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D. H. Lehmer, Mathematical methods in large-scale computing units, Proceedings of a Second Symposium on Large-Scale Digital Calculating Machinery, 1949, Harvard University Press, Cambridge, Mass., 1951, 141–146

Joel N. Franklin, Deterministic simulation of random processes, Math. Comp., 17 (1963), 28–59, reprinted in [4]

R. R. Coveyou, Serial correlation in the generation of pseudo-random numbers, J. Assoc. Comput. Mach., 7 (1960), 72–74, reprinted in [4]

A. Rotenberg, A new pseudo-random number generator, J. Assoc. Comput. Mach., 7 (1960), 75–77, reprinted in [4]

A. van Wijngarden, Mathematics and computing, Automatic Digital Computation, Proc. Symposium of the National Physics Laboratory, H.M. Stationery Office, London, 1954, 125–129

Gösta Neovius, Artificial traffic trials using digital computers, Ericsson Technics, 11 (1955), 279–291

M. Donald MacLaren, George Marsaglia, Uniform random number generators, J. Assoc. Comput. Mach., 12 (1965), 83–89

W. J. Westlake, A uniform random number generator based on the combination of two congruential generators, J. Assoc. Comput. Mach., 14 (1967), 337–340

G. E. Forsythe, Generation and testing of $1,217,370$ “random” binary digits on the SWAC, Bull Amer. Math. Soc., 57 (1951), 304–, Abstract

E. Lucas, Theory of simply periodic numerical functions, Amer. J. Math., 1 (1878), 184–240, 289–321, (In French.)

R. D. Carmichael, On the numerical factors of the arithmetic forms $\alpha\sp n\pm\beta\sp n$, Ann. of Math. (2), 15 (1913/14), 30–48

R. D. Carmichael, On the numerical factors of the arithmetic forms $\alpha\sp n\pm\beta\sp n$, Ann. of Math. (2), 15 (1913/14), 49–70

R. D. Carmichael, A Simple Principle of Unification in the Elementary Theory of Numbers, Amer. Math. Monthly, 36 (1929), 132–143

D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525–532

D. W. Robinson, The Fibonacci matrix modulo m, Fibonacci Quart, 1 (1963), 29–36

John Vinson, The relation of the period modulo to the rank of apparition of m in the Fibonacci sequence, Fibonacci Quart, 1 (1963), 37–45

J. H. Halton, On Fibonacci residues, Fibonacci Quart, 2 (1964), 217–218

John H. Halton, On a general Fibonacci identity, Fibonacci Quart., 3 (1965), 31–43

J. H. Halton, A note on Fibonacci subsequences, Fibonacci Quart., 3 (1965), 321–322

John H. Halton, On the divisibilty properties of Fibonacci numbers, Fibonacci Quart., 4 (1966), 217–240

John H. Halton, Some properties associated with square Fibonacci numbers, Fibonacci Quart, 5 (1967), 347–355

J. Certaine, On sequences of pseudo-random numbers of maximal length, J. Assoc. Comput. Mach., 5 (1958), 353–356, reprinted in [4]

V. D. Barnett, The behavior of pseudo-random sequences generated on computers by the multiplicative congruential method, Math. Comp., 16 (1962), 63–69, reprinted in [4]

J. L. Allard, A. R. Dobell, T. E. Hull, Mixed congruential random number generators for decimal machines, J. Assoc. Comput. Mach., 10 (1963), 131–141, reprinted in [4]

T. E. Hull, A. R. Dobell, Mixed congruential random number generators for binary machines, J. Assoc. Comput. Mach., 11 (1964), 31–40, reprinted in [4]

A. van Gelder, Some new results in pseudo-random number generation, J. Assoc. Comput. Mach., 14 (1967), 785–792

N. C. Metropolis, G. Reitwiesner, J. von Neumann, Statistical treatment of values of first 2,000 decimal digits of e and of $\pi$ calculated on the ENIAC, Math. Tables and Other Aids to Computation, 4 (1950), 109–111

