Garrett Birkhoff

Q: What Schools Are Affiliated With Garrett Birkhoff

Garrett Birkhoff is affiliated with the following schools: University of Cambridge, Harvard University

Garrett Birkhoff's AcademicInfluence.com Rankings

Garrett Birkhoff

Mathematics

#54

World Rank

#168

Historical Rank

#18

USA Rank

Measure Theory

#22

World Rank

#44

Historical Rank

#10

USA Rank

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Mathematics

Why Is Garrett Birkhoff Influential?

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According to Wikipedia, Garrett Birkhoff was an American mathematician. He is best known for his work in lattice theory. The mathematician George Birkhoff was his father. Life The son of the mathematician George David Birkhoff, Garrett was born in Princeton, New Jersey. He began the Harvard University BA course in 1928 after less than seven years of prior formal education. Upon completing his Harvard BA in 1932, he went to Cambridge University to study mathematical physics but switched to studying abstract algebra under Philip Hall. While visiting the University of Munich, he met Carathéodory who pointed him towards two important texts, Van der Waerden on abstract algebra and Speiser on group theory.

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Garrett Birkhoff's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

A survey of modern algebra (1942) (1246)
The Logic of Quantum Mechanics (1936) (1109)
On the Structure of Abstract Algebras (1935) (978)
Ordinary Differential Equations (1964) (755)
Explosives with Lined Cavities (1948) (556)
Orthogonality in linear metric spaces (1935) (392)
Hydrodynamics : a study in logic, fact, and similitude (1950) (388)
Extensions of Jentzsch’s theorem (1957) (379)
Rings of sets (1937) (306)
Proceedings of Symposia in Applied Mathematics (1960) (303)
Piecewise Hermite interpolation in one and two variables with applications to partial differential equations (1968) (232)
Smooth interpolation in triangles (1973) (200)
Subdirect unions in universal algebra (1944) (182)
On the combination of subalgebras (1933) (165)
Numerical Solution of Elliptic Problems (1984) (156)
Representations of lattices by sets (1948) (144)
Alternating Direction Implicit Methods (1962) (140)
Lattice-ordered Rings (1940) (140)
Subgroups of Abelian Groups (1935) (139)
A note on topological groups (1936) (132)
On splines and their minimum properties (1966) (128)
A ternary operation in distributive lattices (1947) (119)
Lattice Theory Revised Edition (1948) (115)
Moore-Smith Convergence in General Topology (1937) (112)
Representability of Lie Algebras and Lie Groups by Matrices (1937) (111)
Spherical Bubble Growth (1958) (109)
Integration of functions with values in a Banach space (1935) (108)
Modern Applied Algebra (1999) (106)
Linear Transformations with Invariant Cones (1967) (102)
Smooth Surface Interpolation (1960) (98)
Formation of Vortex Streets (1953) (92)
Reactor Criticality and Nonnegative Matrices (1958) (87)
Do vortex sheets roll up? (1959) (84)
The mean ergodic theorem (1939) (84)
Lattice-Ordered Groups (1942) (82)
Implicit alternating direction methods (1959) (78)
Quantum mechanics and asymptotic series (1933) (73)
DISCRETIZATION ERRORS FOR WELL-SET CAUCHY PROBLEMS.I., (1965) (72)
On the combination of topologies (1936) (71)
The convexity lattice of a poset (1985) (65)
A Source Book in Classical Analysis (1975) (64)
RISING PLANE BUBBLES (1957) (64)
Abstract Linear Dependence and Lattices (1935) (63)
