Rigorous Definition and 154 Threads

Hello, I am searching for a geometry book, a rigorous one. I have taken a look at Moise's and Downs's book but it looked too short, I want something more advanced but keeping the focus on elemtary issues at the same time. Thanks.

Well, I just finished a linear algebra course using David C Lay's book. Thinking to go deeper on the subject. I am never good with proofs, so I actually prefer books that may build some skills on that. On that regard, the book perhaps should be fairly rigorous. Right now I have several...

I'm wondering if anybody knows about or has used a good introductory physics textbook that is mathematically rigorous. I'm really interested in physics, but I'm a mathematics student and I CAN'T STAND any of the books I've tried to use so far (eg. Knight's Physics). I've really grown to dislike...

rigorous statement of virtual work principle?? in the texts on mechanics the virtual work principle is always stated in 'infitesimal form'. is there a "proper" way to write the principle of virtual work in which we don't leave it in terms of INFINITESIMALS.

I've spent a lot of time soul searching after having some academic "failures" in the previous semesters, and what I found is that often when I'm not studying, it's not because I can't study, but it's because the book we're using is unreadable to me. For example, after sailing through Calculus...

These words have been pulled directly from Wikipedia, although I find the exact logical construction in my textbooks: --- The (ε, δ)-definition of the limit of a function is as follows: Let ƒ be a function defined on an open interval containing c (except possibly at c) and let L be a real...

What is the easiest way to see that, in a regular polyhedron, the sum of the face angles about each vertex is less than 2π? This seems elementary, but I truly have very little background in geometry. Preliminary searches on PF and Google/Wikipedia didn't turn up anything substantial aside from...

Hi, I wish to enter AP calculus first thing in my final High school year, and so I am Essentially skipping some precalculus content, and wish to learn/review Pre-calculus by myself. I need a book that is not application heavy, and does not rely on graphing calculators, and is overall more...

I am an undergrad that will be a sophomore in the fall, and I've completed the first level class in calc-based classical mechanics, as well as Calc I and Calc II. The math presented to me was a typical plug-n-chug, cookbook, focus on techniques rather than concepts style. In short, I don't...

Please don't start by saying there is no such thing as th best text or the most rigiorus text about anthing. I simply mean like we know Apostol's text fo calculus friedberg's or Hoffman's text on linear agebra Rudin's analysis text and ... what's the one about relativity? As far as I've googled...

If a quantum system is subjected to a time dependent Hamiltonian with one parameter lambda, then its entropy does not change provided lambda is changed slowly enough between two values. How can this be proved rigorously? The http://en.wikipedia.org/wiki/Adiabatic_theorem" is not enough, since...

Homework Statement But I think the definition is as follows: Let an be a sequence of real numbers. Then an->a iff for ALL ε>0, there exists an integer N such that n≥N => |an - a|< ε. The definition says that it has to be true for ALL ε>0, but in the example above, they just let ε to...

Homework Statement Definition: Let an be a sequence of real numbers. Then an->a iff for all ε>0, there exists an integer N such that n≥N => |an - a|<ε. [for all of the following, "lim" means the limit as n->∞] Theorem: Suppose lim an =a and lim bn =b. Then lim (an + bn) = a + b. Proof...

Homework Statement Definition: Let an be a sequence of real numbers. Then an->a iff for all ε>0, there exists N such that n≥N => |an - a|<ε. Let an=(n2+1)/(n2-9). PROVE that an->1 as n->∞. Proof: Assume n≥4. Then | 1-an | = 10/(n2-9). 10/(n2-9) < 10/n provided n2 - 9 > n, i.e. n2 - n...

I've decided to major in Physics and just finished E&M as well as Calculus 3. I understand how to do most of the problems in my Calc book (the same text was used for all three courses) mechanically. Our classes used James Stewart's text and I had Ron Larson's as another reference. My concern...

Hi all, I'm looking for a rigorous (in a mathematical sense) treatment of statistical thermodynamics. I'm at the tail end of a class on stat thermo that used the book by Bowley and Sanchez. This book is not what I'm looking for. Does anyone have any suggestions?

Title says it all. But to further elaborate... it's been about 12 years since I had general chemistry, I don't remember any of it, and would like to pick up a textbook to refresh my knowledge. I majored in math and physics, so I would prefer the book not to dodge the use of, say, calculus...

Hey everybody, since the previous thread got locked I thought I would open this thread as a place to discuss rigorous issues in quantum field theory, be it on the constructive or axiomatic side of things. I apologize if one is not supposed to start a discussion with posts from old threads...

this may be too much to ask of you, but if possible, please give me ideas, have you any knowledge of anything in the us that will give one college credit for a high school student? not some trivial sh*t like ap/ib calculus, multivar calculus, or diff eqs... something more proof based, like...

What are some good textbooks that treat physics in an axiomatic and mathematically rigorous fashion? I came across a cheap copy of A Unified Grand Tour of Theoretical Physics and so far it seems to be a good overview of physics. What books would serve to branch off from this book?

I know that the definition of completeness is that a set contains the limits of rational numbers. and I know the definition of convergence is that for all e>0 there exists N such that for n>=N |xn - x| < e where x is the limit of the sequence. how to combine the two? thanks in advance

I was asked to write a rigorous proof for the following theorem: 0x = 0 ,for all x. Is the following rigorous proof correct?? 1) 0x = 0x+0...........by using the axiom:for all ,a : a+0=a 2) x+(-x) = 0..........by using the axiom: for all ,a: a+(-a) = 0 3) 0x = 0x...

how is freshman physics different from ap physics? i hear that physics at freshman year is a lot harder than ap physics. also i know calculus, although not rigorously. kinda "for dummies" level, where derivative is "instantaneous rate of change", etc. i know how the definitions work, but still.

