Bibliography

Tord M. Johnson

May 9, 2021

Notes on the Exercies

Primary: knuth1963 [Knu63], leveque1956 [LeV56, chapter 3], ribenboim1979 [Rib79], wiles1995 [Wil95]; Secondary: bell1990 [Bel90], euclid2006 [Euc06], gauss1965 [Gau65], heath2008 [Hea08], singh1998 [Sin98].

1.1 Algorithms

Primary: floyd1994 [FB94, chapter 3.3], markov1954 [Mar54], markov1988 [MN88], zemanek1981 [Zem81]. Secondary: church1985 [Chu85], church1996 [Chu96], church2019 [Chu19], copeland2004 [Cop04], copeland2013 [CPS13], davis2004 [Dav04], godel2001a [Göd01a], godel2001b [Göd01b], godel2001c [Göd01c], godel2013a [Göd13a], godel2013b [Göd13b], hoare1972 [HA72], hofstadter1999 [Hof99], kleene2012 [Kle12], vanheijenoort2002 [vH02], whitehead2011 [WR11].

1.2 Mathematical Preliminaries

Primary: graham1994 [GKP94].

1.2.1 Mathematical Induction

Primary: bussey1917 [Bus17], cajori1918 [Caj18], conway1996 [CG96, chapter 2], dijkstra1975 [Dij75], dijkstra1976 [Dij76], floyd1967 [Flo67], floyd1972 [Flo72], gardner1986 [Gar86, chapter 16], golomb1965 [Gol65], hardy1999 [Har99, chapters 6, 8], henkin1960 [Hen60], hoare1971 [Hoa71], king1972 [Kin72], morris1984 [MJ84], naur1966 [Nau66], polya1954 [Pól54, chapter 7], rashed1972 [Ras72], sduk1838 [Soc38, pp. 465–466], turing1949 [Tur49], vonneumann1963 [vN63, pp. 91–99]. Secondary: conway2001 [Con01], fraleigh2002 [Fra02], hardy2008 [HW08].

1.2.2 Numbers, Powers, and Logarithms

Primary: cajori1913a [Caj13a], cajori1913b [Caj13b], cajori1913c [Caj13c], cajori1913d [Caj13d], cajori1913e [Caj13e], cajori1913f [Caj13f], cajori1913g [Caj13g], chen1972 [Che72], linskii1957 [Lin57], knuth1986d [Knu86c, § 120–147], meggitt1962 [Meg62], meggitt1963 [Meg63]. Secondary: feynman1999 [Fey99], hamming1997 [Ham97], hey2002 [Hey02], knuth1986a [Knu86e], knuth1986b [Knu86d], knuth1986c [Knu86b], knuth1986e [Knu86a].

1.2.3 Sums and Products

Primary: apostol1974 [Apo74, 1st edition: chapter 12; or 2nd edition: chapter 8], binet1813 [Bin13], cauchy1815 [Cau15], cauchy1841 [Cau41], chebyshev1882 [Che82], demoivre1738 [dM38, pp. 197–199], euler1827a [Eul27a, § 1169], knuth1992 [Knu92], krattenthaler1990 [Kra90], sylvester1857 [Syl57], todd1961 [Tod61], waring1779 [War79]. Secondary: cauchy1840 [Cau40, pp. 151–159], cauchy1844 [Cau44], cauchy1847 [Cau47], euler1824 [Eul24], euler1827b [Eul27b], euler1845 [Eul45], krattenthaler1988 [Kra88], livio2003 [Liv03].

1.2.4 Integer Functions and Elementary Number Theory

Primary: busche1909 [Bus09], eisele1990 [EH90], eisenstein1844 [Eis44], hamel1905 [Ham05], hermite1884 [Her84], mordell1958 [Mor58], yoder1975 [Yod75].

1.2.5 Permutations and Factorials

Primary: arbogast1800 [Arb00, § 52], capelli1893 [Cap93], davis1959 [Dav59], dutka1984 [Dut84], faadibruno1857 [dB57], good1961 [Goo61], hankel1864 [Han64], knopp1951 [Kno51, pp. 518–520, 527, 534], kramp1808 [Kra08, p. 219], legendre1808 [Leg08, p. 8], stirling1753 [Sti53, p. 137], struik1969 [Str69, pp. 244–253], toscano1939 [Tos39], uhler1955 [Uhl55], wall1938 [Wal38]. Secondary: euler1729 [Eul29], hermite1917 [Her17, proof of 1900, pp. 529–543], kramp1801 [Kra01], shanks1962 [SW62], smith1958a [Smi58a], smith1958b [Smi58b], stickelberger1890 [Sti90], tweddle2003 [Twe03], vacca1899 [Vac99], waring1782 [War82, 1st edition: p. 218; or 3rd edition: p. 380], weeks1991 [Wee91].