F. Gruenberger, Further statistics on the digits of e, Math. Tables Aids Comput., 6 (1952), 123–124

R. K. Pathria, A statistical analysis of the first 2,500 decimal places of e and $1/e$, Proc. Nat. Inst. Sci. India Part A, 27 (1961), 270–282

R. K. Pathria, A statistical study of randomness among the first $10,000$ digits of $\pi$, Math. Comp., 16 (1962), 188–197

R. K. Pathria, A statistical study of randomness among the first $60,000$ digits of e, Proc. Nat. Inst. Sci. India Part A, 30 (1964), 663–674

R. D. Richtmyer, Marjorie Devaney, N. Metropolis, Continued fraction expansions of algebraic numbers, Numer. Math., 4 (1962), 68–84, reprinted in [4]

J. Lach, Random number generators, Memo., 27, Yale University Computer Center, New Haven, Connecticut, 1963

M. Greenberger, Method in randomness, Comm. ACM, 8 (1965), 177–179

Martin Greenberger, An a priori determination of serial correlation in computer generated random numbers, Math. Comp., 15 (1961), 383–389, reprinted in [4]

M. Greenberger, Notes on a new pseudo-random generator, J. Assoc. Comput. Mach., 8 (1961), 163–167, reprinted in [4]

Birger Jansson, Autocorrelations between pseudo-random numbers, Nordisk Tidskr. Informations-Behandling, 4 (1964), 6–27, (BIT)

Donald E. Knuth, Construction of a random sequence, Nordisk Tidskr. Informations-Behandling, 5 (1965), 246–250, (BIT)

D. L. Jagerman, Some theorems concerning pseudo-random numbers, Math. Comp., 19 (1965), 418–426

R. R. Coveyou, R. D. Macpherson, Fourier analysis of uniform random number generators, J. Assoc. Comput. Mach., 14 (1967), 100–119

G. H. Hardy, E. M. Wright, An Introduction to the Theory of Numbers, Clarendon Press, Oxford, 1960

J. F. Koksma, Diophantische Approximationen, Springer, Berlin, 1957, Chelsea, New York, 1936

J. F. Koksma, L. Kuipers, Asymptotic distribution modulo 1, Papers presented at the NUFFIC International Summer Session in Science, sponsored by NATO, held in Breukelen (The Netherlands), August 1-11, P. Noordhoff N. V., Groningen, 1965iv+203

J. F. Koksma, The theory of asymptotic distribution modulo one, Compositio Math., 16 (1964), 1–22 (1964)

H. Weyl, On uniform distribution of numbers modulo one, Math. Ann., 77 (1916), 313–352

J. G. van der Corput, Diophantine inequalities. I: On uniform distribution modulo one, Acta Math., 56 (1931), 373–456, [In German.]

J. F. Koksma, A set-theoretical theorem on uniform distribution modulo one, Compositio Math., 2 (1935), 250–258

N. G. de Bruijn, P. Erdös, Sequences of points on a circle, Nederl. Akad. Wetensch., Proc., 52 (1949), 14–17 = Indagationes Math. 11, 46–49 (1949), reprinted in [4]

K. F. Roth, On irregularities of distribution, Mathematika, 1 (1954), 73–79, reprinted in [4]

H. Davenport, Note on irregularities of distribution, Mathematika, 3 (1956), 131–135, reprinted in [4]

Vera T. Sós, On the theory of diophantine approximations. I, Acta Math. Acad. Sci. Hungar, 8 (1957), 461–472

V. T. Sós, On the distribution mod 1 of the sequence $n\alpha$, Ann. Univ. Sci. Budapest Eötvös Sect. Math., 1 (1958), 127–134

J. Surányi, On the ordering of the multiples of a real number mod 1, Ann. Univ. Sci. Budapest Eotvos Sect. Math., 1 (1958), 107–111, (In German.)

