Algebra Definition and 999 Threads

https://www.physicsforums.com/threads/derivative-of-1-x.211489/ In the last post, three last steps. He changes -h into -1, how does this work? I know that if you for example have h/h it's equal to 1 regardless of what value h has, since they're both the same value. I don't see that being...

I am preparing myself for a BSEE starting next year. I have just finished Stewarts Calculus for Calc I,II,III and Diff Eqs up to solving 2nd order non-hom diff eqs by undet. coeffs, variation of parameters and power series. In high school some 15 years ago I saw some very basic linear algebra...

Homework Statement Suppose a linear transformation T: [P][/2]→[R][/3] is defined by T(1+x)= (1,3,1), T(1-x)= (-1,1,1) and T(1-[x][/2])=(-1,2,0) a) use the given values of T and linearity properties to find T(1), T(x) and T([x][/2]) b) Find the matrix representation of T (relative to standard...

Homework Statement What is the volume of the parallelepiped with vertices (3, 0, −1), (4, 2, −1), (−1, 1, 0), (3, 1, 5), (0, 3, 0), (4, 3, 5), (−1, 2, 6), and (0, 4, 6)? Homework Equations The volume of a parallelepiped is given by the triple scalar product, (a × b) ⋅ c The Attempt at a...

Right now I'm using "Affine Lie Algebras and Quantum Groups" by Fuchs. I'm getting sick of it. As a Physicist the structure and focus of the text is attractive to me. But, to give one example... The text constructs two vector spaces: L and Lw. Lw is dual to L. The text goes on to state...

Hi, I want to learn Linear Algebra in its most rigorous and expansive form. I have narrowed down to two books (well, one is a series). On one hand, I want to try Linear Algebra by Hoffman/Kunze, but my school's library has Lang's Introduction to Linear Algebra, and his second book on the...

Homework Statement Let V be the set of all ordered pairs of real numbers. Suppose we define addition and scalar multiplication of elements of V in an unusual way so that when u=(x1, y1), v=(x2, y2) and k∈ℝ u+v= (x1⋅x2, y1+y2) and k⋅u=(x1/k, y1/k) Show detailed calculations of one case...

[FONT=Times New Roman]Homework Statement From Linear Algebra with applications 7th Edition by Keith Nicholson. Chapter 9.2 Example 2. Let T: R3 → R3 be defined by T(a,b,c) = (2a-b,b+c,c-3a). If B0 denotes the standard basis of R3 and B = {(1,1,0),(1,0,1),(0,1,0)}, find an invertible matrix P...

Frustratingly although I can solve the ODE, I am getting a different answer to the book. Now going in circles so would appreciate a fresh pair of eyes. The ODE (for a boat coasting with resistance proportional to $V^n$) starts as $ m\frac{dV}{dt} =-kV^n $ Find V(t) and x(t), V(0) = $V_0$ I...

Hey all. So I have been reading this article and have a question I would like to ask. I will be referring to this article extensively so it would be kind of you to open it: http://www.ee.ucr.edu/~yhua/MILCOM_2013_Reprint.pdf I believe reading the article is not required to answer my questions...

Homework Statement Let T:V→V be a linear operator on a vector space V over C: (a) Give an example of an operator T:C^2→C^2 such that R(T)∩N(T)={0} but T is not a projection (b) Find a formula for a linear operator T:C^3→C^3 over C such that T is a projection with R(T)=span{(1,1,1)} and...

My situation is that I'm 17, and graduated high school early due to the CHSPE test. The only math I have any real knowledge of is algebra 1, since I forgot geometry and barely got into algebra 2 before I graduated. No books have worked, Gelfand's Algebra frustrated me exceptionally because it...

Homework Statement First off i wasn't sure if i should put this in precalc or here so i just tossed a coin[/B] I must find the roots of the expression z^4 +4=0 (which I've seen repeatedly on the internet) Use it to factorize z^4 +4 into quadratic factors with real coefficients The answer is...

I just finished up Stewart's Calculus Textbook, and the last section was on solving 2nd Order Non-Homogeneous Diff Eqs using power series. I've looked through Paul's Calculus page in the Differential Sections, and can see that there is still a lot more beyond Stewart's that I'd like to study...

