bib.tex

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% \bibitem[Abbot]{Abbot}
%   Edwin Abbott,
%   \emph{Flatland},
%   Dover.

\bibitem[Ackerson]{Monthly55p721}
  R.\ H.\ Ackerson,
  \emph{A Note on Vector Spaces},
  American Mathematical Monthly,
  vol.\ 62 no.\ 10 (Dec.\ 1955),
  p.~721.

% \bibitem[Agnew]{Agnew}
%   Jeanne Agnew,
%   \emph{Explorations in Number Theory},
%   Brooks/Cole,
%   1972.

\bibitem[Am.\ Math.\ Mon., Jun.\ 1931]{Monthly31p355}
  C.\ A.\ Rupp (proposer), H.\ T.\ R.\ Aude (solver),
  problem 3468,
  American Mathematical Monthly,
  vol.\ 37 no.\ 6 (June-July 1931),
  p.~355.

\bibitem[Am.\ Math.\ Mon., Feb.\ 1933]{Monthly33p118}
  V.\ F.\ Ivanoff (proposer), T.\ C.\ Esty (solver),
  problem 3529,
  American Mathematical Monthly,
  vol.\ 39 no.\ 2 (Feb.\ 1933),
  p.~118.

\bibitem[Am.\ Math.\ Mon., Jan.\ 1935]{Monthly35p47}
  W.\ R.\ Ransom (proposer), Hansraj Gupta (solver),
  Elementary problem 105,
  American Mathematical Monthly,
  vol.\ 42 no.\ 1 (Jan. 1935),
  p.~47.

\bibitem[Am.\ Math.\ Mon., Jan.\ 1949]{Monthly49p33}
  C.\ W.\ Trigg (proposer), R.\ J.\ Walker (solver),
  Elementary problem 813,
  American Mathematical Monthly,
  vol.\ 56 no.\ 1 (Jan.\ 1949),
  p.~33.

\bibitem[Am.\ Math.\ Mon., Jun.\ 1949]{Monthly49p409}
  Don Walter (proposer), Alex Tytun (solver),
  Elementary problem 834,
  American Mathematical Monthly,
  vol.\ 56 no.\ 6 (June-July 1949),
  p.~409.

\bibitem[Am.\ Math.\ Mon., Nov.\ 1951]{Monthly51p614}
  Albert Wilansky,
  \emph{The Row-Sums of the Inverse Matrix},
  American Mathematical Monthly,
  vol.\ 58 no.\ 9 (Nov.\ 1951),
  p.~614.

\bibitem[Am.\ Math.\ Mon., Feb.\ 1953]{Monthly53p115}
  Norman Anning (proposer), C.\ W.\ Trigg (solver),
  Elementary problem 1016,
  American Mathematical Monthly,
  vol.\ 60 no.\ 2 (Feb.\ 1953),
  p.~115.

\bibitem[Am.\ Math.\ Mon., Apr.\ 1955]{Monthly55p257}
  Vern Haggett (proposer), F.\ W.\ Saunders (solver),
  Elementary problem 1135,
  American Mathematical Monthly,
  vol.\ 62 no.\ 4 (Apr.\ 1955),
  p.~257.

\bibitem[Am.\ Math.\ Mon., Jan.\ 1963]{Monthly63p93}
  Underwood Dudley, Arnold Lebow (proposers), David Rothman (solver),
  Elementary problem 1151,
  American Mathematical Monthly,
  vol.\ 70 no. 1 (Jan.\ 1963),
  p.~93.

\bibitem[Am.\ Math.\ Mon., Dec.\ 1966]{Monthly66p1114}
  Hans Liebeck,
  \emph{A Proof of the Equality of Column Rank and Row Rank of a Matrix}
  American Mathematical Monthly,
  vol.\ 73 no.\ 10 (Dec.\ 1966),
  p.~1114.

\bibitem[Anton]{Anton}
  Howard Anton,
  \emph{Elementary Linear Algebra},
  John Wiley \& Sons,
  1987.

\bibitem[Arrow]{Arrow}
  Kenneth J.~Arrow,
  \emph{Social Choice and Individual Values},
  Wiley,
  1963.

\bibitem[Austin]{Austin}
  David Austin,
  \emph{How Google Finds Your Needle in the Web's Haystack},
  \url{http://www.ams.org/samplings/feature-column/fcarc-pagerank},
  retrieved Feb.~2012.