1.2.6 Binomial Coefficients

Primary: abel1826a [Abe26a], barton1960 [BDM60], barton1963 [BDM63], cauchy1843 [Cau43], chakravarti1932 [Cha32], demoivre1730 [dM30, p. 101], diaconis1991 [DZ91], dickson1902 [Dic02], dixon1891 [Dix91], dixon1903 [Dix03], dougall1907 [Dou07], dutka1984 [Dut84], euler1774 [Eul74], fine1947 [Fin47], fostemann1835 [Fös35], gasper1990 [GR90], gauss1813 [Gau13], gauss1808 [Gau08], gould1956 [Gou56], gould1962 [SMG62, p. 572], gould1966 [GK66], graham1994 [GKP94, § 5.5, 5.6, 5.8, 6.1, 6.2, 6.5; exercises 5.75, 5.83, 5.106, 6.57], heine1847 [Hei47], hui1407 [Hui07, chapter 16,344], hurwitz1902 [Hur02], hwang1995 [Hwa95], jacobi1846 [Jac46], karamata1935 [Kar35], knuth1971 [Knu71], knuth1989 [KW89], knuth1992 [Knu92, pp. 403–422; pp. 410–422], kramp1808 [Kra08, p. 359], kummer1852 [Kum52], lovasz1993 [Lov93, problem 13.31], lucas1878b [Luc78b, pp. 229–230], macmahon1902 [Mac02], mahavira1912 [Mah12, chapter 6], moser1958a [MW58b], moser1958b [MW58a], needham1959 [Nee59, pp. 138-139], newton1676a [New76a], newton1676b [New76b], pascal1665 [Pas65], pascal1887 [Pas87], patwardhan2006 [PNS06, § CXX, CXXII], petkovsek1996 [PWZ96], pfaff1797 [Pfa97, pp. 38–57], pingala1874 [Piṅ74], poincare1896 [Poi96, pp. 56-60], ramshaw1977 [Ram77], ramus1834 [Ram34], redheffer1996 [Red96], rogers1895 [Rog95, pp. 15–32; § 8], rothe1793 [Rot93], rothe1811 [Rot11, p. xxix], scherk1828 [Sch28], schweins1820 [Sch20, § 151], stirling1753 [Sti53], temme1993 [Tem93], torelli1895 [Tor95], vandermonde1772 [Van72], vonettingshausen1826 [vE26, § 31], wilf1993 [Wil93]. Secondary: alder2002 [Ald02], logan1987 [Log87], lucas1878a [Luc78a], lucas1878c [Luc78c], needham1954 [Nee54], needham1956 [Nee56].

1.2.7 Harmonic Numbers

Primary: cullen2007 [Cul07], euler1734 [Eul34], gould1961 [Gou61], graham1994 [GKP94, § 6.5], hardy2008 [HW08, section 7.8], klamkin1962 [KKWvL62], nanjundiah1963 [Nan63], selfridge1960 [SS60]. Secondary: waring1782 [War82, 2nd edition: p. 383].

1.2.8 Fibonacci Numbers

Primary: bergman1957 [Ber57], bernoulli1728 [Ber28, § 7], boncampagni1857 [Bon57, pp. 283–285], conway1996 [CG96, pp. 113–126], cook1979 [Coo79, p. 420], coxeter1953 [Cox53], demoivre1722 [dM22], dickson2005a [Dic05a, chapter 17], gardner1961 [Gar61, chapter 8], graham1994 [GKP94, § 6.6], jarden1966 [Jar66, pp. 30–33], kepler1608 [Kep08], kepler2014 [Kep14, p. 21], klarner1968 [Kla68], lekkerkerker1952 [Lek52], lucas1878b [Luc78b, pp. 201–204], markowsky1992 [Mar92], pisano1202 [Pis02], riordan1962 [Rio62], schreiber1995 [Sch95], singh1985 [Sin85], stolarsky1976 [Sto76], schwenk1970 [Sch70], whinihan1963 [Whi63]. Secondary: bernoulliiii1771 [III72], boncampagni1862 [Bon62], cooper1995 [CK95], dickson2005b [Dic05b], dickson2005c [Dic05c], frey1947 [Fre47, pp. 705–706], gardner2008a [Gar08b, chapter 8], gardner2008b [Gar08a], gardner2009 [Gar09], gardner2014 [Gar14], jacob1565 [Jac65], jarden1949 [JM49], kepler1955 [Kep55, pp. 154–165,429] leger1837 [Lég37], lucas1876a [Luc76a], lucas1876b [Luc76b], markov1882 [Mar82], matiyasevich1993 [Mat93], shallit1994 [Sha94], sigler2003 [Pis03, pp. 404–405], vorobev2002 [Vor02], zeckendorf1972 [Zec72].

1.2.9 Generating Functions

Primary: demoivre1722 [dM22], stirling1753 [Sti53, proposition 15], euler1741 [Eul41], euler1750 [Eul50], laplace1814 [Lap14], bell1923 [Bel23], niven1969 [Niv69], henrici1974 [Hen74, chapter 1], zave1976 [Zav76], spiess1990 [Spi90], cauchy1826 [Cau26, pp. 95–113], polya1956 [Pól56], graham1994 [GKP94, chatper 7], wilf2006 [Wil06], polya1954 [Pól54, chapter 6], newton1707 [New07], struik1969 [Str69, pp. 94–95], girard1629 [Gir29], gauss1813 [Gau13, § 33, Eq. [75]], abel1826b [Abe26b, pp. 314–315], knopp1956 [Kno56], carlitz1965 [Car65], egorychev1977 [Ego77], knuth1994 [Knu94]. Secondary: henrici1977 [Hen77], henrici1986 [Hen86], knopp1951 [Kno51, section 66], polya1945 [Pól45], richter1949 [Ric49].

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