Free Boundaries in Partial Lubrication (1963) (61)
Elliptic Problem Solvers II (1984) (60)
Non-linear network problems (1956) (59)
Hermite Interpolation Errors for Derivatives (1967) (58)
Note on Taylor instability (1954) (58)
Lie groups simply isomorphic with no linear group (1936) (51)
Piecewise affine functions and polyhedral sets (1994) (47)
Two families of Newman lattices (1994) (46)
The establishment of functional analysis (1984) (46)
A brief survey of modern algebra (1953) (45)
Compatible triangular finite elements (1974) (43)
Combinatorial Relations in Projective Geometries (1935) (43)
Fourier synthesis of homogeneous turbulence (1954) (43)
Uniformly semi-primitive multiplicative processes (1962) (43)
Numerical Fluid Dynamics. (1983) (43)
An extended arithmetic (1937) (41)
Mathematics for engineers — III: Dimensional analysis of partial differential equations (1948) (40)
Numerical Quadrature of Analytic and Harmonic Functions (1950) (40)
The draftsman's and related equations (1968) (39)
FOR GENERALIZED ARITHMETIC (38)
Stability of spherical bubbles (1956) (38)
Mathematics and Psychology (1969) (36)
The Theory of Splines and Their Applications (J. H. Ahlberg, E. N. Nilson and J. L. Walsh) (1969) (35)
Fluid Flow Patterns (1949) (34)
Von Neumann and lattice theory (1958) (32)
Selected Papers of Richard von Mises (1966) (30)
House monotone apportionment schemes. (1976) (30)
Current Trends in Algebra (1973) (28)
Trends in Lattice Theory (1970) (27)
Lattices and their applications (1938) (27)
Review: George Grätzer, General lattice theory (1979) (26)
On Product Integration (1937) (26)
On the Lattice theory of ideals (1934) (25)
Review: Gr. C. Moisil, Recherches sur l'algebre de la logique (1936) (24)
The Numerical Solution of Elliptic Equations (1987) (24)
Wall Effects in Cavity Flow - I (1950) (24)
Tricubic polynomial interpolation. (1971) (23)
Neutral elements in general lattices (1940) (21)
Confocal Conics in Space-Time (1962) (21)
Interpolation to boundary data in triangles (1973) (20)
A Characterization of Boolean Algebras (1939) (20)
Orbit theory : [proceedings of the Ninth Symposium in Applied Mathematics of the American Mathematical Society, held at New York University, April 4-6, 1957 (1959) (18)
Applications of lattice algebra (1934) (18)
Nuclear Reactor Theory (1961) (18)
Representation of Jordan and Lie algebras (1949) (17)
Harmonic solutions of transport equations (1969) (17)
The Meaning of Completeness (1937) (15)
Metric foundations of geometry. I (1944) (14)
Difference methods for solving convection-diffusion equations (1990) (14)
Classification of Partial Differential Equations (1954) (14)
Computers in Algebra and Number Theory (1971) (14)
Convexity lattices (1985) (13)
Angular singularities of elliptic problems (1972) (13)
Transition and Turbulence in Hypersonic Wakes (1966) (13)
A variational principle for nonlinear networks (1963) (12)
The Topology of Transformation-Sets (1934) (12)
Isotropic distributions of test matrices (1979) (12)
Selected Papers On Algebra And Topology (1987) (12)
Averaged Conservation Laws in Pipes (1964) (11)
Distributive postulates for systems like Boolean algebras (1946) (10)
On the Completeness of Sturm-Liouville Expansions (1960) (10)
Lecture notes on ordinary differential equations (1960) (9)
On the order of groups of automorphisms (1936) (9)
Felix Klein and his "Erlanger Programm" (1988) (9)
Computing Developments 1935–1955, as Seen from Cambridge, U.S.A. (1980) (8)
Extensions of Lie groups (1950) (8)
The role of order in computing (1988) (8)
