#Algebraic Operations

[9nid]

📘 Algebraic Operations on Complex Numbers – Class 11 Maths | Complete Guide by 9nid & IITKiTayyari

If you’re a Class 11 student or preparing for IIT-JEE or competitive exams, mastering complex numbers is essential. In this post, we’ll break down algebraic operations on complex numbers — one of the most foundational topics in higher mathematics. This blog is based on our latest YouTube video from the 9nid and IITKiTayyari YouTube channels. You can watch the full lecture for visual…

[edusquaremaths]

📘 Algebraic Operations on Complex Numbers – Class 11 Maths | Complete Guide by 9nid & IITKiTayyari

If you’re a Class 11 student or preparing for IIT-JEE or competitive exams, mastering complex numbers is essential. In this post, we’ll break down algebraic operations on complex numbers — one of the most foundational topics in higher mathematics. This blog is based on our latest YouTube video from the 9nid and IITKiTayyari YouTube channels. You can watch the full lecture for visual…

[minmin-vs-physics]

Time-Energy Uncertainty Principle

This derivation is lovingly taken from my intermediate quantum mechanics prof's lectures. But, I think it's a standard treatment of the subject. I apologize that it's not as accessible as my previous post, but I hope to make a follow-up post to explain my thoughts on this derivation and other approaches to the theory.

Please yell at me if I got sloppy or was just plain wrong lmao

[floralfractals]

Oh btw I didn't update you guys about my new thesis project: I'll be working on quantum measurements and the metaphors surrounding them

[locally-normal]

Ok so suppose you have a torsion free group, G. That is, there's no g such that g^n=e the identity. That's fine right.

Now take a field, k, of characteristic 0, so something like the rationals, reals, complex numbers, that sort of thing.

We can form the group ring k[G], by saying the elements are of the form k_1g_1 + ... + k_ng_n where k_i are in the field and g_n are in the group. Essentially these are like polynomials in as many variables as there are elements of the group. Add an multiply like polynomials, except, when you multiply, you also do the multiplication in the group.

This sort of thing comes up a bunch in representation theory, they're well studied objects.

In general, it's not known that these have no zero divisors. That is, are there elements f,g of the group ring such that fg=0? Which is fucked up imo. It sounds obvious that they shouldn't have zero divisors like where would they come from. And yet.

[then-ponder]

Time to start a wrestle with the mathematicians

[22ums115]

Mathematics in Daily life and Basic concept

[math-cult-novel]

just saw a post about manipulation and the first thiing that came to my mind was manipulating a set mathematically

the plan is working

[bubbloquacious]

You can define the ring of integers as the set of group endomorphisms of the free abelian group on one point (the infinite cyclic group, i.e. the integers under addition) under pointwise addition and composition of morphisms. This works for any category with free objects and morphism objects. The reason you can identify the set of endomorphisms with the original set of elements is exactly the universal property of the free object on one point: a morphism is uniquely determined by its action on the generator. It happens that rings are monoid objects in the category of abelian groups (but not in the category of all groups!), so for which monoidal closed categories (monoidal to define monoid objects, closed to define morphism objects) with free objects does this endomorphism construction give you a monoid object?

[irregodless]

i do have a question about the math post

do you not multiply into the parentheses first

so instead of 5(2+3) 5(5) 25

its

5(2+3) (10+15) 25

i mean it comes out the same for addition but say if there was multiplication inside the parentheses you multiply everything in there by the first number first right

otherwise it would be written as (2+3)*5

[alexythimya]

once again thinking about the teacher who apparently told last years advanced 7th grade that they were doing 9th/10th grade math and also told them that when they were solving equations eg x + 3 = 10 that they could do the algebraic manipulation if they wanted to but they didn't need to if they just knew which is. such bad practice like we love building habits we love communicating what we're doing

thus making me have a conversation with a now 8th grader, probably still in advanced math, who was visiting us where i asked him to show his work and not only did he not know what i meant but he then tried to be like oh like 7 + 3 = 10? do you mean that? like even the advanced kids are being left to flounder

[a9saga]

Programming is boring.

[danielleurbansblog]

Review: Everything You Need to Know to Ace Pre-Algebra and Algebra I

Synopsis: Millions and millions of BIG FAT NOTEBOOKS sold! Pre-Algebra & Algebra 1? No Problem! The BIG FAT NOTEBOOK covers everything you need to know during a year of Pre-Algebra and Algebra 1 class, breaking down one big fat subject into accessible units. The number system, ratios, and proportions, scientific notation, introduction and equations, functions, graphing a line, square roots and…

[floralfractals]

@whale-in-that-case YOU ACTIVATED MY TRAP CARD I LOVE LINEAR ALGEBRA

i could write an actual book about linear algebra so instead ill let you choose which chapter infodump i should give

free module endomorphisms (i.e. matrices except they dont have to be over a field)

cayley-hamilton theorem and standard forms of matrices (eigendecomposition, and when that doesnt work, and what to do then)

random matrices (the entries are randomly distributed, what do the eigenvalues look like)

linear analysis (infinite dimensional linear algebra, their applications in advanced theoretical mathematics)

One thing about me is I infodump about math subjects on request

[math-journal]

Inverse Function Operations

[more-mathematics-mor-lam]

Stop asking, it’s never happening