Algebra Definition and 999 Threads

Hey y'all! I am taking my first linear algebra course next semester and we are using Bretscher's book. I have heard some pretty awful things about the way it is laid out, so I would like to hear your thoughts on the text. For some background information I have completed Calculus 1-3 (using...

What would be a good way to prepare for a final linear algebra exam (vectors, planes, matrices) where every question is asking for a proof? Thanks

I am a Physics major looking into Mathematical Biology (perhaps) in the future, and regardless of where I go, I'm trying to build a solid math background for myself. I've taken (or plan to take): Linear Algebra I Calculus I, II, III, IV ODE Non-linear ODE PDE Complex Variables (I will...

I was wondering about the following Λ=I+iT T are the generators and Λ a continuous LT transformation, thus it is real. Therefore T needs to be imaginary. And we can find two sets one being the generators for SO(3) J_i and the other for boosts K_i, which are both imaginary. Now I am wondering...

I'm reading Alvarez-Gaume review on Seiberg-Witten theory: http://arxiv.org/abs/hep-th/9701069. Around page 23 you can find the following claim: "This is a Clifford algebra with 2N generators and has a 2N-dimensional representation. From the point of view of the angular momentum algebra, a^I...

Homework Statement In an experiment to study a black body radiator, the intensity of emitted radiation is measured as a function of the wavelength of the radiation. At a particular temperature T1 the wavelength of the highest intensity radiation is determined to be λ1. When the temperature is...

Is the following correct? We begin with a set. Then, we specify a certain collection of subsets and thereby create a topology. This endows the set with certain properties, one of which is “nearness” and “boundedness.” Then we specify that the topology be smooth. In so doing, our topology...

Dear Physics Forum advisers, I am a college sophomore in US with a major in mathematics, and an aspiring algebraic number theorist and cryptographer. I wrote this email to seek your advice about taking the Analysis I (Real Analysis I), Abstract Algebra I, and Linear Algebra with Proofs. At...

Dear Physics Forum personnel, I am a college sophomore in U.S. with a major in mathematics and an aspiring algebraic number theorist. I wrote this email to seek a recommendation on one or two outstanding linear algebra textbook that can supplement the Linear Algebra (Friedberg et al.), which...

I'm trying to understand something in my notes here... So if we call the real part of the complex algebra 'even' and the imaginary part 'odd' then this graded algebra is communitive but NOT graded commutative. so ab = ba for all a and b in C. If we call the whole complex algebra 'even' and...

Hey guys, I'm hoping to get some advice on how to approach this course I'm currently enrolled in. I'm currently enrolled in linear algebra 1, while I think they're pretty generic for outlines, this is what my school says: Before the midterm I was doing the assignments and, for the most part...

Homework Statement T(a0 + a1t+a2t2) = 3a0 + (5a0 - 2a1)t + (4a1 + a2)t2 Find the image of the vectors : 1. 1 2. t 3. t2 Homework Equations T(a0 + a1t+a2t2) = 3a0 + (5a0 - 2a1)t + (4a1 + a2)t2 The Attempt at a Solution I don't know how my book solves these transformations, but the answers are...

Question: At what angles must be the two forces ##\vec A+\vec B## and ##\vec A-\vec B## act so that the resultant may be : $$\sqrt{ A^2+B^2}$$ Attempt at solution : Let the given forces be ##\vec F_1=\vec A+\vec B## and ##\vec F_2=\vec A-\vec B## . Now, Resultant vector : ##\vec F_1 + \vec...

Do you have very hard problems about work? I referred to my algebra book and googled in vain. Not talking about the product of the force magnitude and the displacement magnitude. This is what I’m talking about – Jennifer takes 4 hours to do a job. John takes 6 hours to do the same job. Working...

Dear friends! I am interested to study quantum physics at deep level.For that I think I should be well versed with many mathematical tools.Though I have some knowledge of algebra up to Galois Theory and some more related topics of commutative algebra. I am a mathematics teacher(more a student...

(Again, I am sorry for the simplicity of these questions. I am a mechanical engineer learning this stuff late in life.) I have read the following terms or phrases: group algebra group algebra the algebra of a group an algebra group an algebraic group a group of algebras So... could someone...

Homework Statement The problem goes like this: The sum of 2 numbers is 25. If 2/3 of the smaller one is 2 more than 1/4 of the larger one, find the 2 numbers. Any hints on how to start off this one? What should I let x= be? When i attempted to solve this i let 2/3x = the smaller number and...