Asymptotic behavior of solutions of first-order linear differential-delay equations (1966) (8)
Kinematics of Homogeneous Turbulence (1958) (8)
Transfinite subgroup series (1934) (8)
Multivariate approximation by locally blended univariate interpolants. (1974) (8)
Integro-differential delay equations of positive type (1966) (8)
Fluid dynamics, reactor computations, and surface representation (1990) (7)
EXACT ANALYTIC SOLUTIONS OF TRANSPORT EQUATIONS. (1970) (7)
Galois and Group Theory (1937) (7)
The Rise of Modern Algebra to 1936 (1987) (7)
Third order positive cyclic systems of linear differential equations (1969) (7)
Continuous groups and linear spaces (1987) (6)
Essentially positive systems of linear differential equations (1965) (6)
Universal Algebra and Automata (1987) (6)
Well-set Cauchy problems and C0-semigroups (1964) (6)
Ordered Sets in Geometry (1982) (6)
Théorie et applications des treillis (1949) (6)
The Role of Modern Algebra in Computing (1987) (5)
Numerical solution of hydrodynamic problems (1975) (5)
STATISTICALLY WELL-SET CAUCHY PROBLEMS (1973) (5)
Linear second-order differential equations of positive type (1967) (4)
The Rise of Modern Algebra, 1936 to 1950 (1987) (4)
Two Hadamard numbers for matrices (1975) (4)
Note on the paper “On the combination of subalgebras” (1934) (4)
What is a Lattice (1943) (4)
Higher-Order Linear Finite Element Methods. (1974) (4)
A Survey of Modem Algebra: The Fiftieth Anniversary of its Publication (1992) (4)
Applications in Algebra (1940) (4)
AVERAGING OPERATORS ON (4)
Lattice theory and its applications : in celebration of Garrett Birkhoff's 80th birthday (1995) (4)
A history of numerical analysis from the 16th through the 19th century (1978) (4)
Preliminary edition of modern applied algebra (1967) (4)
The Impact of Computers on Undergraduate Mathematical Education in 1984 (1972) (3)
Note on Newtonian Force-Fields (1949) (3)
Positive linear operators (1940) (3)
SOLVING ELLIPTIC PROBLEMS: 1930–1980 (1981) (3)
Calculation of Potential Flows with Free Streamlines (1961) (3)
Landau on Number Theory (1929) (3)
The Birkhoff prize talks Atlanta, 1978 (1978) (3)
NOTE ON THE HEAT EQUATION (1954) (3)
Types of lattices (1940) (3)
Richard von Mises' Years at Harvard (1983) (2)
Regular partial differential equations (1958) (2)
LAGRANGIAN HYDRODYNAMIC COMPUTATIONS AND MOLECULAR MODELS OF MATTER (1961) (2)
Mathematics and Computer Science (1975) (2)
The origin, nature, and influence of relativity (1926) (2)
TRANSPORT THEORY. SIAM--AMS PROCEEDINGS HELD IN NEW YORK CITY, APRIL 5-- 8, 1967. VOLUME I. (1969) (2)
Autonomous families of differential systems (1976) (2)
SOME MATHEMATICAL PROBLEMS OF NUMERICAL OCEAN ACOUSTICS (1985) (2)
Errata: Reactor Criticality and Nonnegative Matrices (1959) (2)
Some current questions on solving linear elliptic problems (1990) (2)
Survey of modern algebra / Garret Birkhoff, Saunders McLane (1953) (2)
ELLPACK and ITPACK as research tools for solving elliptic problems (1990) (2)
The radical of a group with operators (1943) (1)
Problems for Solution: 3673-3678 (1934) (1)
Lattice-ordered monoids (1940) (1)
A New Interval Topology for Dually Directed Sets (1987) (1)
Adventures of a mathematician: By S. M. Ulam. New York (Scribners). 1976. 317 pp. $17.50 (1977) (1)
Added mass of cylinders (1980) (1)
Positive cyclic systems of linear differential equations (1970) (1)
Metric and topological lattices (1940) (1)
Higher Algebra. (Scientific Books: Modern Higher Algebra) (1938) (1)