\bibitem[Ball \& Coxeter]{Ball}
 W.W.~Rouse Ball,
 \emph{Mathematical Recreations and Essays},
 revised by H.S.M.~Coxeter,
 MacMillan,
 1962.

% \bibitem[Bennett]{Bennett}
%   William J.~Bennett,
%   \emph{Quantifying America's Decline},
%   in
%   \emph{Wall Street Journal},
%   15 March, 1993.

\bibitem[Beck]{Beck}
  Matthias Beck, Ross Geoghegan,
  \emph{The Art of Proof},
  \url{http://math.sfsu.edu/beck/papers/aop.noprint.pdf},
  2011-Aug-08.

\bibitem[Beardon]{Beardon}
  A.F.\ Beardon,
  \emph{The Dimension of the Space of Magic Squares},
  The Mathematical Gazette,
  vol.\ 87, no.\ 508 (Mar.\ 2003), p.~112-114.

\bibitem[Birkhoff \&~MacLane]{BirkhoffMaclane}
  Garrett Birkhoff, Saunders MacLane,
  \emph{Survey of Modern Algebra},
  third edition,
  Macmillan, 
  1965.

\bibitem[Blass~1984]{Blass84}
  A.~Blass,
  \emph{Existence of Bases Implies the Axiom of Choice},
  pp.\ 31\dash 33,
  Axiomatic Set Theory, J.\ E.\ Baumgartner, ed.,
  American Mathematical Society,
  Providence RI, 1984.

\bibitem[Bridgman]{Bridgman}
  P.W.~Bridgman,
  \emph{Dimensional Analysis},
  Yale University Press,
  1931.

\bibitem[Brin \& Page]{BrinPage}
  Sergey Brin and Lawrence Page,
  \emph{The Anatomy of a Large-Scale Hypertextual
        Web Search Engine},
  \url{http://infolab.stanford.edu/pub/papers/google.pdf},
  retrieved Feb.~2012.

\bibitem[Bryan \& Leise]{BryanLeise}
  Kurt Bryan, Tanya Leise,
  \emph{The \$25,000,000,000 Eigenvector: the Linear Algebra Behind Google},
  SIAM Review, 
  Vol.\ 48, no.\ 3 (2006), p.\ 569-81. 

\bibitem[Casey]{Casey}
  John Casey,
  \emph{The Elements of Euclid, Books~I to~VI and~XI},
  ninth edition,
  Hodges, Figgis, and Co.,
  Dublin,
  1890.

\bibitem[ChessMaster]{ChessMaster}
  User ChessMaster of StackOverflow,
  answer to   
  \textit{Python determinant calculation(without the use of external libraries)},
  \url{http://stackoverflow.com/a/10037087/238366},
  answer posted 2012-Apr-05,
  accessed 2012-Jun-18.

\bibitem[Chicken Scheme]{ChickenScheme}
  Free software implementation,
  Felix L. Winkelmann and The Chicken Team,
  \url{http://wiki.call-cc.org/},
  accessed 2013-Nov-20.

\bibitem[Clark \&~Coupe]{BangorRpt}
  David H.\ Clark, John D.\ Coupe,
  \emph{The Bangor Area Economy Its Present and Future},
  report to the city of Bangor ME,
  Mar.\ 1967.

\bibitem[Cleary]{Cleary}
  R.~Cleary,
  private communication,
  Nov.\ 2011.

\bibitem[Clarke]{Clarke}
  Arthur C.~Clarke,
  \emph{Technical Error},
  Fantasy, December 1946,
  reprinted in
  Great SF Stories~8 (1946),
  DAW Books, 1982. 

\bibitem[Con.\ Prob.\ 1955]{ContestProb1955no38}
  \emph{The Contest Problem Book},
  1955 number 38.

\bibitem[Cost Of Tolls]{CostOfTolls}
  \emph{Cost of Tolls},
  \url{http://costoftolls.com/Tolls_in_New_York.html},
  2012-Jan-07.

\bibitem[Coxeter]{Coxeter}
  H.S.M.~Coxeter,
  \emph{Projective Geometry},
  second edition,
  Springer-Verlag, 1974.

