Algebra Definition and 999 Threads

Homework Statement Hi I am having trouble solving for y for the following equation: e^(y) = y^(2) - 2 Homework Equations ln(x)^(y) = y*ln(x) ln(e^(y)) = y ln(2) = 1 The Attempt at a Solution My attempt: e^(y) = y^(2) -2 ln(e^(y)) = ln(y^(2)) - ln(2) y = 2*ln(y) - 1 y - 2*ln(y) + 1 = 0...

Hi, I'm currently having trouble getting past Algebra 2 at my college. I got local credit in Algebra 2 in high school. My current college major is Chemistry with an emphasis on materials science/engineering. I obviously need Calculus 3 and differential equations and my ultimate roadblock is...

Hello, I've been working through some Digital Signal Processing stuff by myself online, and I saw a system that I wanted to write down as a Linear Algebra Equation. It's a simple delay feedback loop, looks like this: The (+) is an adder that adds 2 signals together, so the signal from x[n]...

One of the last classes I'm taking before finishing my degrees as an undergraduate is abstract algebra. My professor uses the textbook 'Contemporary Abstract Algebra' by Joseph Gallian. The book isn't written terribly nor is the teacher a poor one, but I just find this subject so...

I'm just getting into 3D quantum mechanics in my class, as in the hydrogen atom, particle in a box etc. But we have already been thoroughly acquainted with 1D systems, spin-1/2, dirac notation, etc. I am trying to understand some of the subtleties of moving to 3D. In particular, for any...

Homework Statement Not for homework, but just for understanding. So we know that if a matrix (M) is orthogonal, then its transpose is its inverse. Using that knowledge for a diagonalised matrix (with eigenvalues), its column vectors are all mutually orthogonal and thus you would assume that...

Homework Statement >Find the sum of the roots, real and non-real, of the equation x^{2001}+\left(\frac 12-x\right)^{2001}=0, given that there are no multiple roots. While trying to solve the above problem (AIME 2001, Problem 3), I came across three solutions on...

Hi, my name is "Bob" I have a particular question about a specific book. Preface... It has been a while since I formally studied Physics. The type of Physics book I remember using last was I believe, Algebra-based. This was in high school. Based on my degree, I studied Algebra and Trigonometry...

Hi. I am working on the quantum harmonic oscillator Schrodinger's equation and need help with the algebra or whatever it is I am missing. Here are the 2 steps I can't understand: d^2psi/dx^2 + (2mE/h^2 - m^2w^2/h^2 * x^2)psi = 0 You substitute this into it: y = sqrt(mw/h)*x I...

Homework Statement The period of oscillation of a nonlinear oscillator depends on the mass m, with dimensions M; a restoring force constant k with dimensions of ML-2T-2, and the Amplitude A, with dimensions L. Use dimensional analysis to show what the period of oscillation would be proportional...

Homework Statement I for some reason can't seem do become sure of this. There are 2 variables x and y. And two constants, a and c, which are both positive. Homework Equations x+2y ≤ (3/4)*(a^2/c) x + 2y < a The Attempt at a Solution Does this mean that: (3/4)*(a^2/c) < a ? Mons

The theorem that allows one to distribute the limit over addition is the following: Let ##(a_n), (b_n)## be sequences that converge to ##L## and ##M## respectively. Then ##\lim (a_n+b_n) = L + M##. So evidently, a hypothesis of distributing the limit is that we know ##a_n## and ##b_n##...

I’m in an honors calc-based physics 1 course at my college and I can’t audibly understand my professor. I tried looking for tutorials online, but I have no idea if what I’m looking at is calc-based physics or alg-based physics, and I don’t want to learn the wrong methods. Is there a difference...

I was just doing a homework problem that involved logarithms. I noticed that order of operations matters when applying logarithm rules. I'll use a different example from my homework problem to illustrate what I'm talking about. ln(5*2^3) does not equal 3*(ln(5*2)) Apparently you have to do...

Is there any simplest way to learn algebra?

Homework Statement Find y; $$y=\lim_{x \rightarrow 0} {\frac {1} {x^2}-\frac{1}{tan^2(x)}}$$ Homework Equations $$\lim_{x \rightarrow 0} {\frac{tan(x)}x}=1$$ $$\lim_{x \rightarrow 0} {\frac{sin(x)}x}=1$$ The Attempt at a Solution \begin{align} y & = \lim_{x \rightarrow 0} {\frac {1}...

In Arnold's book, ordinary differential equations 3rd. WHY Arnold say Tg:M→M instead of Tg:G→S(M) for transformations Tfg=Tf Tg, Tg^-1=(Tg)^-1. Let M be a group and M a set. We say that an action of the group G on the set M is defined if to each element g of G there corresponds a...

