Algebra Definition and 999 Threads

HI all, I am working my way slowly through some classical mechanics books, and I don't think I could function without my CAS (most often my trusty HP 50g, sometimes Giac/Xcas). I have never been very good at pages of algebra, often dropping negatives or whatever, bad enough that working...

Entering my third year of my bachelor of science majoring in maths/physics and having some trouble deciding what courses to do this semester. I know for sure I will be taking complex analysis and 3rd year quantum however am having trouble picking between 3 in particular for my final two courses...

Is there anywhere that teaches tensor analysis in both tensor and non tensor notation, because I'm having to pause each time i look at something in tensor notation and phrase it mentally in non tensor notation at which point it becomes staggeringly simpler. Any help apreciated

Hi all, I am taking Quantum Mechanics II this coming spring semester. However, I haven't taken Linear algebra yet but I don't want to take the class just because for some few topics. What linear algebra topics should I learn before the class? Thanks!

Homework Statement A line is perpendicular to the line 2x - 4y + 7 = 0 and that passes through the point P(7,2). Determine the equation of this line in Cartesian form. Homework Equations n/a 3. The Attempt at a Solution Okay, so how I generally believe how to solve these problems may be...

for this question i got up to obtaining [1 0 1 a-c; 0 1 1 c; 0 0 0 b-a+c] matrix im supposed to find a b and c so that the linear system has an infinitely many solutions I just can't work this out!

I am working through linear algebra from MITs MOOC online courses. One of the question refers to the uncertainty principle. It states: AB-BA=I can happen for infinite matrices with A A=A^{ T }\\ and\\ B=-B^{ T }\\ Then\\ x^{ T }x=x^{ T }ABx-x^{ T }BAx\le 2\parallel Ax\parallel \parallel...

Why, when a fraction has repeated linear terms in its denominator e.g. (11x2+14x+5)/[(x+1)2(2x+1)] does it have to be split into three partial fractions, A/(x+1) + B/(x+1)2 + C/(2x+1)? When my first saw this example, my initial reaction was to split it into A/(x+1)2 +B/(2x+1), but after working...

Dear Physics Forum personnel, I am a college sophomore with double majors in mathematics and microbiology. I apologize for this interruption but I wrote this email to seek your advice and recommendation on linear algebra textbook. I will be taking the "theoretical, proof-based" introductory...

Hiya. Im having problems with Questions 2.(c,i),(c,ii) and (c,iii) question on this past exam paper. http://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2014/91261-exm-2014.pdfCan someone check my answers and explain the questions where I face planted? Thanks! 2. (c,i). I got h/(rx-t) = x, I...

Dear all, I am trying to understand the fundamental theorem of algebra from the text (Alan F. Beardon, Algebra and Geometry) attached in this post. I have understood till the first two attachments and my question is from the 3rd attachment onwards. I will briefly describe what...

I'm stuck on deriving the follow. Context: FRW Metric, dust dominated universe, use of conservation of energy-momentum tensor. I'll now state all the equations I can see are relevant. (But just in case the source is http://arxiv.org/pdf/gr-qc/9712019.pdf and it's eq 8.43). ## \frac{d}{dt}(\rho...

Homework Statement In Game 6 of a 6-team double-elimination tournament, Team 1, the top-ranked team, faces the loser of a previous game involving Team 2, the second-ranked team, against one of either Team 3, the third-ranked team or Team 6, the sixth-ranked team. This exercise tests the limits...

I am currently studying A level Further Pure Mathematics, and I will be joining university next year. I want to brush up on precalculus (algebra, trigonometry, geometry) and calculus (differential, integral [single variable]), except that this time I need a more rigorous treatment of those...

I am planning my courses for next semester, and I am unsure of which direction to go in with linear algebra. I have already taken the following course: Linear Algebra I Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces...

Homework Statement Please refer to : http://math.stackexchange.com/questions/1068948/how-to-prove-that-int-0-infty-sinx-arctan-frac1x-mathrm-dx-fra/1069065#1069065 The answer by @venus. What is the procedure in converting that single integral, dividing it into parts, and making it a double...

