Σ Reference

bigΨ · ref 4
updated: 2013-12-6

Σ.4. Library of Links

The mathematical literature and webpages we've consulted and recommend for further reading. To show more library items, select the page extension option -- or ++ in the control form on the top left.
The items are marked as:

  • Introductory information, suitable for an interested amateur
  • Professional books and articles, comprehensive or ground breaking, dry
  • Online sources – our earlier webpages are meant for inspiration only
  • Entertainment and fiction, religious and philosophical sources

σ.4.1. Big number news, art & fun

σ.4.2. Home grown Big numbers

σ.4.3. Big numbers on the web

σ.4.4. Big numbers on paper

  • Wilhelm Ackermann "On Hilbert's construction of the real numbers" 1928
    in Jean van Heijenoort's source book "From Frege to Gödel" 1967
  • Archimedes "The Sand Reckoner" annotated by James R. Newman, 1956
    from: "The works of Archimedes" 3d century BC, by Th. Heath 1897
    also in: Hutchins "Great Books of the Western World, vol.11" 1952
  • Brian Clegg "A brief history of Infinity" 2003
  • John H. Conway, Richard K. Guy "The Book of Numbers" 1996, pp.59-62
  • R. Crandell, C. Pomerance "Prime Numbers, a computational perspective" 2005
  • Philip J. Davis "The lore of large numbers" 1961
  • Martin Gardner "Mathematical Games" 1977, on Graham's number
  • R.L. Graham, B.L. Rothschild "Ramsey's Theorem for n-Parameter Sets" 1971
  • Bhikshu Jin Yong "How Large is One Asamkhyeya?" Nov. 2008
  • Edward Kasner, James R. Newman "New Names for Old" 1940
    in James R. Newman "The world of mathematics, vol.3" 1956, p.2009
  • Donald Knuth "Mathematics and Computer Science: Coping with Finiteness" 1976
    in Campbell, Higgins "Mathematics people problems results, vol.2" 1984, pp.210-211
  • David Wells "The Penguin Dictionary of Curious and Interesting Numbers" 1997

σ.4.5. Recursion theory

  • C.J. Ash, J.F. Knight "Computable Structures and the Hyperarithmetical Hierarchy" 2000
  • Gregory Chaitin "Meta Maths, the quest for omega" 2005
  • P. Clote, J.B. Remmel, ed. "Feasible Mathematics II" 1995
  • Ershov, Goncharov, Nerode, Remmel "Handbook of Recursive Mathematics"
    vol.1 "Recursive model theory" 1998
    vol.2 "Recursive algebra, analysis and combinatorics" 1998
  • M.C. Fitting "Fundamentals of Generalized Recursion Theory" 1981
  • R.L. Goodstein "Recursive Number Theory" 1957
  • Edward R. Griffor, ed. "Handbook of Computability Theory" 1999
  • Andrzej Grzegorczyk "Some classes of recursive functions" 1953
  • Peter G. Hinman "Recursion-Theoretic Hierarchies" 1978
  • A.I. Mal'cev "Algorithms and recursive functions" 1970
  • Dag Normann "Recursion on the countable functionals" 1980
  • Piergiorgio Odifreddi "Classical Recursion Theory" 1989
    and his "Classical Recursion Theory Volume II" 1999
  • Rózsa Péter "Recursive Functions" 1967, 3d ed. (1st ed. German 1951)
  • H. Rogers "Theory of recursive functions and effective computability" 1967
  • H.E. Rose "Subrecursion, Functions and hierarchies" 1984
  • Luis E. Sanchis "Recursive Functionals" 1992
  • Andrea Sorbi, ed. "Complexity, logic and recursion theory" 1997
  • R.M. Smullyan "Recursion Theory for Metamathematics" 1993