Hi I'm trying to solve; t / 2t-s = 3s for t the answer I get is; t = -3s^2/1-6s. However, the answer given is; 3s^2/6s-1 The steps I use are; t = 3s(2t - s) t = 6st - 3s^2 t - 6st = -3s^2 t(1 - 6s) = -3s^2 t = 3s^2 / 1 - 6s If someone could point out where I'm going wrong that would be...

Hello, Having a lapse in memory how was this 1) changed into 2) algebraically 1) du=-30x^2dx 2) x^2 dx = -(1/30)du thank you for any help.

hi everyone, I'm electrical engineer student and i like a lot arnold's book of ordinary differential equations (3rd), but i have a gap about how defines action group for a group and from an element of the group.For example Artin's algebra book get another definition also Vinberg's algebra book...

I'm a physics student who has the option to take some advanced math courses (Real analysis through Rudin and beyond, functional analysis if I have time, as well as algebra through Artin). I'm only just going into my second year this term, and will either be retaking linear algebra 2, or taking...

I want to get a copy of historical Algebra literature that essentially the equivalent of Euclid’s Elements for Algebra. Does anyone have any recommendations?

I would like to see a College Algebra forum. It is a course at Lehman College that gives students lots of trouble. At Lehman, the course is known as MA104.

Homework Statement Suppose that AB = 0, where A is a 3 x 7 full rank matrix and B is 7 x 53. What is the highest possible rank of matrix B. Homework EquationsThe Attempt at a Solution Since each column of B is in the null space of A, the rank of B is at most 4. I don't understand why it is...

I'm teaching myself some algebra using Paul's Online Math Notes. I've been doing very well, (I understand the concepts, and I do well on Practice/Assignment Problems) but I would like to know how long it will be until I get to Calculus I? What are the hardest concepts to grasp when learning this...

Hi, I’m going to be entering my first year of University this fall to study physics. In my second semester I will have to take a linear algebra course; however, my school has two different lower level linear algebra courses, and I must choose one. One course is focused more on applications of...

Hey, I found an interesting algebra problem combined with log. It was quite an unique one so I wanted to share it with you guys. Problem: There is a city where the population increases at a constant rate. At the end of 2016, the population of the city was 2 times larger than the population...

I am reading The Basics of Abstract Algebra by Paul E. Bland ... I am focused on Section 3.2 Subrings, Ideals and Factor Rings ... ... I need help with another aspect of the proof of Theorem 3.2.19 ... ... Theorem 3.2.19 and its proof reads as follows...

After seeing so much higher-level physics and proofing for special relativity, I imagine I'll need to take this at some point to continue do grad-level physics. I'm taking calc III at the start of year two, and then on to diff eq. When should I take linear algebra in that case? My adviser seemed...

Homework Statement In the follow cases find a maximal linearly independent subset of set ##A##: (a) ##A = \{(1,0,1,0),(1,1,1,1),(0,1,0,1),(2,0,-1,)\} \in \mathbb{R}^4## (b) ##A = \{x^2, x^2-x+1, 2x-2, 3\} \in \mathbb{k}[x]## The Attempt at a Solution The first part of the exercise is...

Homework Statement Let ##V## and ##W## be vector spaces, ##T : V \rightarrow W## a linear transformation and ##B \subset Im(T)## a subspace. (a) Prove that ##A = T^{-1}(B)## is the only subspace of ##V## such that ##Ker(T) \subseteq A## and ##T(A) = B## (b) Let ##C \subseteq V## be a...

Homework Statement a) Let ##D_n(\mathbb{k}) = \{A \in M_n(\mathbb{k}) : a_{ij} = 0 \iff i \neq j\}## Prove that ## D_n(\mathbb{k}) \cong \mathbb{k}^n ## b) Prove that ##\mathbb{k}[X]_n \cong \mathbb{k}^{n+1}## I have one other exercise, but I would like to resolve it on my own. However, an...

Homework Statement [/B] Homework Equations The Attempt at a Solution [/B] I am not sure if this is the correct way of finding the difference between two vectors. I thought that if "B" was negative then it's direction would change as well as it's angle. If the angle changes then are my...

Homework Statement Homework Statement (a) Let ##V## be an ##\mathbb R##-vector space and ##j : V \rightarrow V## a linear transformation such that ##j \circ j = id_V##. Now, let ##S = \{v \in V : j(v) = v\}## and ##A = \{v \in V : j(v) = -v\}## Prove that ##S## and ##A## are subspaces and...

Homework Statement 1. (a) Prove that the following is a linear transformation: ##\text{T} : \mathbb k[X]_n \rightarrow \mathbb k[X]_{n+1}## ##\text{T}(a_0 + a_1X + \ldots + a_nX^n) = a_0X + \frac{a_1}{2}X^2 + \ldots + \frac{a_n}{n+1}## ##\text{Find}## ##\text{Ker}(T)## and ##\text{Im}(T)##...