\bibitem[Courant \& Robbins]{CourantRobbins}
  Richard Courant, Herbert Robbins,
  \emph{What is Mathematics?},
  Oxford University Press, 1978.

\bibitem[Cullen]{Cullen}
  Charles G.\ Cullen,
  \emph{Matrices and Linear Transformations},
  second edition,
  Dover,
  1990.

\bibitem[Dalal, et.~al.]{Stats}
  Siddhartha R.~Dalal, Edward B.~Fowlkes, \& Bruce Hoadley,
  \emph{Lesson Learned from Challenger: A Statistical Perspective},
  Stats: the Magazine for Students of Statistics,
  Fall 1989,
  p.~3.

\bibitem[Davies]{Davies}
  Thomas D.~Davies,
  \emph{New Evidence Places Peary at the Pole},
  National Geographic Magazine,
  vol.~177 no.~1 (Jan.~1990),
  p.~44.

\bibitem[de Mestre]{deMestre}
  Neville de~Mestre,
  \emph{The Mathematics of Projectiles in Sport},
  Cambridge University Press,
  1990.

\bibitem[De~Parville]{DeParville}
 De~Parville,
 \emph{La~Nature},
 Paris, 1884,
 part~I,
 p.~285\dash 286
 (citation from \cite{Ball}).

% \bibitem[Derksen]{Derksen}
%  H~Derksen,
%  \emph{The Fundamental Theorem of Algebra and Linear Algebra},
%  American Mathematics Monthly,
%  vol.~10 (2003)
%  p.~620-623.

% \bibitem[Duncan]{Duncan}
%   W.J.~Duncan,
%   \emph{Method of Dimensions},
%   in
%   \emph{Encyclopaedic Dictionary of Physics}
%   Macmillan,
%   1962.

\bibitem[Ebbing]{Ebbing}
  Darrell D.~Ebbing,
  \emph{General Chemistry},
  fourth edition,
  Houghton Mifflin,
  1993.

\bibitem[Ebbinghaus]{Ebbinghaus}
  H.\ D.\ Ebbinghaus,
  \emph{Numbers},
  Springer-Verlag,
  1990.

\bibitem[Einstein]{Einstein1911}
  A.~Einstein,
  Annals of Physics,
  v.~35, 1911,
  p.~686.

\bibitem[Eggar]{Eggar}
  M.H.~Eggar,
  \emph{Pinhole Cameras, Perspecitve, and Projective Geometry},
  American Mathematical Monthly,
  August-September 1998,
  p.~618\dash 630.

\bibitem[Falbo]{Falbo}
  Clement Falbo,
  \emph{The Golden Ratio\Dash a Contrary Viewpoint},
  College Mathematics Journal,
  vol.~36, no.~2, March 2005,
  p.~123\dash 134.

\bibitem[Feller]{Feller}
  William Feller,
  \emph{An Introduction to Probability Theory and Its Applications}
  (vol.~1, 3rd~ed.),
  John Wiley, 1968.

% \bibitem[Federal Reserve]{FedReserve}
%   Federal Reserve Bank of Richmond,
%   \emph{FAQs Currency and Coin},
%   \url{http://www.richmondfed.org/faqs/currency/}
%   Jan~2012.

% \bibitem[Finkbeiner]{Finkbeiner}
%   Daniel T.\ Finkbeiner~III,
%   \emph{Introduction to Matrices and Linear Transformations},
%   third edition,
%   W.\ H.\ Freeman and Company,
%   1978.

\bibitem[Fuller \&~Logan]{FullerLogan}
  L.E.~Fuller \& J.D.~Logan,
  \emph{On the Evaluation of Determinants by Chi\`o's Method},
  p~49-52, in Linear Algebra Gems,
  Carlson, et~al,
  Mathematical Association of America,  
  2002.

% \bibitem[Fraleigh \&~Beauregard]{FraleighBeauregard}
%   Fraleigh \& Beauregard,
%   \emph{Linear Algebra}.

\bibitem[Gardner]{Gardner}
  Martin Gardner,
  \emph{The New Ambidextrous Universe},
  third revised edition,
  W.\ H.\ Freeman and Company,
  1990.

\bibitem[Gardner 1957]{Gardner57}
 Martin Gardner,
 \emph{Mathematical Games:~About the remarkable similarity between
   the Icosian Game and the Tower of Hanoi},
 Scientific American,
 May 1957,
 p.~150\dash 154. 

