Algebra Definition and 999 Threads

There is a movie out--"Hidden Figures"--about how three women launched the space program; or something like that. My daughter wants to write about them for a school project. I keep suggesting my daughter write about Sophie Germain, or Emmy Noether, Daubechies or Hypatia. But my daughter...

Homework Statement http://prntscr.com/eqhh2p http://prntscr.com/eqhhcg Homework EquationsThe Attempt at a Solution I don't even know what these are, it is not outlined in my textbook. I'm assuming I am is image? But how do you calculate image even? As far as I'm concerned I am has to do wtih...

Homework Statement I can't understand how abstract aljebra helps in creating graphical patterns. I don't find eq related to Groups. Do we consider predefined structures [/B] Homework Equations No equation only patterns. one pattern is attached The Attempt at a Solution I don't know how it...

A little background first: As my https://www.physicsforums.com/members/usablethought.611113/ explains, I'm a retired writer/editor, never good at math as a kid but always fascinated by physics, who has decided to take a long, slow, pleasurable road toward learning the necessary math to get to at...

Hello everyone, After about 6 years I'm finally getting out of the military in May and start going to school full time starting in the fall. I want to do engineering, but I know I'm behind in math and am worried about starting calculus. I want to improve my math by taking both College Algebra...

Homework Statement Hello there physicsforums, I have a problem that I'd like feedback on as I'm not sure if I had solved it or approached it correctly. A ball that is traveling 5m/s is 30 meters above a person who is standing still. How fast must the person travel in order to catch the ball...

https://www.physicsforums.com/threads/discriminant-of-cubic-equation-in-terms-of-coefficients.715480 The thread is really old and didn't want to post this trivial question in there. The problem is: A cubic equation x³ + px² + qx + r = 0 has three different roots x1, x2, x3. Find...

Homework Statement Let ##S = \{\frac{1}{n} + \mathbb{Z} ~|~ n \in \mathbb{N} \}##. I am trying to show that ##f : \mathbb{N} \rightarrow S## defined by ##f(n) = \frac{1}{n} + \mathbb{Z}## is a bijection. Surjectivity is trivial, but injectivity is a little more involved. Homework EquationsThe...

1. The problem statement, all variables and given/known If each element of a group, G, has order which is a power of p, then the order of G is also a prime power. Homework EquationsThe Attempt at a Solution I am not sure really where to get started. I know that the class equation will be used...

I am investigating the mathematical properties of a vector-product. I am wondering if it might be old-hat in GA (which is new to me)? I am using the working-title "spin-product" for a vector-product that combines RANDOM rotation-only of a direction-vector [a unit 1-vector; say...

I am just curious about this. Must one of these be taught before the other, or does the order not really matter? Should a student be taught beginning computer programming AFTER being taught introductory algebra 1? Or can the reverse order be done? My guess is that learning Algebra 1 first is...

NO TEMPLATE BECAUSE SUBMITTED TO NON-HOMEWORK FORUM I'm stuck on substituting the following (where gamma is the specific heat ratio): W=(P1v1 - P2v2) / (gamma-1) P1v1^gamma = P2v2^gamma substituting for v2... <= this is where I get stuck... W = [(P1v1) / (gamma-1)] * [(P2 /...

I'm in a bit of a dilemma. At my university, Calc 2 is a prerequisite to Linear Algebra. However, I have been told that it's totally doable to take both at the same time. What do you guys think? Do most universities wave this requirement if you take them concurrently? Thanks!

I am looking for an accessible textbook in group theory. The idea here is to use it to learn basic group theory in order to take up Galois Theory. My background includes Calculus I-IV, P/Differential Equations, Discrete Mathematics including some graph theory, Linear algebra, and am currently...

Hi guys, Am I totally lost if I am searching for help in financial engineering here- I have been struggling with a question for way too long now. Thanks,

Hi, I'm trying to get a deeper understanding of some concepts required for my next semesters but, sadly, I've found there are lots of things that are quite similar to me and they are called with different names in multiple fields of mathematics so I'm getting confused rapidly and I'd appreciate...

Not sure how to start this one: Yolanda invests \$6000. Some of the money is invested in stocks paying 6% a year and some in bonds paying 11% per year. She receives a total of \$580 each year from these investments. How much money is invested in stocks and how much money in bonds?