σ.4.6. Foundations

  • J.L. Bell, M. Machover "A Course in Mathematical Logic" 1993
  • R.D. Carmichael "Groups of Finite Order" 1937
  • C.C. Chang, H. Jerome Keisler "Model Theory" 1977
  • Dirk van Dalen "Logic and Structure" 4th ed. 2004
  • Paul R. Halmos "Naive Set Theory" 1960
  • David Hilbert "On the infinite" 1925
    in: Heijenoort "From Frege to Gödel" 1967
  • Wilfred Hodges "Building Models by Games" 1985
  • Thomas Jech "Set theory" 2002
  • Akihiro Kanamori "The Higher Infinite" 1997
  • Stephen C. Kleene "Introduction to Meta-mathematics" 1952
  • Ulrich Kohlenbach "Applied Proof Theory: proof interpretations..." 2008
  • S. Mac Lane "Categories for the working mathematician" 1997
  • S. Mac Lane, I. Moerdijk "Sheaves in Geometry and Logic" 1992
  • Jerome Malitz "Introduction to Mathematical Logic" 1979
  • Yu. I. Manin "A Course in Mathematical Logic (for Mathematicians)" 2010
  • Elliott Mendelson "Introduction to Mathematical Logic" 1964
  • J. Donald Monk "Mathematical Logic" 1976
  • Wolfram Pohlers "Proof Theory, the first step into impredicativity" 2009
  • S. Shelah "Classification Theory" 1990
  • Edwin H. Spanier "Algebraic Topology" 1966
  • Paul-Hermann Zieschang "Theory of Association Schemes" 2005

σ.4.7. Mathematics

Bearded man standing tall, mobile snapshot, art dots
Gregori Perelman:
"I don't need anything!"
  • Stephen Abbott "Understanding Analysis" 2001
  • P. Abramenko, K.S. Brown "Buildings: theory and applications" 2008
  • Martin Aigner "A Course in Enumeration" 2007
  • Jörg Arndt, Christoph Haenel "Pi-unleashed" 2001
  • Avner Ash, Robert Gross "Fearless Symmetry" 2006
  • Jerome Barkley Improved lower bound on a Euclidean Ramsey problem
    Graham's hypergraph has minimal dimension 13, arXiv 2008
  • John L. Casti "Five Golden Rules" 1996
  • P.M. Cohn "Further Algebra and Applications" 2002
  • Mariana Cook "Mathematicians, an outer view..." 2009
  • Dedekind "Essays on the Theory of Numbers" 2nd ed. 1893
    in Stephen Hawking "God created the Integers" 2007
    online: Project Gutenberg ebook, Internet Archive 1901 ed.
  • Ebbinghaus, Hermes, et al. "Numbers" 1991
  • George Gheverghese Joseph "The Crest of the Peacock" 1991
  • Gowers, ed. "The Princeton Companion to Mathematics" 2008
  • Graham, Rothschild, Spencer "Ramsey Theory" 1990
  • Peter D. Grünwald "The Minimum Description Length Principle" 2008
  • Julian Havil "Gamma" 2003
  • Heikkilä, Lakshmikantham "Monotone iterative techniques..." 1994
  • Georges Ifrah "... A universal history of numbers" 1985
  • Nathan Jacobson "Basic Algebra I" 1974
  • Khalil Jaouiche India's contribution to Arab mathematics 1997
  • Eli Maor "e: the Story of a Number" 1998
  • Jun-Iti Nagata "Modern Dimension Theory" 1965
  • Marcus du Sautoy "Finding Moonshine" / "Symmetry" 2008
  • H.A. Thurston "The Number System" 1956
  • Eric W. Weinstein "CRC Concise Encyclopedia of Mathematics" 1999