Hey guys, I'm currently enrolled to take Linear Algebra in the fall, however, after talking with a friend in math, he recommended since it's quite a brutal course that I take it over the summer. Does anyone here think that's a terrible idea? My reasoning for asking is because here we don't...

If $\dfrac{(x-y)(y-z)(z-x)}{(x+y)(y+z)(z+x)}=\dfrac{2014}{2015}$, evaluate $\dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}$.

Pre-knowledge If V and W are finite-dimensional vector spaces, and dim(V) does not equal dim(W) then there is no bijective linear transformation from V to W. An isomorphism between V and W is a bijective linear transformation from V to W. That is, it is both an onto transformation and a one...

Pre-knowledge A matrix is a linear transformation if, T(u+v)= T(u) +T(v) and T(cu)=cT(u). Theorem 8.4.2 If V is a finnite dimensional vector space, and T: V-> V is a linear operator then the following are equivalent. a) T is one to one, b) ker(T)=0, c)...

Homework Statement Given the matrices A, B, C, D, X are invertible such that (AX+BD)C=CA Find an expression for X. Homework Equations N/A Answer is A^{-1}CAC^{-1}-A^{-1}BD The Attempt at a Solution I know you can't do normal algebra for matrices. So this means A≠(AX+BD)?

First off: I am not complaining about any of the members here or elsewhere. I do not post questions expecting help. When I post a question I would like an answer but I do not require it. Getting an answer depends on who is around and who is willing to help when I post the question. Still...

Hi, Are Calculus I, II, III courses a prerequisite requirement for studying Abstract Algebra? I have read that Proofs and a willingness to work hard is. I am studying Logic and Set Theory and want to study Abstract Algebra in the distant future. I am focused on Foundational and Pure...

Hi can anyone give me some hints with this question thanks A = \begin{pmatrix} 3 & -2 &1 & 0 \\ 1 & 6 & 2 & 1 \\ -3 & 0 & 7 & 1 \end{pmatrix} be a matrix for T:ℝ4→ℝ3 relative to the basis B = {v1, v2, v3, v4} and B'= {w1, w2, w3} v1 = \begin{pmatrix} 0 \\ 1 \\ 1 \\ 1 \end{pmatrix} v2 =...

Physics First, instead of the typically required Earth Science and Biology - Good idea, but for which students? For everybody, or just for those with enough Algebra and Trigonometry qualifications? http://en.wikipedia.org/wiki/Leon_M._Lederman

So I have been out of Math Courses for 5 years then this semester Spring Semester I completed Pre Algebra with an A, this Summer I have two Semesters of which I am taking College Algebra for Science and Engineering Majors and Plane Trigonometry. My question is during the Fall Semester should I...

Do you have to take algebra/trig based physics first in order to understand calculus based physics better? Or is algebra based physics even required for calculus based physics?

I am doing a problem in math which I can't seem to solve.The problem is apart of my discrete functions unit it grade 11 math. The question is: Toothpicks are used to make a sequence of stacked squares as shown. Determine a rule for calculating the total number of toothpicks needed for a stack of...

Homework Statement See attached picture Homework Equations For any rectangular prism, the formulas are the following: Surface Area = 2(lw + wh + hl); l is length, w is width, and h is height. Volume = lwh; l is length, w is width, and h is height. For a square-based prism, the formulas are...

Let $a,\,b,\,x,\,y,\,z$ be real numbers such that $x^2y+y^2z+z^2x=a$ and $xy^2+yz^2+zx^2=b$. Express $(x^3-y^3)(y^3-z^3)(z^3-x^3)$ in terms of $a$ and $b$.

Homework Statement A clock gains x min. every 24 hr. If it is y min. slow at present, in how many hours will it show the correct time? Homework Equations N/A The Attempt at a Solution I called the current time Tc so I have: Tc = Tc- y I know x will get added to the above equation every 24...

Homework Statement Here is the question, i know how to do part (i) but I do not understand part (ii): The Attempt at a Solution [/B] here's the solution from the marking scheme: i understand how they formed the matrix from their working out (i can se the pattern), but I do not understand...

Homework Statement If ##|P(x)|<=|e^{x-1}-1|## for all x> 0 where ##P(x)=\sum\limits_{r=0}^na_rx^r## then prove that ##|\sum\limits_{r=0}^nra_r|<=1## Homework Equations None The Attempt at a Solution ##P(1)=a_0+a_1+...## If the constants are positive, then ##P(1)<=|e^0-1|## So P(1)<=0 so...