S. Świerczkowski, On successive settings of an arc on the circumference of a circle, Fund. Math., 46 (1959), 187–189

John H. Halton, The distribution of the sequence $\{n\xi \}\,(n=0,\,1,\,2,\,\cdots )$, Proc. Cambridge Philos. Soc., 61 (1965), 665–670, reprinted in [4]

Robert E. Greenwood, Coupon collector's test for random digits, Math. Tables Aids Comput., 9 (1955), 1–5

F. Gruenberger, A. M. Mark, Tests of random digits, Math. Tables Aids Comput., 4 (1950), 244–245, The d2-test, 5 (1951), pp. 109–110

A. Ostrowski, Remarks on the theory of Diophantine approximation, Abh. Math. Sem. Univ. Hamburg, 1 (1922), 77–98

J. H. Halton, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math., 2 (1960), 84–90, reprinted in [4]; Algorithm 247: radical-inverse quasi-random point sequence [G5], Comm. ACM, 7 (1964), pp. 701–702 (with G. B. Smith)

Hyman Gabai, On the discrepancy of certain sequences ${\rm mod}\ 1$, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math., 25 (1963), 603–605

Seymour Haber, On a sequence of points of interest for numerical quadrature, J. Res. Nat. Bur. Standards Sect. B, 70B (1966), 127–136

J. H. Halton, S. C. Zaremba, The extreme and $L\sp{2}$ discrepancies of some plane sets, Monatsh. Math., 73 (1969), 316–328

P. Roos, L. Arnold, Numerical experiments in multidimensional quadrature, Sitz. Osterreich. Akad. Wiss. (Math. Natur. Kl.), 172:II (1963), 271–286

R. D. Richtmyer, The evaluation of definite integrals, and a quasi-Monte-Carlo method based on the properties of algebraic numbers, Rep., LA-1342, Los Alamos Scientific Laboratory, Los Alamos, New Mexico, 1951

L. G. Peck, On uniform distribution of algebraic numbers, Proc. Amer. Math. Soc., 4 (1953), 440–443

R. D. Richmyer, A non-random sampling method, based on congruences, for “Monte Carlo” problems, NYO 8674, Atomic Energy Commission Computer and Applied Mathematics Center, New York University, 1958

S. C. Zaremba, Good lattice points in the sense of Hlawka and Monte Carlo integration, Monatsh. Math., 72 (1968), 264–269

S. C. Zaremba, Some applications of multidimensional integration by parts, Ann. Polon. Math., 21 (1968), 85–96

J. H. Halton, On sequences of random variables in separable Frechet spaces, in preparation

J. H. Halton, An Introduction to the Monte Carlo Method, Prentice-Hall, Englewood Cliffs, New Jersey, to be published

J. H. Halton, On the strong convergence of linear averages of generalized random variables, in preparation

S. Faedo, Order of magnitude of Euler-Fourier coefficients of functions of two variables, Ann. Scuola Norm. Sup. Pisa, II (1937), 225–246

J. G. van der Corput, Distribution functions, Nederl. Akad. Wetensch. Proc. Ser. A, 38 (1938), 813–821, 1058–1066, 39 (1939), pp. 10–19, 19–26, 149–153, 339–344, 489–494, 579–590. (See especially 38 (1938), pp. 1058–1066.) [In German.]

J. H. Halton, On the inadequacy of the sample-variance as an error-estimate in quasi-Monte-Carlo calculations, in preparation

J. H. Halton, E. A. Zeidman, Monte Carlo integration with sequential stratification, Comp. Sci. Tech. Rep., 61, University of Wisconsin, Madison, 1969

Jerome Spanier, Ely M. Gelbard, Monte Carlo principles and neutron transport problems, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969xiv+234

J. H. Halton, A retrospective and prospective survey of the Monte Carlo method, Comp. Sci. Tech. Rep., 13, University of Wisconsin, Madison, 1968

E. A. Zeidman, The evaluation of multidimensional integrals by sequential stratification, in preparation

I. M. Gelfand, Lectures on linear algebra, Translated from the revised second Russian edition by A. Shenitzer, Interscience Tracts in Pure and Applied Mathematics, No. 9. Interscience Publishers, New York-London, 1961ix+185

Georgi E. Shilov, An introduction of theory of linear spaces, Translated from the Russian by Richard A. Silverman, Prentice-Hall Inc., Englewood Cliffs, N.J., 1961ix+310