A Guide to the J. Barkley Rosser Papers,
19311989





Creator 
Rosser, J. Barkley (John
Barkley), 1907 

Title 
J. Barkley Rosser
Papers 

Dates: 
19311989 

Abstract 
The J. Barkley Rosser
Papers (19311989) consist of correspondence, manuscripts of publications and
lectures, notes, reprints, calculations, and books. Topics covered include
logic, analytic number theory, and ballistics. 

Accession No. 
911 

Extent 
10 ft., 8 in. 

Language 
Materials are written in English. 

Repository: 
Dolph Briscoe Center for American
History, The University of Texas at
Austin 
J. Barkley Rosser was born in Jacksonville, Florida in 1907. He earned
both his Bachelor of Science (1929) and his Master of Science (1931) from the
University of Florida. He obtained his Ph.D. from Princeton University in 1934.
After getting his Ph.D., Rosser taught at Princeton, Harvard, and Cornell and
spent the latter part of his career at the University of WisconsinMadison. He
continued to lecture well into his late 70s, and died at his home in Madison in
1989.
Rosser contributed to many committees and professional associations in
addition to his teaching: he served as president of the Association for
Symbolic Logic and the Society of Industrial and Applied Mathematics; was a
member of the space vehicle panel for the advisory committee of the Apollo
project; was an early contributor to computer science theory; and helped
develop the Polaris missile. While at the University of WisconsinMadison, he
served as the director of the U. S. Army Mathematics Research Center. Rosser is
known for his part in the ChurchRosser theorem, in lambda calculus, and he
developed the Rosser sieve.
His areas of expertise include symbolic logic, ballistics, rocket
development, and numerical analysis.
The J. Barkley Rosser Papers (19311989) consist of correspondence,
manuscripts of publications and lectures, notes, reprints, calculations, and
books. Topics covered include logic, analytic number theory, and
ballistics.
Forms part of the Archives of American Mathematics.
Access Restrictions
Unrestricted access.
Use Restrictions
These papers are stored remotely at CDL. Advance notice required for retrieval.
Contact repository for retrieval.







Subjects (Persons) 


Rosser, J. Barkley (John
Barkley), 1907 


Schoenfeld, Lowell,
1920 

Subjects (Organizations) 


The University of
WisconsinMadison. Mathematics Dept. 


Mathematics Research Center
(United States. Army) 

Subjects 


MathematicsStudy and
teachingUnited States 


Logic, Symbolic and mathematical 


Number theory. 


Numerical analysis. 


Rockets (Ordnance) 


Ballistics. 


Magic squares. 




Materials relating to Dr. Rosser's work at the Army Math Research Center
can be found at the Wisconsin Historical Society in Madison, Wisconsin. 
J. Barkley Rosser Papers, 19311989, Archives of American
Mathematics, Dolph Briscoe Center for American History, University of Texas at Austin.
Detailed Description of the Collection















Correspondence: 
box 
911/1 


Candy, A. L.,
19381941 



Church, Alonzo [includes correspondence photocopied by
Church],
ca. 1983 



Erdos, Paul,
19381939 



Sacks, Gerald [includes mathematical work],
1961 and undated 



Schoenfeld, Lowell,
19551976 
box 
911/2 


Thays, Leslie,
1973 and undated 



Van Waarden, John,
19751977 



American Mathematical Monthly
[problem and solution],
1974 



Centre de Recherches Mathematiques,
19721973 



Hawaii lectures,
1981 



Journal of Symbolic Logic,
1965 



Magic squares [Coxeter, Stern, Thomas],
19381941 



New Orleans talks,
1980 



Lawrence Rad. Lab.,
19711974 



Rational proofs,
19381939 



Stewart Committee,
1983 



Sieve method,
1955 



Miscellaneous mathematics related correspondence [includes
requests for reprints],
19631989 



“Miscellaneous,”
19611963 



Assorted,
undated 















Publications: 
box 
911/2 


Books: 