Homework Statement In the text, the products pq and qp of the permutations (2 3 4) and (1 3 5) were seen to be different. However, both products turned out to be 3-cycles. Is this an accident? Homework Equations p=(3 4 1)(2 5) q=(1 4 5 2) where p and q are permutations The Attempt at a...

How to find ##\sqrt{(a+b) + 2 \sqrt{ab}} = \sqrt{a} + \sqrt{b}## ?

Homework Statement A series of 5 measurements of Y are recorded with increasing X. (i.e. gradient has units Y/X) The error in measurement of Y is ±0.05 The error in measurement of X is ±0.005. How is the error in the gradient calculated? Homework Equations - measurements[/B] Y | X...

Hey there, I'm thinking about if one of the eigenvalues is zero (means determinant is 0. right?) So, is there any possibility to non-zero eigenvalue also exists?

Can someone please explain why the F( X, Y ) is XY' + XY ? IMO , it is X'Y' + X'Y +XY' +XY ... or the author simplified it to become XY' + XY ? how to simplify it?

Homework Statement Let Hom(V,W) be the set of linear transformations from V to W. Define addition on Hom(V,W) by (f + g)(v) = f(v) + g(v) and scalar multiplication by (af)(v) = af(v. If V is a vector space over a field K, define V* = Hom(V,K). This is called the dual space of V. If...

In Srednicki's text on quantum field theory, he has a chapter on quantum Lorentz invariance. He presents the commutation relations between the generators of the Lorentz group (equation 2.16) as follows: $$[M^{\mu\nu},M^{\rho\sigma}] =...

Homework Statement If the coefficient of kinetic friction in the previous problem was actually 0.11 and the slope 30 degrees, to the nearest meter how far up the hill does he go? **the problem prior was: A skier traveling at 31.9 m/s encounters a 12 degree slope. If you could ignore friction...

I was enrolled in College Algebra for this upcoming winter because the hours will overlap with the class that I enrolled for spring. The reason why I want to learn this, is to refresh my Algebra skills, since I forgot most of it (I only remember matrices, radicals and identities). The purpose...

The title may seem a little confusing and possibly stupid :D What I mean is like a plane doesn't go through the origin? Can we describe a basis for this? If so, how?

2m+(50s)(0.5m/s) = 2m + 25m/{s}^{2} = Not possible My teacher keeps saying this is pure piffle and shaking his head. Can someone please explain this to me?

Homework Statement Let V be a finite dimensional vector space over ℂ . Show that any linear transformation T:V→V has at least one eigenvalue λ and an associated eigenvector v. Homework EquationsThe Attempt at a Solution Hey everyone I've been doing sample questions in the build up to an exam...

Homework Statement Let V be a finite-dimensional real vector space with inner product <⋅,⋅> and L: V → R a linear transformation. Show that there exists a unique vector a ∈ V such that L(x) = <a,x>. Homework Equations Hey everyone, so I'm a physics student who had to choose a few electives in...

I'm a second year student at university studying mathematics. I'm having troubles deciding between a few modules and I hope you can help. http://www.ucl.ac.uk/maths/courses/undergraduates is where all the modules are, please take a look at "Honours Year 2" I get to choose four modules, and so...

Not quite sure, could someone kindly explain the concept of the topic to me? Thanks, it really means a lot. :)

I am in Calculus BC in high school right now and I am really enjoying it and have finished all of the material for the year and I have heard different things about what class comes after Calculus BC (I believe BC is equivalent to Calc 1 & 2 in college). I have heard the next class, aka Calc 3...

Hey, I am a freshman in High School and I have a very superior IQ but I am in normal classes. This is due to ADHD and I used to be lazy in school. Anyways, algebra 1 is VERY boring. I want to teach myself geometry, algebra 2, Pre Cal, and Calculus because I love math. Also I feel like it will...

Homework Statement As a string in my program. Homework Equations Solving a system with the forward phase of row echelon reduction and a consecutive back substitution. All done by numpy here. (The book suggested MATLAB, etc). The Attempt at a Solution import numpy """ In a wind tunnel...

1- How can infer from the determinant of the matrix if the latter is real or complex? 2- Can we have tensors in an N-dimensional space with indices bigger than N?