Next year, I want to take AP Physics 1 but I am worried that it would be confusing since I would still be learning about Algebra 2. Is it recommended to do this?

The problem states that the wavelength and frequency in a waveguide are related by: ##\lambda = \frac{c}{\sqrt{f^2 - f_0^2}}## then asks to express the group velocity ##v_g## in terms of c and the phase velocity ##v_p = \lambda f## Solution: Given that ##\omega = 2\pi f##, ## \omega(k) =...

Hey everyone, I'm currently studying A Course in Algebra by E.B. Vinberg, and I was wondering if anyone is studying the same book. I think it will be a less lonely journey for all of us self learners if we can form a book study group to discuss ideas and exercises.

Homework Statement Find the coordinates of each member of set S relative to B. B = {1, cos(x), cos2(x), cos3(x), cos4(x), cos5(x)} S = {1, cos(x), cos(2x), cos(3x), cos(4x), cos(5x)} I am to do this using Mathematica software. Each spanning equation will need to be sampled at six separate...

Dear teachers, I am curious if you know some good books that have problems well supplemented to "Commutative Algebra I-II" by Zariski/Samuel. I am really enjoying it, but it does not have any exercise, leaving me to try coming up with my own problems (it is fun to do, but I would like to solve...

The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

http://imgur.com/a/xIydC The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

I am taking a linear algebra class, and it has a required lab associated with it. Here is the following problem that I must solve using Matlab 1. Homework Statement Write a function using row reduction to find the inverse for any given 2x2 matrix. Name your function your initial + inv(M), the...

Dear Physics Forum advisers, I am very interested in studying the art of algebraic geometry, motivated by its applications in the machine learning and data analytics. I recently came across Grothendieck's EGA/SGA/FGA saga, and I am really interested in reading it as I like how it presents the...

By space, I mean a vector space which could be a representation of a group or even have some expanded algebraic structure. So I am not sure if this question goes here or in the Algebra subforum. Consider the tensor square r\otimes r of an irreducible group representation r with itself, and...

Homework Statement The group ##G = \{ a\in M_n (C) | aSa^{\dagger} =S\}## is a Lie group where ##S\in M_n (C)##. Find the corresponding Lie algebra. Homework EquationsThe Attempt at a Solution As far as I've been told the way to find these things is to set ##a = exp(tA)##, so...

Homework Statement Show the (real) dimension of su(n) is ##n^2-1##. Homework EquationsThe Attempt at a Solution ##su(n) = \{ A \in M_n(\mathbb{C}) | A+A^T = 0, tr(A) =0 \}## Maybe the solution is obvious, because I can't find a thing online about how to do this. But I can't see how to do it! I...

Homework Statement Hi I am stuck on a small algebra set in the weak limit theorem to recover Newtonian equations The text I am looking at: ##\frac{d^2x^i}{ds^2}+\Gamma^i_{tt}\frac{dt}{ds}\frac{dt}{ds}=0## (1) ##\Gamma^{i}_{tt}=-1/2 \eta^{ij}\partial_{j}h_{tt} ## (to first oder in the...

Homework Statement Sonia walks up an escalator which is going up. When she walks at one step per second, it takes her 20 steps to get to the top. If she walks at two steps per second, it takes her 32 steps to get to the top. She never skips over any steps. How many steps does the escalator...

given P(-1,1,2), Q(-3,0,4), R(3,2,1), find an equation of the line through P that is parallel to the line through Q and R. All the words after the given three points really confuse me and I just need some help on where to start to tackle this problem. Thanks

Before I go any further, I do understand the ways that mechanical engineering textbooks explain why stress is a tensor. But all of those explanations seem infused with geometry (which I do NOT mean in a negative way at all); and are demonsrtrations. I am searching for a more concise/abstract...

Homework Statement Homework Equations N/A The Attempt at a Solution I proved the first part of the question (first quote) and got stuck in the second (second quote). I defined Im(E1) as U and Im(E2) as W and proved that v=u+w where v ∈ V, u ∈ U and w ∈ W. After that however I got stuck at...