\bibitem[Gardner, 1970]{Gardner70}
  Martin Gardner,
  \emph{Mathematical Games, Some mathematical curiosities embedded in the
        solar system},
  Scientific American,
  April 1970,
  p.~108\dash 112.

\bibitem[Gardner, 1980]{Gardner80}
  Martin Gardner,
  \emph{Mathematical Games, From counting votes to making votes count:
        the mathematics of elections},
  Scientific American,
  October 1980.
%  p.~??-??.

\bibitem[Gardner, 1974]{Gardner74}
  Martin Gardner,
  \emph{Mathematical Games, On the paradoxical situations that arise from
        nontransitive relations},
  Scientific American,
  October 1974.
%  p.~??-125.

\bibitem[Giordano, Wells, Wilde]{Giordano83}
  Frank R.~Giordano,  Michael E.~Wells, Carroll O.~Wilde,
  \emph{Dimensional Analysis}, 
  UMAP Unit 526,
  in
  \emph{UMAP Modules, 1987},
  COMAP,
  1987.

\bibitem[Giordano, Jaye, Weir]{Giordano82}
  Frank R.~Giordano,  Michael J.~Jaye, Maurice D.~Weir,
  \emph{The Use of Dimensional Analysis in Mathematical Modeling}, 
  UMAP Unit 632,
  in
  \emph{UMAP Modules, 1986},
  COMAP,
  1986.

% \bibitem[Glazer]{Glazer}
%   A.M.~Glazer,
%   \emph{The Structure of Crystals},
%   Adam Hilger,
%   1987.

\bibitem[Google Maps]{GoogleMaps}
  \emph{Directions\Dash Google Maps},
  \url{http://maps.google.com/help/maps/directions/},
  2012-Jan-07.

\bibitem[Goult, \emph{et al.}]{Goult}
  R.J.~Goult, R.F.~Hoskins, J.A.~Milner, M.J.~Pratt,
  \emph{Computational Methods in Linear Algebra},
  Wiley,
  1975.

\bibitem[Graham, Knuth, Patashnik]{GrahamKnuthPatashnik}
 Ronald L.~Graham, Donald E.~Knuth, Oren Patashnik,
 \emph{Concrete Mathematics},
 Addison-Wesley,
 1988.

\bibitem[Halmos]{Halmos}
  Paul R.~Halmos,
  \emph{Finite Dimensional Vector Spaces},
  second edition,
  Van Nostrand,
  1958.

% \bibitem[Halmos74]{NaiveSetThy}
%   Paul R.~Halmos,
%   \emph{Naive Set Theory},
%   Springer-Verlag,
%   1974.

\bibitem[Hamming]{Hamming}
  Richard W.\ Hamming,
  \emph{Introduction to Applied Numerical Analysis},
  Hemisphere Publishing,
  1971.

\bibitem[Hanes]{Hanes}
  Kit Hanes,
  \emph{Analytic Projective Geometry and its Applications},
  UMAP Unit 710,
  UMAP Modules, 1990,
  p.~111.

\bibitem[Heath]{Heath}
  T.\ Heath,
  \emph{Euclid's Elements},
  volume 1,
  Dover,
  1956.

\bibitem[Hef{}feron]{Hefferon}
  J~Hef{}feron,
  \emph{Introduction to Proofs, an Inquiry-Based approach},
  \url{http://joshua.smcvt.edu/proofs/},
  2013.

\bibitem[Hoffman \&~Kunze]{HoffmanKunze}
  Kenneth Hoffman, Ray Kunze,
  \emph{Linear Algebra},
  second edition,
  Prentice-Hall,
  1971.

\bibitem[Hofstadter]{Hofstadter}
 Douglas R.~Hofstadter,
 \emph{Metamagical Themas:~Questing for the Essence of Mind and Pattern},
 Basic Books,
 1985.

\bibitem[Iosifescu]{Iosifescu}
  Marius Iofescu,
  \emph{Finite Markov Processes and Their Applications},
  John Wiley, 1980.

\bibitem[joriki]{joriki}
  Mathematics Stack Exchange user joriki,
  \url{http://math.stackexchange.com/a/118914/205168},
  2012.

