basically doing this otehr than my old notebooks I took a book of general Mathematics, it's in italian (i'm italian) it roughly translate to
>Let's know Mathematics: From the theories of the ancients to the logic of the computers of today
It explain math IG from the past to today and not in a historian way but a mathematician way and it's really interesting and even i'm learning a lot, even the intro of the book explain:
>Many people study math by the rules but never from the theory this book is for people who are studying in school in a rule way and not in a mathematician way.
And I noticed that's true that many don't know the basics.

>>16838280
>"THICK"
Lol. At this level of math, idk why they don't just go the CS route and use variables to represent the names of other objects. It just doesn't seem like good practice.

I would appreciate help filling in the blanks.

Say you got a list of smooth [math] g_i: S \rightarrow \mathbb{R} [/math], where the functions are made into constraints so now you got a space to do calculus on, so [math] X = \{\vec{x} \in S |\ g_i(\vec{x}) = 0 \} [/math]. For all smooth curve [math] \gamma: I \subset \mathbb{R} \rightarrow X [/math] then, we have [math] \vec{\nabla} g_i\big|_{\gamma(t)} \cdot \tfrac{d\vec{\gamma}}{dt}\big|_t = 0 [/math].
Let [math] f: S \rightarrow \mathbb{R} [/math] and we wish to find the point or (or set of points) [math] \gamma_0 [/math] that max/minimizes f restricted to X, so [math] \max/\min f|_X [/math] means finding all points [math] \gamma_0 \ \ \text{s.t.}\ \ \forall \gamma \ \ \text{where} \ \ \gamma(0) = \gamma_0,\ \ \text{then} \ \ \vec{\nabla} f\big|_{\gamma_0} \cdot \tfrac{d\vec{\gamma}}{dt}\big|_0 = 0 [/math]

If there's only 1 constraint making a surface, the simple rationale given next is that both normal vectors [math] \vec{\nabla} g\big|_{\gamma(0)} \ \ \text{and}\ \ \vec{\nabla} f\big|_{\gamma(0)} [/math] are perpendicular to ALL possible tangent vectors [math] \tfrac{d\vec{\gamma}}{dt}\big|_0 \ \ \text{at} \ \ \gamma_0 [/math], which is a tangent space plane, implying that the normal vectors are parallel, or [math] \vec{\nabla} f\big|_{\gamma(0)} = \lambda \vec{\nabla} g\big|_{\gamma(0)} [/math].
If there's 2 constraints g_1 and g_2 whose intersection is a smooth curve, the simple rationale is that the tangent space is only a 1 dim line, and since the 3 normal vectors are perp to it, they're coplanar, or [math] \vec{\nabla} f\big|_{\gamma(0)} = \lambda_1 \vec{\nabla} g_1\big|_{\gamma(0)} + \lambda_2 \vec{\nabla} g_2\big|_{\gamma(0)} [/math].

But what's the general rationale? Why does [math] 0 = Df\big|_{\gamma(0)} \dot\gamma|_0 = Dg_i\big|_{\gamma(0)} \dot\gamma|_0 [/math] where [math] \dot\gamma|_t \in \bigcap_i T(g_i) [/math] imply that [math] Df|_{\gamma(0)} = \sum \lambda_i Dg_i\big|_{\gamma(0)} [/math]?

>>16835273 (OP)
Hello everyone. I have a few questions for all of you. What kind of background do you have in mathematics? Do you do math on your own, as a recreational activity? Or are the posts here relevant to your employment?

>>16838280
The notation is well-known to be shit. But there aren't really any better options.

>>16838280
Filtered. Maybe webdev is more your speed.

>>16839202
see >>16840215

[math]\dfrac{x^n D^n}{n!}=\binom{xD}{n}[/math]

>>16840213
One thing would be to write C(-,-) instead of Hom_C(-,-) like some other cat theorists do. I just seriously dislike these concatenated sub-/superscripts

>>16840529
Well they don't necessarily mean the same thing. C(-,-) usually implies more than Hom_C(-,-). i.e. C(-,-) is typical notation for an internal hom

How do I achieve math wizard aura like Grothendieck

>>16841010
>>16841010
Start reading EGA, SGA, FGA. Or go for the Stacks project in case you can't read French