The state of arithmetic today is disgusting. The textbooks on it are absolutely repelling, the authors treat it like a subject that will be of concern to only babies. They don't show any love, they treat the subject like a dirty rug. It's been two years since I majored in mathematics, since...

can you recommend a good book on complex analysis? I would like a book that can sharpen my skills in solving complex number problems through graphs and also improve the algebraic part like solving problems related to roots of unity etc. (I have studied calculus myself. I have done a lot of self...

Explain, plase to me: 2D covariant, conravariant and physical components of vector. I can not find this thematic in my official study book.

I need a book that is under 400-500 pages which covers all of basic physics nicely. Every introductory algebra-based physics book I have seen has over 1000 pages and I just need a concise book right now, for some personal reasons. It should cover the following topics: 1. General physics 1.1...

First it starts as r= p* (50K^-.5 100^.5) then K=[(50p100^.5/r]^2 So how does the power of 2 get there in the second part when moving K to the other side?

i find here a representation of the Lorentz algebra. Starting from the matrix representation (with the ##\lambda## parameter) i see how one gets the matrix form of ##iJ_z## I am less comfortable with the ## -i y\partial_x + x \partial_y## notation Where does it come from? They say that it is a...

Good day, Did anyone here use Serge Lang's "Algebra" as an undergraduate text?

What are some rigorous theoretical books on mathematics for each branch of it? I have devised a fantastic list of my own and would like to hear your sentiments too. Elementary Algebra: Gelfand's Algebra Gelfand's Functions & Graphs Burnside's Theory of Equations Euler's Analysis of the...

Does anyone know of any gentle, introductory books to LA that assume little prerequisites, even in the way of vectors and matrices? I want something that will give intuition and reasonable proofs, and will provide enough background for something like computational neuroscience. I do not know...

What is a good book on algebra that is highly theoretical and covers functions, the binomial theorem, sequences/series (basically all algebra topics in college) and if possible, elementary number theory? Most books on high school-college algebra today don't cover theory at all and when they do...

Hello! On this Fall Semester, I will be taking the Linear Algebra with Proofs (Friedberg), Analysis I (Rudin-PMA) or Abstract Algebra I (Dummit/Foote), and Combinatorics (Brualdi). Since I can take only one from Analysis I or AAI on Fall, I am trying to figure out if the introductory...

Dear Physics Forum advisers, Today, I got two gifts from my research mentor: "Topics in Algebra" by I.N. Herstein and "Abstract Algebra" by Dummit/Foote. I am very happy and grateful for his gifts, but I already have been studying the abstract algebra through Michael Artin and Hoffman/Kunze...

Hi! I would like to know if my assumptions are right: Topology is the merging domain of analysis and algebra; Relational algebra use topological operators; Relational algebra is a specification of topology ?

In my school LA requires a pre req proof class vs matrix algebra which doesn't. Would matrix algebra even be worth taking?

Hello folks. I pulled out my algebra and trigonometry book that I kept from college (that I never ended up going). I am brushing up with algebra right now and this is something that stumped me. If you do not mind, I would love to learn how I can think differently in order to complete this...

Is the fundamental theorem of algebra (for polynomials on the complex plane) equivalent to the statement that any polynomial p of degree n>0 can be written p(z) = c(z - a_1 ) (z- a_2) \cdot \cdot \cdot (z - a_n ) or am I missing some subtle distinction? And if not equivalent, does the theorem...

Homework Statement Find Fg if G=6.67*10-11m3 kg-1s-2, M=2.6*1023 kg, m=1200kg, and r = 2000m Homework Equations Fg= -GMm/r2 The Attempt at a Solution Fg=-GMm/r2 Fg=- (6.67*10-11m3kg-1s-2)(2.6*1023 kg)(1200kg)/(2000m)2 Fg=- (6.67*10-11m3kg-1s-2)(2.6*1023 kg)(1200kg)/4000000 m2 Fg= -...

I haven't gotten any knowledge of physics. I didn't have the opportunity to take it during my high school due to the biology state exam. Will it hurt to take it this semester? Will the calculus based physics be taught the same as general physics (non-calculus based)? If this isn't a good idea...

Homework Statement Determine whether or not the vector functions are linearly dependent? u=(2t-1,-t) , v= (-t+1,2t) and they are written as columns matrixes. Homework Equations Wronskian, but I don't think I should use it because I need to take derivatives so it doesn't seem like it would...