\bibitem[Kahan]{Kahan}
  William Kahan,
  \emph{Chi\`’s Trick  for  Linear Equations  with  Integer Coefficients},
  \url{http://www.cs.berkeley.edu/~wkahan/MathH110/chio.pdf}, 1998,
  retrieved 2012-Jun-18.

\bibitem[Kelton]{Kelton}
  Christina M.L.~Kelton,
  \emph{Trends on the Relocation of U.S.\ Manufacturing},
  UMI Research Press, 1983.

\bibitem[Kemeny \& Snell]{KemenySnell}
  John G.~Kemeny, J.~Laurie Snell,
  \emph{Finite Markov Chains},
  D.~Van Nostrand, 1960.

\bibitem[Kemp]{Kemp}
  Franklin Kemp
  \emph{Linear Equations},
  American Mathematical Monthly,
  volume 89 number 8 (Oct.\ 1982),
  p.~608.

% \bibitem[Knuth]{Knuth}                %Verify!!!
%   Donald E.~Knuth,
%   \emph{The Art of Computer Programming},
%   Addison Wesley,
%   1988.     

% \bibitem[Lang]{Lang}
%   Serge Lang,
%   \emph{Linear Algebra},
%   Addison-Wesley,
%   1966.

\bibitem[Leontief 1951]{Leontief1951}
  Wassily W.\ Leontief,
  \emph{Input-Output Economics},
  Scientific American,
  volume 185 number 4 (Oct.\ 1951),
  p.~15. 

\bibitem[Leontief 1965]{Leontief1965}
  Wassily W.\ Leontief,
  \emph{The Structure of the U.S.\ Economy},
  Scientific American,
  volume 212 number 4 (Apr.\ 1965),
  p.~25. 

% \bibitem[Lieberman]{Lieberman}
%   David Lieberman,
%   \emph{The Big Bucks Ad Battles Over TV's Most Expensive Minutes},
%   TV Guide,
%   Jan.\ 26 1991,
%   p.~11.

\bibitem[Macdonald \& Ridge]{MacdonaldRidge}
  Kenneth Macdonald, John Ridge,
  \emph{Social Mobility},
  in \emph{British Social Trends Since 1900},
  A.H.~Halsey,
  Macmillian, 1988.

% \bibitem[Macmillan Dictionary]{MacmillanDict}
%   William D.~Halsey,
%   Macmillan, 1979.

\bibitem[Math.\ Mag., Sept.\ 1952]{MathMag52p48}
  Dewey Duncan (proposer), W.\ H.\ Quelch (solver),
  Mathematics Magazine,
  volume 26 number 1 (Sept-Oct.\ 1952),
  p.~48.

\bibitem[Math.\ Mag., Jan.\ 1957]{MathMag57p173}
  M.\ S.\ Klamkin (proposer),
  Trickie T-27,
  Mathematics Magazine,
  volume 30 number 3 (Jan-Feb.\ 1957),
  p.~173.

\bibitem[Math.\ Mag., Jan.\ 1963, Q237]{MathMag63Q237}
  D.\ L.\ Silverman (proposer), C.\ W.\ Trigg (solver),
  Quickie 237,
  Mathematics Magazine,
  volume 36 number 1 (Jan.\ 1963).

\bibitem[Math.\ Mag., Jan.\ 1963, Q307]{MathMag63Q307}
  C.\ W.\ Trigg (proposer).
  Quickie 307,
  Mathematics Magazine,
  volume 36 number 1 (Jan.\ 1963),
  p.~77.

\bibitem[Math.\ Mag., Nov.\ 1967]{MathMag67p232}
  Clarence C.\ Morrison (proposer),
  Quickie,
  Mathematics Magazine,
  volume 40 number 4 (Nov.\ 1967),
  p.~232.

\bibitem[Math.\ Mag., Jan.\ 1973]{MathMag73p286}
  Marvin Bittinger (proposer),
  Quickie 578,
  Mathematics Magazine,
  volume 46 number 5 (Jan.\ 1973),
  p.~286, 296.

\bibitem[Munkres]{Munkres}
  James R.\ Munkres,
  \emph{Elementary Linear Algebra},
  Addison-Wesley,
  1964.