Mathematical Theory of Rocket
Light, New York and London: McGrawHill Book Company, Inc. [bound
photocopy],
1947 




Theory and Application of $intsb {0sp
z}esp {xsp {2}}dx$ and $intsb {0sp z}esp {psp {2}ysp {2}}dyintsp
ysb 0 esp {xsp {2}}dx$, Brooklyn: Mapleton House Publishers [bound
photocopy],
1948 




ManyValued Logics, Amsterdam:
NorthHolland Publishing Company [bound photocopy],
1952 
box 
911/3 



Logic for
Mathematicians: 





Logic for Mathematicians, New
York: McGrawHill Book Company, Inc. [includes correspondence],
1953 





Logic for Mathematicians, New
York: Chelsea Publishing Company [includes correspondence],
1978 





Draft: 






Chapter 1,
undated 






Chapter 2,
undated 






Chapter Three and Four,
undated 






Chapter 3 and 4,
undated 






Chapter 5,
undated 






Chapter 6,
undated 
box 
911/2 



Simplified Independence Proofs: Boolean
Valued Models of Set Theory, New York: Academic Press,
1969 




Pocket Calculator Supplement for
Calculus, Reading, Massachusetts: AddisonWesley Publishing Company,
1979 
box 
911/4 


Reprints: 




“Explicit Bounds for Some Functions of Prime Numbers,”
January 1941 




“Axiom Schemes for MValued Propositional Calculi” [with
A. R. Turquette],
1945 




“Axiom Schemes for MValued Functional Calculi of First
Order, Part I: Proof of Plausibility” [with A. R. Turquette],
December 1948 




“A Note on the Deductive Completeness of MValued
Propositoinal Calculi” [with A. R. Turquette],
January 1950 




“Real Roots of Real Dirichlet Lseries,”
December 1950 




“Real Roots of Real Dirichlet Lseries, II,”
undated 




“Transformations to Speed the Convergence of Series,"
January 1951 




“Axiom Schemes for MValued Functional Calculi of First
Order, Part II: Deductive Completeness” [with A. R. Turquette],
March 1951 




“Explicit Remainder Terms for Some Asymptotic Series,”
July 1955 




“Deux Esquisses de Logique,”
1955 




“Some Sufficient Conditions for the Existence of an
Asymptotic Formula or an Asymptotic Expansion,”
1959 




“Approximate Formulas for Some Functions of Prime
Numbers” [with Lowell Schoenfeld],
March 1962 




“Rigorous Computation and the Zeros of the Riemann
ZetaFunction” [with Lowell Schoenfeld and J. M. Yohe],
1969 




“Mathematics Courses in 1984,"
JuneJuly 1972 




“Sharper Bounds for the Chebyshev Functions theta (x)
and psi (x)” [with Lowell Schoenfeld]: 





Draft,
1974 





Published reprint,
January 1975 




“NinePoint Difference Solutions for Poisson’s
Equation,”
April 1975 




“Effect of Discontinuous Boundary Conditions on
FiniteDifference Solutions,”
1976 




“Finitedifference Solution of Poisson’s Equation in
Rectangles of Arbitrary Proportions,”
1977 




“Majorization Formulas for a Biharmonic Function of Two
Variables,”
April 1980 




“Mathematics and Mathematicians in World War II”
[includes galley proof],
October 1982 




“Mathematics and Mathematicians in World War II,”
A Century of Mathematics in America, Part
I [includes galley proof],
1982 




"Highlights of the History of the LambdaCalculus,"
October 1984 




“Stuff on Asymptotic,”
19511955 and undated 



Manuscripts: 




“On the Extension of Certain Theorems of Mathematical
Physics and Their Subsequent Application to Problems of Wave Mechanics”
[Master’s thesis],
1931 




“Factorial Expansions for Certain Bessel Functions,”
undated 




“The GoldbackVinogradoff Theorem” [Xerox master copy],
“
1949 and undated 
box 
911/3 