A couple of notes first: 1. \hom_{A}(-,N) is the left-exact functor I'm referring to; Lang gives an exercise in the section preceeding to show this. 2. This might be my own idiosyncrasy but I write TFDC to mean 'The following diagram commutes' 3. Titles are short, so I know that the hom-functor...

Construct a linear system determined by four numbers whose sum is 40, with the first three numbers adding up to 20 and the last three to 30. a) Explain why this system has infinitely many solutions. b) Add another condition on the numbers so that a unique solution can be found and then find...

I have a problem with the derivation of the the form of QM starting from the Lie algebra of the Galilei Group like the one given in Ballentine's cap 3. My Issue is that the procedure is shown almost as unavoidable, And my feeling is that there have to be more postulates that I'm not seeing...

Hi, I'm going to start learning Abstract Algebra, and I was wondering which book, either Lang (his graduate version) or Dummit and Foote, is better. I'm totally okay with terseness to any degree so that isn't an issue for me. Now, I know that Lang is a hardcore graduate book (at least according...

I am having trouble proving that two multivariate formulas are equivalent. I implemented them in MATLAB and numerically they appear to be equivalent. I would appreciate any help on this. Prove A = B A = (Σπ^-1 + Σy^-1)^-1 * (Σπ^-1*π + Σy^-1*y) y = π+ X*β Σπ =τ*Σ Σy = X' * Σβ * X + ΣεB =...

Homework Statement Q0=Q1+Q2 Q1/C1 =Q2/C2 I substituted it Q1/C1=Q0-Q1/C2 then I got Q1=C1Q0-C1Q1/C2 but the answer has to be Q1=Q0C1/C1+C2 my algebra isn't good enough to solve it what are the steps that I have to take to make it to the answer Homework Equations The Attempt...

I am reading Paolo Aluffi's book, Algebra: Chapter 0. I have a question related to Aluffi's description of monoid rings ... ... In Chapter III, Section 1.4 on monoid rings, we read the following: In the above text we find:"Given a monoid $$(M, \cdot )$$ and a ring $$R$$, we can obtain a new...

I can most of the time successfully convert between base 10 and another base or another base and base 10 or between 2 bases where one of them is a power of the other(like base 2 and base 4 or base 3 and base 9). With negative bases I sometimes don't get what I want in that negative base and...

This isn't homework, I'm just trying to refresh my memory on cyclic groups. My question is, in this problem solution, how does ##{\sigma_i}^m=1## follow from ##\sigma_i## being disjoint?

Homework Statement Hello guys So I have the following problem, given the mapping above I have to check weather it's ring homomorphism, and maybe monomorphism or epimorphism. The Attempt at a Solution So the mapping is obviously well defined, and I have proven it's homomorphism, and it's...

OK, either I'm looking at this the wrong way, or this is way above what a 10 year old should be. Following are 2 equations containing A, B and C. A solution must be found that solves both equations, i.e. A, B and C are the same in each formula. Also, A, B and C must be whole numbers; C+2A=3B+2...

Hi please i need help in number 3 of the tutorial questions. It is not an assignment its just a tutorial (read title in the image). I am currently studying for my final and i need help in (3b). the only way I am thinking of solving this questions is to use the equation given in part (d). But...

Dear Physics Forum advisers, My name is Phoenix, a sophomore with major in mathematics and an aspiring applied mathematician in the theoretical computing. I wrote this email to seek your recommendation on the textbooks for abstract algebra. I want to self-study the abstract algebra during...

Suggest good books to read in an order for one to gain profundity in the particular subject. This may seem to be a rather baffling task, due to the amount of subjects and it's vastness, but if it is done, it could certainly be extremely useful, especially for people like me who are highly...

Hi I'm new here! I've always loved math and have been really good at figuring out how to solve word problems logically and figuring out math in general. When my teachers explain how to do problems i get confused/can't follow what they're saying but its usually fine because i can just figure it...

Homework Statement If I have the characteristic equation: -λ3 + 3λ2 + 9λ + 5 And I'm told that one of its eigenvalues is -1. How do I find the rest of the eigenvalues? Homework Equations -λ3 + 3λ2 + 9λ + 5 The Attempt at a Solution The furthest I can get is: -λ3 + 3λ2 + 9λ + 5 = (λ + 1) x...