\bibitem[Neimi \&~Riker]{NeimiRiker}
  Richard G.~Neimi, William H.~Riker,
  \emph{The Choice of Voting Systems},
  Scientific American,
  June 1976,
  p.~21\dash 27.

% \bibitem[Nering]{Nering}
%   Evar D. Nering,
%   \emph{Linear Algebra and Matrix Theory},
%   second edition,
%   John Wiley,
%   1970.

% \bibitem[Niven \&~Zuckerman]{Niven}
%   I.\ Niven, H.\ Zuckerman,
%   \emph{An Introduction to the Theory of Numbers},
%   third edition,
%   John Wiley,
%   1972.

\bibitem[Oakley \&~Baker]{Oakley}
  Cletus O.\ Oakley, Justine C.\ Baker,
  \emph{Least Squares and the $3:40$ Mile},
  Mathematics Teacher,
  Apr.\ 1977.

\bibitem[Ohanian]{Ohanian}
  Hans O'Hanian,
  \emph{Physics},
  volume one,
  W.\ W.\ Norton,
  1985.

\bibitem[Onan]{Onan}
  Michael Onan,
  \emph{Linear Algebra},
  Harcourt,
  1990.

\bibitem[Online Encyclopedia of Integer Sequences]{OnlineEncyclopedia}
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  2012-Feb-17.

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  G.\ M.\ Petersen,
  \emph{Area of a Triangle},
  American Mathematical Monthly,
  volume 62 number 4 (Apr.\ 1955),
  p.~249.

\bibitem[Polya]{MathematicsPlausReason}
  G. Polya,
  \emph{Mathematics and Plausible Reasoning},
  Princeton University Press,
  1954.

\bibitem[Poundstone]{GamingVote}
  W. Poundstone,
  \emph{Gaming the Vote},
  Hill and Wang, 2008.
  ISBN-13: 978-0-8090-4893-9 

% \bibitem[Programmer's Ref.]{MicroProgRef}
%   \emph{Microsoft Programmers Reference}
%   Microsoft Press.

% \bibitem[Putnam, 1988, A-6]{Putnam88}
%   William Lowell Putnam Mathematical Competition,
%   Problem A-6, 1988,
%   solution: American Mathematical Monthly, 
%   volume 96 number 8 (Oct. 1989),
%   p.~688.

\bibitem[Putnam, 1990, A-5]{Putnam90A5}
  William Lowell Putnam Mathematical Competition,
  Problem A-5, 1990.

\bibitem[Rice]{Rice}
  John R.\ Rice,
  \emph{Numerical Mathods, Software, and Analysis},
  second edition,
  Academic Press,
  1993.

% \bibitem[Quine]{Quine}
%   W.\ V.\ Quine,
%   \emph{Methods of Logic},
%   fourth edition,
%   Harvard University Press,
%   1982.

\bibitem[Rucker]{Rucker}
  Rudy Rucker,
  \emph{Infinity and the Mind},
  Birkhauser,
  1982.

\bibitem[Ryan]{Ryan}
  Patrick J.~Ryan,
  \emph{Euclidean and Non-Euclidean Geometry: an Analytic Approach},
  Cambridge University Press, 1986.

\bibitem[Sandifer]{Sandifer}
  Ed Sandifer,
  \textit{How Euler Did It},
  \url{http://www.maa.org/news/howeulerdidit.html},
  2012-Dec-27.

\bibitem[Schmidt]{SchmidtSO}
  Jack Schmidt, % (\url{http://math.stackexchange.com/users/583/jack-schmidt}),
  \url{http://math.stackexchange.com/a/98558/12012}, 
  2012-Jan-12.

\bibitem[Shepelev]{Shepelev}
  Anton Shepelev,
  private communication,
  Feb~19, 2011.

\bibitem[Seidenberg]{Seidenberg}
  A.~Seidenberg,
  \emph{Lectures in Projective Geometry},
  Van Nostrand, 1962.

% \bibitem[Smith]{Smith}
%   Larry Smith,
%   \emph{Linear Algebra},
%   second edition,
%   Springer-Verlag,
%   1984.

\bibitem[Strang 93]{Strang93}
  Gilbert Strang
  \emph{The Fundamental Theorem of Linear Algebra},
  American Mathematical Monthly,
  Nov.~1993, p.~848\dash 855.