“Nonmathematical Theory of Rocket Flight,”
undated 
box 
911/4 



“Rational Proofs of the Existence of Primes in
Arithmetic Sequences,”
1939 




“Real Roots of Real Dirichlet LSeries III,”
1952 and undated 
box 
911/5 



“Some New Extension of Brun’s Method,”
1955 and undated 




“Unusual Properties of Laguerre Polynomials” [with Ragab
and Schoenfeld],
undated 




Analytic Number Theory: 





General correspondence,
19491951 





Correspondence with Chelsea Publishing Company,
1948 





Corrections,
1948 and undated 





Bibliography,
undated 





“Primes in an Arithmetic Progression, Page’s Theorem,”
undated 





Correspondence with Schoenfeld,
1948 





“Notes in Anal. # Th. Chap I,”
undated 





Chap II,
1950 and undated 





Chap III,
undated 





Chap IV and V,
undated 




Supplement to diabolic squares [“Magic Squares,
Supplement”],
undated 




Propositional Calculus,
undated 




Chapter IX,
undated 




Early drafts,
undated 
box 
911/6 



Original [includes reprints by Rieger and Kuhn],
19531954 and undated 




Printed matter [chapters IVIII],
undated 




Carbon,
undated 




Appendices,
undated 




Assorted typed manuscripts,
undated 




Untitled [handwritten],
undated 



Technical reports: 




“Numerical Computation of Low Moments of Order
Statistics from a Normal Population,”
1951 and undated 
box 
911/7 



“Axiomatization of Infinite Valued Logics,”
September 1960 




“A Table of Ei(x) (x1)ex,”
March 1961 




“Table for Estimating Functions of Primes,”
September 1961 
box 
911/8 



“Estimation of Capacity with Bounds for the Error, I”
[April 1966], [includes correspondence and research materials],
1950, 19621973 




“Block Relaxation by Computer,”
April 1964 




“The Direct Solution of Difference Analogs of Poisson’s
Equation,”
October 1967 




“The Riemann ZetaFunction Magnetic Tapes” [with D. R.
Musser, Lowell Schoenfeld, and J. M. Yohe],
March 1969 




“An Iterative Algorithm for Calculating Potentials Near
Small Groups of Finite Charged Plates” [with F. S. Acton],
December 1970 
box 
911/7 



“Approximation of the Riemann ZetaFunction” [with
Lowell Schoenfeld]: 





Early draft,
1970 





Published report,
June 1971 





References,
1924, 19671975 
box 
911/8 



“Bounds for Some Coefficients Related to the Zeta
Function,”
July 1972 




“Potentials of Charged Plates, Part I,”
April 1973 




“FiniteDifference Solution of Poisson’s Equations in
Rectangles of Arbitrary Shape,”
September 1973 




“Potentials of Charged Plates, Part III,”
December 1973 




“A Power Series Solution of a Harmonic Mixed Boundary
Value Problem” [with N. Papamichael],
December 1973 




“FiniteDifference Solution of Poisson’s Equation in
Rectangles of Arbitrary Shape,”
February 1974 




“Potentials of Charged Plates,”
October 1974 




“Fourier Series in the Computer Age,”
February 1974 




“A Power Series Solution of a Harmonic Mixed Boundary
Value Problem” [with N. Papmichael],
January 1975 




“NinePoint Difference Solutions for Poisson’s
Equation,”
March 1975 
box 
911/6 



“Calculation of Potential in a Sector, Part I” [includes
notes],
May 1975 
box 
911/8 



“High Precision Coefficients Related to the Zeta
Function” [with Fred D. Crary],
May 1975 




“Fourier Transform Evaluation,”
June 1976 




“Cancellation and Rounding Errors” [with J. Michael
Yohe],
August 1976 




“Solution of Partial Differential Equations by Means of
Finite Elements: An Introductory Sketch,”
December 1976 
box 
911/7 



“Harmonic Functions on Regions with Reentrant Corners,
Part I” [includes draft],
1977 and undated 




“Majorization Formulas for a Biharmonic Function of Two
Variables” [includes draft],
August 1978 
box 
911/8 