Okay, here's the deal: I am going to run out of math classes at my high school at the end of this [junior] year. I'll have finished AP Calc BC (with Larson/Edwards as the text), but I already studied almost all of Gilbert Strang's free online text. So I'm really bored redoing material I...

Jobs, which require a good set of intelligence and hard work?

Give a rigorous proof using the appropriate axioms and the definition ,\frac{a}{b}=a\frac{1}{b} of the following: \frac{a}{b}*\frac{c}{d}=\frac{ac}{bd} \frac{a}{b}:\frac{c}{d} =\frac{ad}{bc}

I'm highly interested in pure mathematics, so I wanted to know some of the best textbooks that would prepare me for advanced pure math classes in college. I already understand most math that would be taught in high school, however I would like to re-learn it in a more rigorous way. (Our school's...

I took classical (engineering) thermodynamics a few years ago, and this semester I am taking a statistical thermodynamics class from the physics department. We are using the book "Fundamentals of statistical and thermal physics" by Reif, which seems to be a pretty good book. Unfortunately I...

Hi, Recently I'm trying to understand some explanation of RCWA, which introduces to computational analysis of diffraction grating efficiences. For explanation I use Soifer book, but cannot understand or don't agree with it. I tried to understand the derivation, not to write it straightforward...

My plan is to work thru Rudin's Real and Complex Analysis, and then functional analysis, and then move on to DEs/PDEs. Right now its looking like Arnold for DEs, and Evans for PDEs. Any other recommendations? thanks

whats a good book to learn multivariable and vector calculus in a rigorous fashion, similar to spivak. id prefer the vector calculus to stick to R3 (ie stokes), ill save the n case for analysis. apostol II looks like a good book, but its very expensive and i generally don't like apostol...

Hey, in my Schaum' Outline Calculus it says Dx(ex) = ex Let y = ex. Then ln(y) = x. By implicit differentiation, \frac{1}{y}y' = 1 therefor y' = y = exFor a more rigorous argument, let f(x) = ln(x) and f-1(y) = ey. Note that f'(x) = \frac{1}{x}. By Theorem 10.2(b). (f-1)'(y) =...

One is Spivak's book. What are other good ones which compare to it?

Homework Statement Prove that the set of algebraic numbers is countable using ONLY the following information: - We consider algebraic numbers to be the root of a polynomial with integer coefficients - The height of a polynomial of degree n of the form a0 + a1x + ... + an*x^n is given...

Rigorous proof of basic "absolute value" theorem? Hey :) I'm working through a Real Analysis text, and I came across this theorem and "proof": http://img352.imageshack.us/img352/6725/proofbx2.png It kind of took me by surprise, because the author of the text is usually very careful about...

Homework Statement 1) Test the following series for Uniform Convergence on [0,1] \sum\limits_{n = 1}^{\inf } {\frac{{( - 1)^n }}{{n^{x}\ln (x)}}} Homework Equations The Attempt at a Solution Obviously, it's not uniformly convergent since f(n,1) = \sum\limits_{n =...

I'm a first year university student engaged in my first economics (macroeconomics) course, and, naturally, it isn't very extensive and makes use of a colorful textbook. Though I've been learning quite a few things, I can't help but feel that the explanations provided are too blurry. There's an...

So, for instance, maybe Baby Rudin is the paradigm of "how to do it right" which includes proving stuff like Baire's Theorem. By "rigorous", I don't necessarily mean "Baby Rudin". On the other hand, Thomas and Finney does, in fact, have the formal definition of a limit, for instance, on p70 of...

I want to relearn QM within a rigorous mathematical framework. What classes should I take? Off the top of my head, I expect that I'll need to know functional analysis and group theory. What else?

Hi guys, I have studied special relativity for a while now and am doing a project for one of my physics classes on it. The relativity of simultaneity is a concept that I easily grasped when I began reading S.R. and time dilation was the hardest (easiest now). I grasped it (simultaneity)...

In applied subjects, the differential is often treated as i.e C'(x) approximately equals C(x+1)-C(x) 1 is used instead of h as h->0 because we are talking about discrete units such as items or people. They argue it works because x>>1. i.e considering lots of items, x. However what is rigorous...

It's a word I hear a lot and I've looked it up but I don't understand. What does it mean to be rigorous in one's mathematics?

Is there a book that explain in a formal way the deduction of symmetry/antisymmetry of bosonic/fermionic wave equation e/o commutation relation? I've often noticed that some people use examples for the introcution, but is there an axiomatic deduction?

These are the mathematics courses that are offered at my community college. They also offer an associates in mathematics, which I am curious if I should get before I transfer. However, these are the available mathematics and physics courses. Since I am at a community college, I am curious how...

First, please don't give me too much information or suggest other ways to do it if you think this is not rigorous. This is not supposed to be collaborative. I am asked to prove that n!^{n+1} divides (n^2)!. I thought of a few ways to try to do this, but the first thing I got is the...

[SIZE="5"]The Background: I'm trying to construct a rigorous proof for the divergence theorem, but I'm far from my goal. So far, I have constructed a basic proof, but it is filled with errors, assumptions, non-rigorousness, etc. I want to make it rigorous; in so doing, I will learn how to...

Is there a "rigorous" proof.. -That a "Quantum" of space (a minimum lenght, area or volume for any 4-dimensional Manifold) exist applying Quantum mechanics and GR?..both together or in the "Semi-classical" limit?... - this "Planck lenght" should be obtained directly from math and never...

Well, I'm searching for a rigorous derivation of the famous "perihelium precession problem in General Relativity". Did anyone do it...? Daniel.

Hi: I would like to get a mathematically rigorous "introduction" to QM. Which books would you recommend?

What is the mathematicians modern rigorous definition of number ? thanks Roger