σ.4.8. Science and programming

  • Abiteboul, Hull, Vianu "Foundations of Databases" 1995
  • Darren Aronofsky "Π faith in chaos" 1999, film (+book fiction)
  • Roel Bloo "Preservation of Termination for Explicit Substitution" 1997
  • Peter J. de Bruin "Inductive Types in Constructive Languages" 1995
  • Doets, van Eijck "The Haskell road to logic, maths and programming" 2004
  • David Flanagan "JavaScript, the definitive guide" O'Reilly 2006
  • Franklin, Powell, Emami-Naeini "Feedback Control of Dynamical Systems" 2002
  • Jeffrey Friedl "Mastering Regular Expressions" O'Reilly 2006
  • Douglas R. Hofstadter "Gödel, Escher, Bach" 1979
  • Jan van Leeuwen "Rule-labeled programs" 1972
  • Seth Lloyd "Computational capacity of the universe" arXiv 24-10-2001
  • Nielsen, Chuang "Quantum Computation and Quantum Information" 2000
  • Jennifer Niederst Robbins "Web Design in a Nutshell" O'Reilly 2006
  • Sullivan, Goerzen, Stewart "Real World Haskell" O'Reilly 2008
  • Hermann Weyl "The Theory of Groups and Quantum Mechanics" 1931
  • Ludwig Wittgenstein "Tractatus logico-philosophicus" 6.4, 1918