“Highlights of the History of the LambdaCalculus,”
October 1982 
box 
911/6 



“A Numerical Bound in the Three Prime Theorem”
[Obsolete],
undated 















Work by others: 
box 
911/8 


Bateman, Paul, “Imaginary Quadratic Fields with Unique
Factorization” [with Emil Grosswald],
1961 



Brun, Viggo,
19161931 



Church, Alonzo, “Russell’s theory of Identify of
Propositions” [includes correspondence],
ca. 1985 



Erdös, Paul,
19351950 
box 
911/9 


Feferman, Solomon, “Transfinite recursive progressions of
axiomatic theories,”
undated 



Grimm, Gottfried, Zeroes of Lseries,
1932 



Grosswald, Emil, “”Lfunctions and quadratic fields with
unique factorization,”
19631964 



Harrington, Walter Joel, “A Study of Certain Functions
Auxiliary to Brun’s Method in Number Theory,”
1941 



Hiz, H. [includes notes by Rosser],
1957 and undated 



Hlavka, James L., “Evaluation of a Lower Bound for
Vinogradov’s Three Prime Theorem, with an Improved Error Term” [includes
corrections],
undated 



Jones, J. P., “The Existential GödelRosser Theorem,”
19791981 



Klop, Jan William, “A Counterexample to the ChurchRosser
Property for Lambda Calculus with Subjective Pairing,”
January 1979 



Kuhn, Pavel [reprints and correspondence],
1939, 1954 and undated 



McCurley, Kevin, “Explicit Estimates for Functions of
Primes in Arithmetic Progressions,”
1981 



Mitchell, Emerson, mathematical calculations,
1974 and undated 



Rademacher, Hans,
undated 



Ragab, F. M., “Four titles re: Laguerre Polynomials,”
undated 



Richert, H. E., “Die BrunSelbergsche Siebmethode,”
19621963 



Scarpellin, Bruno, “NonAxiomatizability of the
Infinitelymanyvalued Predicate Calculus x”
[includes correspondence and notes],
1950, 1960 and undated 
box 
911/10 


Schoenfeld, Lowell, “Every Odd Integer Having at Least
350,000 Digits is the Sum of Three Odd Primes” [lecture],
19571959 



Schoenfeld, Lowell, three manuscripts,
undated 



SchoenfeldSelberg [“Chapter V: The GoldbachSnirel’man
Thorem”],
December 22, 1954 



Schroer, David Edward, “The ChurchRosser Theorem,” [Ph.D.
thesis],
June 1965 
box 
911/11 


Teichroew, D.,
19541955 



Laguerre polynomials reprints,
undated 



Laplace Transforms,
1944 



Linear equation reprints,
19461958 



Partial difference equations reprints,
19511959 



Brunel University,
19781982 



Photocopied mathematical notes,
1949 and undated 
box 
911/12 


Reprints [assorted],
19411954 



Assorted reprints [Dutch],
19381940, 19501953 















Mathematical work: 
box 
911/12 


Block relaxation by computer [see filigree],
19621966 and undated 



Computation of Ei(x),
undated 



Direct solution of the difference analog of Poisson’s
Equation,
undated 



Elementary proof – prime number theorem,
undated 



Estimation of S (1, 2, r),
undated 



Expansion of x^n e^x,
undated 



Exponential integer,
undated 



Filigree,
1967 and undated 
box 
911/13 


Logic,
ca. 1963 and undated 



Jan Lulsasiewicz,
1958 and undated 



Miscellaneous results about M(x) and g(x),
undated 



“Numerical Computation of Low Moments of Order Statistics
from a Normal Population,”
19511952 



Orbits [“stuff from Curtiss Schafer, etc.”],
undated 



Order statistics [includes correspondence],
19511955 and undated 



Ramsey’s theorem and creative sets,
undated 



“Reconsideration of Certain Points,”
undated 



Rose, G. F., “Propositional Calculus and Realizability,”
1953 and undated 



Threeprime theorem with Lowell Schoenfeld: 




