29 October 2004

Question about circular motion and general relativity

Editor:

I have a question about circular motion and how general relativity applies.  Assume I am on the earth and observe a very distant celestial object. Then 24 hours later I observe the same object in approximately the same location in the sky.  Furthermore, I choose my location on the earth as the stationary inertial frame of reference. Then if twice the distance of the observed object times pi is such that the object would have to have traveled in excess of the speed of light to be observed in the same location, my question is how do you reconcile this with General Relativity?

If you feel this is a reasonable question, I would appreciate any comments you wish to make.

Sincerely yours,

Farris Mitchell

Readers, can you answer Mr. Mitchell's question? Send replies to Backscatter. Enter "Relativity question" in the subject line. Editor.  

Follow up to Hrabovsky's "Mathematics Corner"

Editor,

I noticed George E. Hrabovsky is resurrecting his "Mathematics Corner" column ["The Return of the Mathematics Corner," 15 October 2004.] His column included a list of books that can be used as reference/learning material. I have attached an HTML page that contains URLs to all the online references I could find using a Google search only. Please add or correct as you see fit.

Some of the notes/papers/books are in PostScript (ps) format while most are pdf. Those who want the ps version and run Windows can use ghostscript and ghostview, http://www.ghostscript.com/ (ghostview is further down the page).

Milton Whitham

George E. Hrabovsky has expressed his appreciation for your important contribution to his column. The hotlinked URL's you sent are given below. Editor.

GENERAL MATHEMATICS REFERENCE BOOKS
Planetmath   Encyclopedia
Mathworld   Encyclopedia
Wikipedia   Encyclopedia
There are hundreds of encyclopedias. Many are topical, e.g., topology; some are sparse, but the info you want is probably there.

TRANSITIONAL MATHEMATICS
Garrity, "All the Mathematics You Missed"   status: Now published.
Gallier,    Algebra and Analysis for Computer Science
Sean Mauch,    Introduction to Methods of Applied Mathematics or Advanced Mathematical Methods for Scientists and Engineers

LINEAR ALGEBRA
David Santos, "Linear Algebra"   status: Not found
Jim Carrel, "Basic Concepts of Linear Algebra"   status: Not found.
Autar Kaw,    Introduction to Matrix Algebra

COMBINATORICS
Chen,    Discrete Mathematics
Marcel Finan, Lecture Notes on Discrete Mathematics
Lovasz and Vestergombi, "Discrete Mathematics"   status: published.

ORDINARY DIFFERENTIAL EQUATIONS
Adkins and Davidson, "Ordinary Differential Equations"   status: Not available; LSU authorized only.
Kutz,    Introduction to Differential Equations-Notes
and
Introduction to Differential Equations (.PDF)

ADVANCED CALCULUS
Goursat, "A Course in Mathematical Analysis"   status: published.
Hardy, "A Course in Pure Mathematics"   status: published.
Whittaker and Watson, "A Course in Modern Analysis"   status: published.
Chen,    Fundamentals of Analysis
Wilde,    Analysis: An Introductory Course (.PDF)
Shlomo Sternburg,    Advanced Calculus (58MB)

ABSTRACT ALGEBRA
Clark,    Elementary Abstract Algebra
Arapura,    Abstract Algebra Done Concretely (.PDF)
Marcel Finan, "Modern Algebra"   status: Not found
Garrett,    Intro Abstract Algebra
Connell,    Elements of Abstract and Linear Algebra (.PDF)

GEOMETRY
David Hilbert, "Foundations of Geometry"   status: published, $100, might use encyclopedias to determine the Riemann conjecture about zeta/primes for first lesson/problem.

TOPOLOGY
Viro, Ivanov, Netsvetaev, and Kharlamov,    Elementary Topology: A First Course Textbook in Problems

DIFFERENTIAL GEOMETRY
Lee,    Differential Geometry, Analysis, and Physics
Koch, "Mathematics 433/533: Class Notes"   status: Not found.
Moore, "Lecture Notes on Curves and Surfaces for Mathematics 147AB"   status: Not found.
Michor,    Topics in Differential Geometry
Shifrin,    Differential Geometry: A First Course in Curves and Surfaces

REAL ANALYSIS
Simms, "Analysis"   status: Insufficient unique search identifiers
Hunter and Nachtergaele "Applied Analysis"   status: Published.
Faris,    Real Analysis: Part I (.PDF)
Faris,    Real Analysis: Part II (.PDF)
Kuttler,    Basic Analysis (.PDF)

COMPLEX ANALYSIS
Cain,    Complex Analysis (.PDF)
Ash and Novinger, Complex Variables

FOURIER ANALYSIS
Miller,    Topics in Harmonic Analysis with Applications to Radar and Sonar
Thiele,    Classical Fourier Analysis
Brown,    Lecture Notes: Harmonic Analysis (.PDF)
Axler, Bourdon, and Ramey,    Harmonic Function Theory (.PDF)

FUNCTIONAL ANALYSIS
Abbas,    Functional Analysis (.PDF)
Hille and Phillips,    Functional Analysis and Semi-Groups (.PDF)
Chen,    Linear Functional Analysis
Angenent, "Math 725 Lecture Notes"   status: Not found.

PARTIAL DIFFERENTIAL EQUATIONS
Birnir,    Elementary Partial Differential Equations and Applications (.PDF)
Showalter,    Hilbert Space Methods for Partial Differential Equations (.PDF)
Herod,    An Introduction to Partial Differential Equations (.PDF)

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