σ.4.9. Religious literature

  • John Daido Loori "The True Dharma Eye" 2005, case 300 (Linji d. 867)
    comments on: Zen master Dogen's 300 koans, collection 1227
  • John Stevens "The Marathon Monks of Mount Hiei" 1988
    Cites on kaihôgyô (founder Sô-ô 859) "The Story of Wandering Saints" 1387
  • Fred "Philémon – Simbabbad de Batbad" 1974 (Dutch)
  • Yram "Practical Astral Projection" ch.8, translation of "Le Médicin de l'Ame" 1925
    Yram is the mystic Marcel Fourhan (1884-1927), electrical engineer in Shanghai
  • B. Malinowski "Baloma; the Spirits of the Dead in the Trobriand Islands" 1916
    Journal of the Royal Anthropological Institute of Great Britain and Ireland, vol.46
    in his: "Magic, Science and Religion" 1954 (courtesy P.C. Willis), p.161
  • Basho "Journal of a weathered skeleton" 1684, haiku 1,9,15
    see: Nobuyuki Yuasa "The Narrow Road to the Deep North"
  • Sri Caitanya "Šrî Brahma-samhitâ" 16th century, vs.40
    from: Joan Wilder "The Hare Krishna Music Book" 1994, p.48
  • Keizan "Denkoroku" 14th century, case 30 (Huike 6th century)
    translation: Thomas Cleary "Transmission of Light"
    in: Classics of Buddhism and Zen vol.4, Shambhala 2001
  • Nichiren Shonin "Letter to Niike" 1280
    in: "The major writings of Nichiren Daishonin" vol.1 1991, p.260
    quotes: "Mahâparinirvâna sûtra" 2nd? century
  • Wumen Huikai (Mumon Ekai) "Wumen-guan" (Mumonkan) 1228, case 3
    translation: Thomas Cleary "Unlocking the Zen Koan" 1993
  • Snorri Sturluson "Gylfaginning" (in Prose Edda) 1220, p.XXXVIII
    Quoted poem: "Edda" Grímnismál 20 (Codex Regius 13th century)
  • Wansong "Ts'ung jung lu" (Shoyo Roku) 12th century compilation, case 3
    in: Thomas Cleary "Book of Serenity" One hundred Zen dialogues 1988
  • Xuedou Chongxiang (Setchô) "Pi-yen lu" (Hekigan Roku) 11th century, case 3
    after: R.D.M. Shaw "The Blue Cliff Records" 1961
    and: Katsuki Sekida "Two Zen Classics" 1977
  • The "Great Vows" of the Bodhisattva, as chanted in Zen buddhism
    own rendering 2009, based on: D.T. Suzuki "Manual of Zen Buddhism" 1950 &
    Maha Karuna & Kanzeon Sangha "Shiguseigan" & San Francisco Conference 1997
  • "The Sutra of Complete Enlightenment" 6th? century
    in: Lu K'uan Yü "Ch'an and Zen Teaching" vol.3, 1962
  • "Prajñâpâramitâ Hrdaya sûtra" (Heart Sutra) 5th? century
    in: Thich Nhat Hanh "The Heart of Understanding" 1988
  • "Vajrachchedika-prajñâpâramitâ sûtra" 4th? century
    compare: "The Diamond Sutra and the Sutra of Hui-neng" 1990, ch.11
  • "Buddhâvatamsaka-mahâvaipulya sûtra" 3d? century
    translation: Thomas Cleary "The Flower Ornament Scripture" 1984-1993
    with: chapter 30 "The Incalculable" annotated by Novaloka 2010
  • "Vimalakîrti-nirdeša sûtra" (Wei mo chieh so shuo ching) 2nd? century
    from: Charles Luk "The Vimalakirti Nirdesa Sutra" 1972, ch.4
  • "Lalitavistara sûtra" 1st? century, as "The Voice of the Buddha" 1983, ch.12
    with: "The mathematical test" annotated by Asamkhyeya dasa 2011
  • "Lañkâvatâra sûtra" 1st? century, translation: D.T. Suzuki 1932, ch.2:17
  • "The Gospel of Mary" 2nd? century, in: Barnstone, Meyer "The Gnostic Bible" 2003
  • King James version of the Holy Bible, St. Mark "The Gospel" 1st century, ch.8:1-9
    in Novak from: The Holy Bible NRSV-1989, "Gospel of Matthew" ch.19:23-26
    from Aramaic via Dutch back to English – Mark 15:34, Matthew 27:46
    St. John the Divine "Book of Revelation" 2nd? century, ch.13:18 (number 666)
  • Apollodorus "The Library" 1st/2nd century,
    modelled on a lost 5th century BC mythography by Pherecydes of Leros?
    in: Atchity "The Classical Greek Reader" 1996, p.332
  • "Anuyogadvâra sûtra" (Mûlagrantha 4, Švetâmbara canon) Jaina 1th? century
  • "Bhagavad Gîtâ" 0th? century, ch.11.13
    A.C. Bhaktivedanta Swami Prabhupâda "Bhagavad Gita As It Is" 1968
  • "Saddharma-pundarîka sûtra" (Lotus Sutra) 1st? century BC
    translation Bunno Kato, et al: "The Threefold Lotus Sutra" 1975, ch.25
    online: Digital Sanskrit Buddhist Canon, in article: "Drops of ink and dust..."
  • Chuang Tsu "Nua-hua chen ching" 4th? century BC
    translation: Gia-Fu Feng "Chuang Tsu, inner chapters" 1974, ch.1
  • Confucius "Li chi" 5th? century BC
    from: Philip Novak "The World's Wisdom" 1994, ch3.2b
    Li Ji - Li Yun (Book of Rites - Evolution of Rites)
  • Lao Tsu "Tao te ching" 6th? century BC, ch.1
    free after Novak, Blok (NL) and a copy (DE) in: "I, WILL McBRIDE" 1997, p.196
  • The Buddha "Udana" 8.3, 6th? century BC
    after: Philip Novak "The World's Wisdom" 1994, ch2.34e
  • "Atharva Veda" 11th? century BC, hymn 8, vs.7-10
    online: Ralph T.H. Griffith – the Atharva Veda 1895
  • "Rg Veda" 11th? century BC, book 10, hymn 90, vs.1-2
    in: Sacred Writings vol. 5 "The Rig Veda", translation: Ralph T.H. Griffith 1896?
The 1000-day Mountain Marathon of Hiei  (& Imuro Valley)
year days track features
source: John Stevens, The Marathon Monks of Mount Hiei
1 100 30 (40) km each day,
255 stations of worship.
1-day Kyoto run, 54 km
Clock: 1:30 ~ 8:30
No socks yet, hat carried.
2 100
3 100
4 100 Gyôja on the road
clothed in the colour of death wearing straw sandals.

30 (40) km daily,
1 day Kyoto run
Socks and hat permitted.
Upon completion: "White-Belted Ascetic"
5 100 Wooden staff permitted.
On 700th day dôiri: 7½ days without food, water or rest.
"Master of Severe Practice"
6 100 60 km each day Sekisan Marathon (steep)
7 100 84 km each day Great Marathon (0:30 ~ 17:00)
  100 30 (40) km, 1 Kyoto run "Saint of the Highest Practice"
1000 days 38,632 (46,572) km
follows: Great 100,000-Prayer Fire-Ceremony 6½ day fast for Fudô Myô-ô