First part, sections I, II [includes correspondence],
1948 




Second part, part of section III,
1948 




Third part, last of section III,
1948 
box 
911/14 



Fourth part, sections IV, V and Vinogradov results,
1948 




Section I: Basic Inequalities and Lemmas,
undated 




Section III: Regions in which <(s, x) 0 and
Estimates for Functions Involving < (s, x),
undated 




Section IV: The Number of Primes in a Progression and
Section V: Vinogradov’s Estimate,
undated 




Section VI: The Three Prime Theorem,
undated 




Intro and Biblio,
undated 




Changes [8 sets of revisions],
undated 




Changes to Section IV,
undated 




Untitled pages,
undated 



From Lowell Schoenfeld,
August 1965 



Real roots of real Dirichlet Lseries,
1950 and undated 



“Reconsideration of Certain Points,”
undated 
box 
911/15 


Study of F_{n} (a,b),
undated 



Study of G_{n} (X),
undated 



Tables of G_{n} (X),
undated 



Table of Zeta Function [printout],
undated 



W. J. Dixon,
1951 and undated 



Zeroes of Lseries,
undated 



Miscellaneous notes on eigenvalues,
undated 



Miscellaneous notes,
undated 



Unlabeled [includes printouts],
undated 
box 
4RM55b 


Unlabeled,
undated 
box 
911/16 


Unlabeled,
undated 



Untitled,
undated 



Unfoldered,
undated 
box 
4RM55c 


Unfoldered,
undated 
box 
4RM55b 


Tables and computer printouts: 




Table I. values of 4^r[alpha]2t (r, r),
undated 




Table II. Values of 4^r[beta]_{A}(r),
undated 




Table III. Table of accurate and approximate means
undated 




Table IV. Table of accurate and approximate extreme
means,
undated 




Computer printouts [on the 1604],
undated 




Computer printouts,
undated 















Research notes: 
box 
911/16 


Ed Cannon Comp. of Ei (X),
undated 



Eigenvalues,
1952, 1962 and undated 



EulerMacLaurin,
undated 



Laplace transform notes,
undated 



The method of Hestenes and Stiefel,
undated 



Order statistics,
1954 and undated 



Problems on asymptotic series [includes correspondence],
undated 
box 
911/17 


Tables of [psi](x) and X(x),
undated 



“Stuff on forcing” [includes reprints and mathematics
work],
19631967 



Bibliographic citation cards,
undated 



Miscellaneous,
undated 















Teaching: 
box 
911/17 


Attendance [Analytic number theory],
undated 



Mathematics 100 and 110,
19471949 



Mathematics 381/382 assignments,
19561957 
box 
4RM194 


Restricted: Mathematics 381/382
gradebooks and assignments,
undated 



Restricted: 381 and 382
homework [includes grade book],
undated 
box 
911/17 


Math. 381 final exam,
1957 



Mathematics 381,
19531955 



Math 381 prelim and final exam,
January 1959 



Math. 382 final exam student work,
1957 and undated 



Math. 382 homework assignments,
1961 and undated 
box 
911/18 


Mathematics 382 theorems,
undated 



382 prelim,
undated 



Prelim Math. 382,
1957 and undated 



Final exam for Logic [Math382, David N. Freeman],
1957 



Logic homework 1955,
undated 



Math 423/424,
19621963 



615 homework assignments, SeptOctNov,
19551957 



Notes used in Mathematics 615,
19551958 



615 Homework DecJan,
19551959 



615 homework 1955,
19551956 
box 
911/19 


615 homework 1956,
1957 and undated 



615 Homework 19578,
September 1957January 1958 



615 1957,
January 1958 and undated 



615 homework 1958,
19581959 



615 homework 1958,
1959 and undated 



615 notes,
undated 



Remarks about rigor in 615,
undated 



Homework 616 FebMar,
1956 and undated 
box 
911/20 


616 assignments, FebMar,
19561959 



Homework 616 AprMay,
1956 



616 homework AprilMay,
19561959 



Homework 616 1957 Feb and March,
1957 and undated 



Homework 616 1957 April and May,
undated 



Mathematics 616,
1959 
box 
911/21 


616 problems,
1961 



Thm. A, B, C, D. Asymptotic Exp. Laplace Trans.
[Mathematics 621622],
undated 



Math. 622, “The HornJeffreysLanger Method (Commonly
known as the BWK or WKB method)” [includes Langer reprints],
19481949 
box 
4RM194 


