General math Definition and 20 Threads

https://www.quantamagazine.org/maze-proof-establishes-a-backbone-for-statistical-mechanics-20240207/

I would appreciate if someone could help me to understand what is happening in section 12.3 from the Howard George's book. First of all, the propose of the section is to show how $SU(3)$ decomposes into $SU(2) \times U(1)$. But i can't understand what is happening. First of all, i can't get the...

I want to calculate eccentric anomaly of all points of ellipse-circle intersection. Ellipse is not rotated and its center is in origin. Circle can be translated to (Cx, Cy) coordinates. I am using python for calculations. Only solution I found, is this...

Hi, PF There are two ways to write domain and range of a function: through set notation, or showing intervals. I've chosen the set notation, and, for ##y=\csc x##, this is the attempt: $$\text{D}:\{x\,|\,x\not\in{n\pi},\,n\not\in{\mathbb{Z}}\}$$ $$\text{R}:\{f(x)\,|\,x=\mathbb{R}\(-1,1)\}$$...

I'm playing a Steam game called Shapez wherein the goal is to produce and deliver given shapes to the Hub by conveyor belt. In the screencap you can see resources of discs and squares and well as green and red, which are to be extracted, chopped up and recombined to form the "product"...

TL;DR Summary: ##(1+ \frac1x)^2 - (1-\frac1x)^2## ##(z+2)^2 -5(z+2)## Upon simplifying the first I get ##\frac4x##. So isn’t the first expression fractional? Upon simplifying the second I get a Quadratic expression.

TL;DR Summary: How do you take notes for math? Hello, I'm wondering how everyone here takes notes for their math classes. In all my most recent math classes we just have a packet we work through that's a combination of problems that the teacher guides us through and that we do on our own for...

If we have two functions C(y(t), r(t)) and I(y(t), r(t)) can we write $$\frac{\frac{dC}{dt}}{\frac{dI}{dt}}=\frac{dC}{dI}$$?

Does anybody know any good books to learn math?

I have Abstract Algebra Course, and my teacher is using the book, "Abstract Algebra" of David S. Dummit, and Richard M.Foote. This book, and other books which my teachers are using for the courses, seem to give definitions, theorems, and problems, in no historical order or are not mentioning the...

Hi, i have this problem..., giving two circle (example radius 1 = 500 units, radius 2 = 200 units, distance between centers = 275.73 units) find Euler Spiral (aka Cornu spiral, aka Clothoid https://en.wikipedia.org/wiki/Euler_spiral) tangent giving circle (unknown tangent points). For this...

I need help to convert 2 variables A,B into 1 representative variable C, which is used to filter A,B: Below is an example with C=A+B, which makes Set 2 the highest value: Set 1: A=65, B=75, C=140; Set 2: A=50, B=100, C=150; Set 3: A=54, B=90, C=144; Set 4: A=72, B=72, C=144; Set 5: A=71, B=73...

Is it true that if you have a good understanding of proof based math courses( like Real Analysis), courses based in computations( like Calculus) become relatively trivial ? And I have another doubt. Do I need to know Real Analysis to formulate Calculus problems and exercises ? Or, is a rigorous...

Let f and g be twice differentiable real-valued functions. If f'(x) > g'(x) for all values of x, which of the following statements must be true? A) f(x) > g(x) B) f''(x) > g''(x) C) f(x) - f(0) > g(x) - g(0) D) f'(x) - f'(0) > g'(x) - g'(0) E) f''(x) - f''(0) > g''(x) - g''(0) The correct...

the question statement is2. In a course, a student's final exam is weighted twice as heavily as his midterm exam. If a student receives a score of 84 on his final exam , 90 on his midterm, what is the average for his courses? now i am pretty confused should I have to know the total marks for...

Homework Statement Homework Equations The Attempt at a SolutionHi, so this is just a general question about how math homework should be submitted. I seem to change between formats, and I'd like to finally get an answer on how I should be doing things.Say I'm working on a problem with a formula...

General Math "Light" Reading Was wondering if anybody would like to recommend or just discuss any general books you may know about concerning math in general, be it historical, biographical or some of the other general works that are out there. I'm curious about what I keep seeing in the...

looking at the quantum mechanical harmonic oscillator, one has the differential equation in the form: \frac{d^2\psi}{du^2}+(\alpha-u^2)\psi=0 when a person who doesn't know any physics sees the equation, he will try a serial solution for psi, and he will find a solution with some recursive...

Can anyone recommend a good book for me to review general math such as fractions, decimals, percenttages, and division etc.. those are my weakest points in math, and I would like to strenghten them a bit.

Do you all know of any great books that focus on general math? I'd like to begin reading voraciously into mathematics and such so what are they? The only one I can think of is Euclid's "The Elements".