What is Rigorous: Definition and 160 Discussions

Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. Rigour frequently refers to a process of adhering absolutely to certain constraints, or the practice of maintaining strict consistency with certain predefined parameters. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as mathematical proofs which must maintain consistent answers; or socially imposed, such as the process of defining ethics and law.

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  1. G

    Most rigorous chemistry course?

    Hi all, I am currently a sophomore chemical engineering major. The focus of the program at my school is definitely practical; we do not go very in detail about the mathematics behind the equations given to us. I enjoy knowing where the equations I am using come from. Some of the things I am...
  2. C

    Is math suppose to be rigorous?

    Is math suppose to be rigorous? I love it and I hate it. Is this right? So far I'm in trig, I'm struggling a bit. Is math suppose to be tough, do you have to work at it everyday and study for 4 to 5 hrs or does it come easy to you? Please share. Thanks..
  3. W

    The Well-Known Result: Rigorous or Not?

    it is a well known result, but it is a rigorious result or not?
  4. L

    Improving Mathematical Proof Writing: Tips and Strategies for Physics Majors

    Looking for a little advice regarding proving things in mathematical way. I am a physics major currently taking a math methods course where we are asked to prove things, basically for the time in my schooling career. Sometimes I have trouble formulating a mathematically rigorous way of...
  5. strangerep

    Rigorous treatments of double-slit , quantum eraser, etc.

    From a recent double-slit thread: Thank you for mentioning those papers! (Probably, I didn't notice the earlier mentions because I hardly ever read the endless "double-slit" threads. :-) The Fourier transform method occurred to me a while back as possibly a better way of deriving this...
  6. Z

    Searching for a Rigorous Geometry Book

    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.
  7. A

    Advice for second rigorous book on linear algebra

    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...
  8. R

    Rigorous Introductory physics textbook

    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...
  9. A

    Rigorous statement of virtual work principle?

    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.
  10. V

    Suggestions for a Rigorous Multivariate Calculus Book

    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...
  11. N

    Rigorous definition of a limit

    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...
  12. T

    Polyhedron Face Angles: Intuitive & Rigorous Explanation for Beginners

    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...
  13. J

    Rigorous precalculus text needed

    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...
  14. C

    How to Self Study Rigorous Texts?

    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...
  15. J

    The most rigorous relativity text is ?

    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...
  16. P

    A mathematically rigorous treatment of adiabatic processes?

    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...
  17. K

    Rigorous proof of limits of sequences (3)

    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...
  18. K

    Rigorous proof of limits of sequences (2)

    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...
  19. K

    Rigorous proof of limits of sequences

    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...
  20. 1

    Searching for a more rigorous math book for Physics.

    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...
  21. J

    Seeking a Rigorous Treatment of Statistical Thermodynamics

    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?
  22. M

    Seeking recommendation for rigorous general chemistry textbook

    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...
  23. DarMM

    Rigorous Quantum Field Theory.

    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...
  24. L

    Schools Accelerated, rigorous courses for college credit

    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...
  25. R

    Mathematically rigorous physics books

    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?
  26. R

    How to write a mathematically rigorous definition of completeness

    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
  27. E

    Proving 0x = 0: A Rigorous Proof and Its Correctness

    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...
  28. L

    Academic concerns. how rigorous should it be

    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.
  29. C

    A rigorous calculus self-study

    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...
  30. A

    What are the intellectually MOST rigorous jobs?

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

    How Do You Give a Rigorous Proof for Fraction Multiplication?

    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}
  32. B

    Most rigorous pure math textbooks

    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...
  33. M

    Rigorous statistical thermodynamics?

    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...
  34. K

    Rigorous Coupled Wave Analisys - help

    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...
  35. R

    Any other recommendations for rigorous DE and PDE books?

    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
  36. K

    Rigorous book for multivariable + vector calc?

    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...
  37. M

    What makes the second argument in Schaum's Outline Calculus more rigorous?

    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) =...
  38. T

    Rigorous Intro to analysis/calculus

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

    Can someone tell me if this is rigorous enough?

    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...
  40. S

    Rigorous proof of basic absolute value theorem?

    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...
  41. E

    Attempt at a rigorous (dis)proof of uniform convergence

    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 =...
  42. W

    Rigorous Economics for First Year University Students

    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...
  43. A

    Is Apostol's Calculus rigorous enough for my level of understanding?

    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...
  44. blindconsole

    What classes are needed for a rigorous understanding of quantum mechanics?

    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?
  45. Δ

    Mathematica Rigorous physical/mathematical proof of relativity of certain aspects of S.R.

    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)...
  46. P

    Really good (and rigorous) electronics text?

    I took two semesters of circuit analysis, two semesters of electronics, two semeters of digital electronics, a semester of optoelectronics, and a semester of solid state electronics. I have a pretty strong background in solid state electronics, opto, digital, and circuits, but I feel like my...
  47. P

    Rigorous treament of differentials?

    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...
  48. C

    What does it mean to be 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?
  49. C

    Rigorous Determination of Bosonic and fermoinic commutation relation

    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?
  50. C

    Courses How rigorous do these courses look?

    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...
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