\bibitem[Strang 80]{Strang}
  Gilbert Strang,
  \emph{Linear Algebra and its Applications},
  second edition,
  Harcourt Brace Jovanovich,
  1980.

\bibitem[Taylor]{Taylor}
  Alan D.~Taylor,
  \emph{Mathematics and Politics: Strategy, Voting, Power, and Proof},
  Springer-Verlag,
  1995.

\bibitem[Tilley]{Tilley}
  Burt Tilley,
  private communication,
  1996.

\bibitem[Trono]{Trono}
  Tony Trono, compiler,
  \emph{University of Vermont Mathematics Department High School Prize
    Examinations 1958-1991},
  mimeographed printing, 1991.

\bibitem[USSR\ Olympiad no.\ 174]{USSROlympiad174}
  \emph{The USSR Mathematics Olympiad},
   number 174.

\bibitem[Velleman]{Velleman}
  Dan Velleman,
  private communication, on multiset in the definition of
  linearly independent set.

\bibitem[Velleman2]{HowToProveIt}
  Daniel J Velleman,
  \textit{How to Prove It: A Structured Approach},
  Cambridge University Press,
  2006.

\bibitem[Weston]{Weston59}
  J.~D.\ Weston,
  \emph{Volume in Vector Spaces},
  American Mathematical Monthly,
  volume 66 number 7 (Aug./Sept.\ 1959),
  p.~575\dash 577.

\bibitem[Ward]{Ward}
  James E.\ Ward~III,
  \emph{Vector Spaces of Magic Squares},
  Mathematics Magazine,
  vol~53 no~2 (Mar~1980),
  p~108\dash 111.

\bibitem[Weyl]{Weyl}
  Hermann Weyl,
  \emph{Symmetry},
  Princeton University Press,
  1952.

\bibitem[Wickens]{Wickens}
  Thomas D.~Wickens,
  \emph{Models for Behavior},
  W.H.~Freeman,
  1982.

\bibitem[Wilkinson 1965]{Wilkinson65}
  \emph{The Algebraic Eigenvalue Problem},
  J.~H.~Wilkinson,
  Oxford University Press,
  1965

\bibitem[Wikipedia, Lo~Shu Square]{WikipediaLoShuSquare}
  \emph{Lo~Shu Square},
  \url{http://en.wikipedia.org/wiki/Lo_Shu_Square},
  2012-Feb-17.

\bibitem[Wikipedia, Magic Square]{WikipediaMagicSquare}
  \emph{Magic square},
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  2012-Feb-17.

\bibitem[Wikipedia, Mens Mile]{WikipediaMensMile}
  \emph{Mile run world record progression},
  \url{http://en.wikipedia.org/wiki/Mile_run_world_record_progression},
  2011-Apr-09.

\bibitem[Wikipedia, Square-cube Law]{Wikipedia}
  \emph{The Square-cube law},
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\bibitem[Wikipedia, Google Page Rank]{WikipediaPageRank}
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  2012-Feb-27.

\bibitem[Wills]{Wills}
  Rebecca S.~Wills,
  \emph{Google's Page Rank},
  Mathematical Intelligencer,
  vol.~28, no.~4, Fall~2006.

\bibitem[Wohascum no.\ 2]{Wohascum2}
  \emph{The Wohascum County Problem Book}
  problem number 2.

\bibitem[Wohascum no.\ 47]{Wohascum47}
  \emph{The Wohascum County Problem Book}
  problem number 47.

\bibitem[Yaglom]{Yaglom}
  I.\ M.~Yaglom,
  \emph{Felix Klein and Sophus Lie: Evolution of the Idea of
   Symmetry in the Nineteenth Century},
  translated by Sergei Sossinsky,
  Birkh\"auser,
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\bibitem[Yuster]{Yuster}
  Thomas Yuster,
  \emph{The Reduced Row Echelon Form of a Matrix is Unique: a Simple Proof},
  Mathematics Magazine,
  vol.~57, no.~2 (Mar.~1984),
  pp.~93-94.

\bibitem[Zwicker]{Zwicker}
  William S.~Zwicker,
  \emph{The Voters' Paradox, Spin, and the Borda Count},
  Mathematical Social Sciences,
  vol.~22 (1991),
  p.~187\dash 227. 

\end{thebibliography}