Hello, A couple of years ago I studied abstract algebra from Dummit and Foote. However, I was never able to gain the intuition on the subject that I would like from that book. I want to study the subject again, and I want to use a different book this time around - one that covers a lot of...

hey all, I've begun my engineering degree and have been enjoying it thoroughly, my first semester naturally wasn't too hot, I've got around a 2.7 so far, but my school states calculus 1 as a prerequisite for linear algebra, I hardly went to class and flipped classes but consistently scored above...

Homework Statement X ={(x1,x2,x2 −x1,3x2):x1,x2 ∈R} f(x1,x2,x2 −x1,3x2)=(x1,x1,0,3x1) 1. Find a basis for X. 2. Find dim X. 3. Find ker f and I am f 4. Find bases for ker f and I am f 5. Is f a bijection? Why? 6. Find a diagonal matrix for f.Homework EquationsThe Attempt at a Solution 1. Put...

Probably a really stupid question.. ##u=t+r+2M ln(\frac{r}{2M}-1) ## From this I get ##\frac{du}{dr}=(1-\frac{2M}{r})^{-1}## But, 1997 Sean M. Carroll lectures notes get ##\frac{du}{dr}=2(1-\frac{2M}{r})^{-1}## . (equation 7.71). No idea where this factor of 2 comes from. Thanks

Hello, I noticed that the solution of a homogeneous linear second order DE can be interpreted as the kernel of a linear transformation. It can also be easily shown that the general solution, Ygeneral, of a nonhomogenous DE is given by: Ygeneral = Yhomogeneous + Yparticular My question: Is it...

Homework Statement Minimize the following using boolean identities 1. AB'CD+(ABC')'+ABCD' Homework Equations Identity 1A=A 0+A = A Null (or Dominance) Law 0A = 0 1+A = 1 Idempotence Law AA = A...

Let $F$ be the set of infinite sequences $(a_1,a_2,a_3...)$, where $a_i \in \Bbb{R}$ that satisfy $a_{i+3}=a_i+a_{i+1}+a_{i+2}$ This describes a finite-dimensional vector space. Determine a basis for $F$.

1. Simplify the expression: F = xyz' + xy'z' + x'yz + xyz2. Postulates and theoremsThe Attempt at a Solution F = xyz' + xy'z' + x'yz + xyz = x(yz' + y'z') + yz(x' + x) (Distributive) = x(yz' + y'z') + yz.1 (Complement) = x(yz' + y'z') + yz (identity) This is where I need...

Hi I recently read a book called "The fundamental theorem of algebra" by Fine and Rosenberger. It focused specifically on polynomials, and proved the theorem using several fields of mathematics; Two of the proofs were algebraic. Abstract algebra has been very difficult for me; Mostly because...

I am finishing up Calculus II, which is mostly just solving integrals using techniques and finding the convergence of a series. My school is offering Linear Algebra in the summer, but it will not be available in Fall. I personally feel math to be my strong suit, since I had an A for my Calc 1...

I'm a physics major taking Linear Algebra right now. It's been pretty boring but I'm doing well. I'm just wondering about which concepts from this subject should I really focus on understanding and knowing how to apply well? Obviously I'm focusing on everything and trying to receive and A in...

I really need help. f(x) is a fourth degree polynomial function f(x) has zeros of plus or minus 2 and plus or minus 3i f(0)=-108 Find an equation for f(x) in general form

I am researching ways linear algebra is integrated into aerospace engineering (I know its alot). I am looking for specific ways. Any help would be appreciated.

1. prove that: X'Y'Z + X'YZ' + XY'Z' + XYZ = (X⊕Y)⊕Z Homework Equations Use postulates and theorems. The Attempt at a Solution X'Y'Z + X'YZ' + XY'Z' + XYZ (original expression) X'Y'Z + X'YZ' + X(Y'Z' + YZ) (distributive) X'Y'Z + X'YZ' + X.1 (complement) X'Y'Z + X'YZ' + X (identity)[/B]...

Homework Statement Homework EquationsThe Attempt at a Solution This whole thing about angular momentum has me totally confused and stumped, but I am trying this problem given in a youtube video lecture I watched. I know of this equation ##L^{2} = L_{\pm}L_{\mp} + L_{z}^{2} \mp \hbar L_{z}##...

Homework Statement Given two arbitrary vectors |\phi_{1}\rangle and |\phi_{2}\rangle belonging to the inner product space \mathcal{H}, the Cauchy-Schwartz inequality states that: |\langle\phi_{1}|\phi_{2}\rangle|^{2} \leq \langle\phi_{1}|\phi_{1}\rangle \langle\phi_{2}|\phi_{2}\rangle...