< Mentor Note -- thread moved to HH from the technical math forums >[/color] My final assignment in graduate algebra is to write an essay about the relationship among the subjects we have learned so far this semester: (1) Module (2) The Field of Fractions of an Integral Domain (3) Integrality...

Hello, I'm debating between taking either abstract algebra, theory of numbers, or intermediate symbolic logic as a math elective. Does anyone have any idea which would make my life easier?

Homework Statement [/B] A 0.20-kg block and a 0.25-kg block are connected to each other by a string draped over a pulley that is a solid disc of inertia 0.50 kg and radius 0.10 m. When released, the 0.25-kg block is 0.30 m off the ground. What speed does this block have when it hits the ground...

Homework Statement 4*(5^x)-3(0.4^2x)=11 In case it doesn't make sense, in the attempted solution it's written out better Homework EquationsThe Attempt at a Solution http://imgur.com/SnpFQZV Thanks!

Homework Statement Given that the force of gravitation between Planet A (the one in the left side of the drawing), Fa=3000/da2 and the force of gravitation between Planet B and the rocket, Fb= 6000/ db2. Assuming that the three bodies involved is in stationary. What are the distances (ranges)...

https://www.amazon.com/dp/1133949010/?tag=pfamazon01-20 https://www.amazon.com/dp/1285057090/?tag=pfamazon01-20 https://www.amazon.com/dp/1133959741/?tag=pfamazon01-20 So I'm planning on buying the books in the links above (Algebra and trig, precalc and calc by Ron Larson), but as they are...

Homework Statement I stated this as a small attached photo, since i still need to learn to write in latex (see photo) Homework Equations How do you transform the first expression into the next expression (on photo)? The Attempt at a Solution [/B]I tried various manipulations with potens...

Homework Statement Hello there everybody! I'm reading a Linear Algebra textbook, specifically on LTV systems solutions. I'm trying to redo this example from the book: Homework Equations But I couldn't understand the passage: The Attempt at a Solution I mean. x1(0) = 1 and x2(0) = 0? I...

Homework Statement goal: solve for t; all else are constants $$cos(\omega t)=1-e^{-(\frac{t}{RC})}$$Homework Equations noneThe Attempt at a Solution i turned the cos to complex notation & rearranged $$e^{i\omega t}+e^{-(\frac{t}{RC})}=1$$ $$ln(e^{i\omega t}+e^{-(\frac{t}{RC})})=0$$ and i...

Hello, I have some problems with understanding some concepts in Quaternions and Clifford Algebra. For example, where can I learn the basic construcion of Clifford Algebra? I'm listing the equalities I did not understand and I appreciate it if you can help me with understanding these : Homework...

Hi all, So I'm going to have my first exposure to linear algebra and I've completed Calc 1 and 2. I've seen Axler and Shilov numerous times and I'm having a hard time choosing it. Here's my syllabus for my Linear Algebra Course. Matrices, Gauss reduction, invertibility. Vector spaces, linear...

1. Calculate the force needed to move the wire in the figure (Figure 1) if it holds a soapy solution (surface tension is 0.025 N/m) and the wire is 16.0 cm long. Express your answer to two significant figures and include the appropriate units. 2. γ(surface tension) = F (force) / l (length)...

Homework Statement let A be the matrix corresponding to the linear transformation from R^3 to R^3 that is rotation of 90 degrees about the x-axis Homework Equations find the matrix A The Attempt at a Solution I got stuck on rotating z component. I tried T([e1,e2,e3])=[0 -1 0]...

Homework Statement This is one part of a wider question, I'm only posting the part I'm having trouble with. $$ \begin{align} \text{Given an impedance network } B &= \frac{Z_1 \parallel Z_3}{Z_2 + Z_1 \parallel Z_3} \\ \text{show that: } \frac{1}{B} &= 1 + \frac{R_2}{R_1} + j\frac{\omega CR_2}{1...

Homework Statement Determine whether the set S spans R3. If the set does not span R3, then give a geometric description of the subspace that it does span S = [ (2,0,3) , (2,0,-1) , (6,0,5) , (4,0,6) ] Homework EquationsThe Attempt at a Solution I know S does not span R3 because the system of...