For the expression: (B and C) or (not B and not C) or (A and (not B) and not C) I get two different answers depending on the order I do the simplification. 1. If I factor C out of the first and third terms I get (B and C) or (A and C) or (not B and not C) 2. If I factor not B out of the...

I am currently brushing on my linear algebra skills when i read this For any Matrix A 1)A*At is symmetric , where At is A transpose ( sorry I tried using the super script option given in the editor and i couldn't figure it out ) 2)(A + At)/2 is symmetric Now my question is , why should it be...

Homework Statement Algebra I.M. Gelfand, problem 134. You know that x+1/x is an integer. Prove that xn+1/xn is an integer for any n = 1, 2, 3, etc. Homework EquationsThe Attempt at a Solution I don't fully understand how the induction below proves anything. (Source) I did attempt the solution...

Homework Statement Show that elementary row operations don't affect solutions sets in linear systems Homework Equations - The Attempt at a Solution It's pretty easy to come up with a random linear system and perform ERO on them and showing that solutions are not affected, but is there all...

Homework Statement Solve each equation for z=a+ib z^{*2}=4z where z* is the complex conjugate The Attempt at a Solution I wrote z and z* in terms of x and iy , and tried solving for x and y, but I get quartic terms for y, it doesn't look like it will boil down, It was like over 2 pages of...

Homework Statement I.M. Gelfand - Algebra: Problem 133. You know that $${x+\frac{1}{x}=7}$$ Compute (a) $$x^2+\frac{1}{x^2}$$ and (b) $$x^3+\frac{1}{x^3}$$ Homework Equations None The Attempt at a Solution I tried solving for x, and then substituting x. But that doesn't produce the correct...

Homework Statement Fractions ##\frac{a}{b}## and ##\frac{c}{d}## are called neighbor fractions if their difference ##\frac{ad - bc}{bd}## has numerator ##\pm 1##, that is, ##ad - bc = \pm 1##. Prove that: (a) in this case neither fraction can be simplified (that is, neither has any common...

Homework Statement Prove that if a² + ab + b² = 0 then a = 0 and b = 0 Hint: Recall the factorization of a³-b³. (Another solution will be discussed later when speaking about quadratic equations.) Homework Equations a² + ab + b² is close to a² + 2ab + b² = (a+b)² a³-b³=(a-b)(a²+ab+b²) The...

This isn't really a homework question, I just need help understanding the example: ===================== ==================== So transformation takes complex n-tuple as input, and it seems output is also a complex n-tuple (which is what makes it "operator"). But permutations of n entries is...

Hi! I'm studying Lie Algebras and Lie Groups. I'm using Brian Hall's book, which focuses on matrix lie groups for a start, and I'm loving it. However, I'm really having a hard time connecting what he does with what physicists do (which I never really understood)... Here goes one of my questions...

Please see attached. I am trying to show that ## T_{p} f (\tau + 1) = T_{p} f (\tau ) ## ##f(\tau) \in M_k ## and so can be written as a expansion as ##f(\tau)=\sum\limits^{\infty}_{0}a_{n}e^{2 \pi i n \tau } ## ##f(\tau + 1) = f(\tau) ## since ##e^{2\pi i n} = 1## Similarly ##f(p\tau + p) =...

Hi all, I'm reading a paragraph from "Geometric Algebra for Physicists" - Chris Doran, Anthony Lasenby. I'm quite interested in applying GA to QM but I've got to a stage where I am not following part of the chapter and am wondering if someone can shed a little light for me. The part...

I'm currently working through the book Algebra by I.M. Gelfand and A. Shen on my own. (As advised here: https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/#toggle-id-1) This isn't really homework so I wasn't quite sure where to post this. Anyway, I've got a question...

I am planning to self-teach myself Trigonometry and all the other required fields before jumping into calculus. I have compiled a list of books that I have researched and would like your opinions and recommendations. Books: Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry...

Homework Statement I have been going through a textbook trying to solve some of of these with somewhat formal proofs. This is a former Putnam exam question. (Seemingly the easiest one I have attempted, which worries me). Consider a polynomial function ƒ with real coefficients having the...

Hi guys, there's a sample problem in m textbook where they simplify an expression from x3-6x2+12x-8/x2-4x+4 to (x-2)3/(x-2)2. Can you explain how they solved this? For reference, I'm learning about limits