Review: S. A. Kiss, Transformations on lattices and structures of logic (1948) (1)
Optimal Smoothing of Gaussian Periodic Data (1971) (1)
Book Review: Transformations on lattices and structures of logic (1948) (1)
4. Relaxation Methods (1972) (1)
WILLIAM FOGG OSGOOD. (1943) (1)
Critical Review of Shaped Charge Information (1954) (1)
Induced mass with variable density (1953) (1)
Algebra [Mac Lane, 1974] (1974) (1)
Corrections to “Current Trends in Algebra” (1974) (1)
IIΙ. Jets, Wakes and Cavities (1961) (1)
Product integration: John D. Dollard and Charles N. Friedman, with an Appendix by Pesi Masani, Addison-Wesley, Reading, Mass., 1979 (1982) (1)
Lattice-ordered demigroups (1961) (1)
Induced mass with free boundaries (1952) (1)
Numerical solution of field problems in continuum physics : proceedings of a symposium in applied mathematics ... (1970) (1)
PIECEWISE ANALYTIC INTERPOLATION AND APPROXIMATION IN TRIANGULATED POLYGONS (1972) (1)
Selected Papers of Richard von Mises, Vol. 2. Probability and statistics, General (1966) (1)
Review: M. H. Stone, Algebraic Characterizations of Special Boolean Rings (1938) (1)
Note on positive linear operators (1965) (1)
6. Direct Variational Methods (1984) (0)
Term Rewriting and Universal Algebra in Historical Perspective (Abstract of Invited Lecture) (1989) (0)
IV. Modeling and Dimensional Analysis (1961) (0)
The Putnam Mathematical Competition for 1946 (1946) (0)
Final report [on solving the multigroup diffusion equations] (1975) (0)
II. Paradoxes of Viscous Flow (1961) (0)
HARMONICS IN TRANSPORT THEORY. (1970) (0)
9. Applications to Boundary Value Problems (1972) (0)
Philosophy of geometry from Riemann to Poincaré: Roberto Torretti, Reidel, 1978 (1979) (0)
Probable implication, the contrapositive, and contingency tables (1989) (0)
Postulates for lattices (1940) (0)
7. Approximation of Smooth Functions (1972) (0)
Algebra of Classes (1941) (0)
Note on maximum shock deflection (1954) (0)
A Conversation with Garrett Birkhoff (1983) (0)
Sound waves in fluids (1987) (0)
THE LOGARITHMIC PART OF MICHELL'S FDNCTION, (1953) (0)
Reversibility and Two-Dimensional Airfoil Theory (1946) (0)
Applications to logic and probability (1940) (0)
Abstract Algebra: An Introduction to Abstract Algebra . By Cyrus C. MacDuffee. 303 pp. John Wiley and Sons. $4.00. (1941) (0)
Origins of modern algebra: By Lubos Novy. Prague (Academia), 1973. 260 p (1974) (0)
Ordinary differential equations / Garrett Birkhoff, Gian-Carlo Reta (1978) (0)
3. Difference Approximations (1972) (0)
Applications of Abstract Algebra (George Mackiw) (1986) (0)
Mathematical models of sound waves in fluids (1987) (0)
Origins and basic concepts (1986) (0)
Axiomatic definitions of perfectly separable metric spaces (1933) (0)
8. Variational Methods (1972) (0)
Discussion: “A Review on Vortex Streets, Periodic Wakes, and Induced Vibration Phenomena” (Marris, A. W., 1964, ASME J. Basic Eng., 86, pp. 185–193) (1964) (0)
Review: A. Tarski, Cardinal algebras (1950) (0)
Borel algebras and von Neumann lattices (1940) (0)
The orbit structure of uniformly positive cyclic systems (1976) (0)
4. Direct and Iterative Methods (1984) (0)
Review: John von Neumann, Continuous geometry (1962) (0)
Proceedings of Symposia in Applied Mathematics, vol. XI, Nuclear Reactor Theory (1963) (0)
A Correction: Some Remarks Concerning Schrodinger's Wave Equation (1933) (0)
6. Integral Equation Methods (1972) (0)
Review: Clarence E. Rose, Matrix and Tensor Algebra for Engineers and Chemists (1941) (0)
Applications to general topology (1940) (0)