Restricted: Answers for 621
[includes gradebooks],
NovemberDecember 1948 
box 
911/21 


Answers in 621,
SeptemberOctober 1948 



Mathematics 621, final exam and answers,
1949 



Final exam 621,
1949 



621 prelim and solutions,
1950 



621 final,
January 1951 



621 course notes,
undated 



Answers in 621622,
JanuaryFebruary 1949 



Problems and answers in 622,
1948 
box 
911/22 


Final exam 622 [includes answers],
1948 



Math 622, final exam and answers,
June 1949 



622 homework,
1949 



622 course notes,
19501951 



Homework 622,
1951 



Final exam 622 [includes answers],
1951 



Math 622 term examination,
May 1952 



Homework from 622,
1949 



426 Assignments,
1963 and undated 
box 
911/23 


Algebra [Cornell University],
ca. 1938, 1964 



Orientation lectures [“Numerical Solutions of Ordinary
Differential Equations”],
19641966 



Computer Science 412,
19751977 



Theorems master set [logic],
undated 



Exercises master set [logic],
undated 
box 
4RM194 


Restricted: Arthur Shaw student
work [includes grade book],
undated 
box 
911/23 


Davis 2323,
undated 



Unlabeled course assignments,
undated 



Unfoldered [includes correspondence],
1957 and undated 















Lectures: 
box 
911/23 


Taft lectures [University of Cincinnati],
19691970 



“Mathematization of U. S. Society from World War II to
Present and Beyond” [James Madison University],
1982 
box 
911/24 


“Calculation of Potential in a Sector” [includes overhead
transparencies],
undated 



The EulerMascheroni constant,
undated 



Thursday talks,
undated 















Conferences and Institutes: 
box 
911/24 


“A Report of the Institute in the Theory of Numbers”
[includes paper by Rosser and errata],
19591960 



Joint Mathematics Meeting,
1960 



1982 ACM Symposium on LISP and Functional Programming,
1982 



NATO Advanced Study Institute,
1973 















Professional organizations: 
box 
911/24 


American Mathematical Society: 




Committee on Information Exchange and Publication in the
Mathematical Sciences,
19651966 




“Uses of the computer in teaching mathematics courses”
special section,
1975 




1982 Toronto meeting,
1982 















Swarthmore College Honors Examination: 
box 
911/24 


19421943 



1961 
box 
911/25 


19611962 



1962 















Security clearance: 
box 
911/25 


General,
19551970 



National Academy clearance,
1968 



NSA 1976,
undated 















box 
911/25 

Institute for Defense,
1976 and undated 















box 
911/25 

Princeton Mathematics Community in the 1930s [interview with
Kleene and Rosser],
19841985 















box 
911/25 

Digital computer needs in universities and colleges,
19661967 















box 
911/25 

Rosser’s retirement,
1978 















box 
911/25 

Overhead projector transparencies,
undated 















Personal: 
box 
911/25 


Grand Guard 50th reunion,
1979 



Insurance,
19671972 



TIAACREF,
19641970 















Photographs: 
box 
4RM203c 


Rosser as graduate student at Princeton,
ca. 1931 



Group photograph at Ballistic Research Laboratory,
Aberdeen Proving Ground, Maryland,
undated 



Visit of President’s Scientific Advisory Committee to the
Kennedy Space Center,
June 1, 1966 



Portrait,
1965 



Rosser at his desk in his office at UCLA as Director of
the Institute for Numerical Analysis,
ca. 1950 



Group photograph, LISP Conference in Pittsburgh,
August 1982 