Hello, One of my children is switching to a new school system next year, and I was surprised to find that they cover subjects such as fractional exponents, exponential functions, rational functions and perhaps other topics as part of algebra 1. Their book has "common core" in the title, if that...

Homework Statement Prove whether or not the following linear transformations are, in fact, linear. Find their kernel and range. a) ## T : ℝ → ℝ^2, T(x) = (x,x)## b) ##T : ℝ^3 → ℝ^2, T(x,y,z) = (y-x,z+y)## c) ##T : ℝ^3 → ℝ^3, T(x,y,z) = (x^2, x, z-x) ## d) ## T: C[a,b] → ℝ, T(f) = f(a)## e) ##...

Will be taking my first abstract algebra course in the fall. I am going through Pinter's:A Book On Abstract Algebra. Pinter is very simple, but the ideas are lucid and gives great motivation. I am familiar with proof writing. I can read books such as Axler LA, Shilov Analysis, and Courant...

⇒Homework Statement [/B] Calculate ##S + T## and determine if the sum is direct for the following subspaces of ##\mathbf R^3## a) ## S = \{(x,y,z) \in \mathbf R^3 : x =z\}## ## T = \{(x,y,z) \in R^3 : z = 0\}## b) ## S = \{(x,y,z) \in \mathbf R^3 : x = y\}## ## T = \{(x,y,z) \in \mathbf R^3 ...

Homework Statement Let ##V## be the vector space of the sequences which take real values. Prove whether or not the following subsets ##W \in V## are subspaces of ##(V, +, \cdot)## a) ## W = \{(a_n) \in V : \sum_{n=1}^\infty |a_n| < \infty\} ## b) ## W = \{(a_n) \in V : \lim_{n\to \infty} a_n...

Hello to everyone who's reading this. The problem I need help with is the following.: Homework Statement "Simplify to obtain minimum SOP. F(A, B, C, D) = A’B’CD’+AC’D’+ABC’+AB’C+AB’C+BC’D" The problem stated above has two provided solutions, the "main" one and the "alternate" one. I'm...

Hello members of PF, my name is Reid Honeycutt. I am a mathematics major at American River College, Sacramento. My mathematical interests are primarily in the areas of algebra and logic. I also love physics and materials science, economics, and programming in python. My motivation in joining...

I wanted to go through Calculus and then Linear Algebra following either of two paths: a) Keisler's Infinitesmal approach>>>Nitecki Deconstructing Calculus>>>Nitecki Calculus in 3D>>>Freidberg's Linear Algebra OR b) Simmons Calculus with analytic geometry>>>Apostol Vol 1>>>>Apostol Vol...

Dear Fellows, I have recently completed the study of Stewart's calculus. Next, I want to read Linear Algebra. I have bought Sheldon Axler's "Linear Algebra done right" textbook. I want to know if my knowledge of calculus is enough to tackle this book or should I first...

Homework Statement Find the distance from point P (1,7,3) to the line (x,y,z) = (-2,1,4) + s(1,-3,4), s is a free variable Homework Equations projnQP = ( QP⋅n/(lengthQP)(lengthn) )(n) The Attempt at a Solution I'm not quite sure about how to find the normal (n) here, but if I make s=0, I'm...

Homework Statement Find the cosine of the angle determined by the intersecting lines m1: (x,y,z) = (-2,1,4)+s(1,-3,4) m2: (x,y,z) = (-2,1,4)+t(-2,3,2) s and t are free variables Homework Equations a⋅b = length(a)length(b) cosθ The Attempt at a Solution I just did this equation using no...

Homework Statement Let A and B be nxn matrices with Eigen values λ and μ, respectively. a) Give an example to show that λ+μ doesn't have to be an Eigen value of A+B b) Give an example to show that λμ doesn't have to be an Eigen value of AB Homework Equations det(λI - A)=0 The Attempt at a...

Homework Statement From Linear Algebra and Its Applications, 5th Edition, David Lay Chapter 4, Section 1, Question 32 Let H and K be subspaces of a vector space V. The intersection of H and K is the set of v in V that belong to both H and K. Show that H ∩ K is a subspace of V. (See figure.)...

Homework Statement Solve the modular equation x2 + 8x ≡ 0 (mod 56) Homework Equations Let a, b = integer n|(a - b), written as a ≡ b (mod n) The Attempt at a Solution I tried to separate them, and got 2|x2 + 8x or x2 + 8x ≡ 0 (mod 2) as well as 7|x2 + 8x or x2 + 8x ≡ 0 (mod 7) but I'm a bit...

1. Homework Statement You’re testing the effect of a noxious substance on bacteria. Every 10 minutes, one-tenth of the bacteria which are still alive are killed. If the population of bacteria starts with 10^6, within which period of 10 minutes will 70% of the bacteria be killed? Homework...