Lattice-ordered Lie groups (1987) (0)
CARATHÉODORY AND HARVARD (1991) (0)
Algebra [Mac Lane, 1967] (1967) (0)
Book Review: Oeuvres de Georges Humbert (1934) (0)
Note on universal topological algebra (1976) (0)
FINITE ELEMENT METHODS IN REACTOR DESIGN CALCULATIONS. (1971) (0)
V. Groups and Fluid Mechanics (1961) (0)
5. Semi-Iterative Methods (1972) (0)
Workshop on the Historical Development of Modern Mathematics (1975) (0)
5. Accelerating Convergence (1984) (0)
Moisil Gr. C.. Recherches sur l'algèbre de la logique. Annales scientifiques de l'Université de Jassy, vol. 22 (1936), pp. 1–118. (1936) (0)
Les grands théorèmes (1978) (0)
Mihailescu Eugen Gh.. Recherches sur l'équivalence, la négation et la réciprocité dans le calcul des propositions. Mathematica (Cluj), vol. 15 (1939), pp. 81–118. (1940) (0)
Review: Eugen Gh. Mihailescu, Recherches sur L'Equivalence, La Negation et la Reciprocite dans le Calcul des Propositions (1940) (0)
7. Finite Element Approximations (1984) (0)
Review: Vito Volterra and Bohuslav Hostinsky, Opérations Infinitésimales Linéaires (1938) (0)
8. Integral Equation Methods (1984) (0)
Tarski A.. Ideale in den Mengenkörpern. Annales de la Société Polonaise de Mathématique , vol. 15 (for 1936, pub. 1937), pp. 186–189. (1938) (0)
COMPUTING ADDED MASS COEFFICIENTS (1984) (0)
VI. Added Mass (1961) (0)
Higher Algebra: Modern Higher Algebra . By Adrian Albert. Chicago University Press, xiv + 319 pages, $4.00. (1938) (0)
HEAVY WATER LATTICE ANALYSES AT ISPRA. (1968) (0)
MATHEMA TICS: G. BIRKHOFF (2005) (0)
Numerical techniques of fluid flow (1973) (0)
Abstracts of Papers (1991) (0)
Book Review: Computational analysis with the $HP\,25$ pocket calculator@@@Book Review: Compact numerical methods for computers: linear algebra and function minimization@@@Book Review: LINPACK: User's guide (1980) (0)
Theory of Functions: The Theory of Functions . By J. E. Littlewood. 243 pp., Oxford University Press. $5.50. (1945) (0)
Stone M. H.. Algebraic characterizations of special Boolean rings. Fundamenta mathemalicae, vol. 29 (1937), pp. 223–303. (1938) (0)
I. Paradoxes of Nonviscous Flow (1961) (0)
Annotated Bibliography of Reports. Supplement Number 5, 1 July 1972 - 30 June 1973, (1973) (0)
Mathematical Physics: Methoden der Mathematischen Physik . By R. Courant and D. Hilbert. 2 volumes. Interscience Press. By permission of the Alien Property Custodian. $8.00 each; $14.00 the pair. (1944) (0)
Johns von Neumann and Norbert Wiener: By Steve Heims. Cambridge, Mass., and London (M.I.T. Press). 1981 (1983) (0)
A Mathematical Classic: Topological Groups . By L. Pontrjagin (translated by Emma Lehmer). ix + 299 pp. Princeton, 1939. (1940) (0)
Review: A. Tarski, Ideale in den Mengenkorpern (1938) (0)
1. Typical Elliptic Problems (1972) (0)
Title pages for Harvard Library Bulletin, Volume IX.2 (1947) (0)
5 – Dimensional Analysis (1980) (0)
Aplikovaná algebra : Modern applied algebra (Orig.) (1981) (0)
House monotone apportionment schemes ( integer programming / optimization ) (0)
Calculus: Calculus . By Lyman M. Kells. Prentice-Hall. $3.75. (1944) (0)
Structure and representation theory (1940) (0)
John von Neumann.By Norman Macrae. New York (Random House). 1992 (1997) (0)
2. Classical Analysis (1972) (0)
THE TABULATION OF MICHELL'S FUNCTION, (1958) (0)
A Limitation of Fourier Analysis (1967) (0)
Book Review: Matrix and Tensor Algebra for Engineers and Chemists (1941) (0)
A theorem on transitive groups (1933) (0)

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