Robert Daniel Carmichael | Academic Influence

Robert Daniel Carmichael's AcademicInfluence.com Rankings

Robert Daniel Carmichael

Mathematics

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Measure Theory

#650

Historical Rank

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Mathematics

Robert Daniel Carmichael's Degrees

PhD Mathematics University of Chicago

Why Is Robert Daniel Carmichael Influential?

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According to Wikipedia, Robert Daniel Carmichael was an American mathematician. Biography Carmichael was born in Goodwater, Alabama. He attended Lineville College, briefly, and he earned his bachelor's degree in 1898, while he was studying towards his Ph.D. degree at Princeton University. Carmichael completed the requirements for his Ph.D. in mathematics in 1911. Carmichael's Ph.D. research in mathematics was done under the guidance of the noted American mathematician G. David Birkhoff, and it is considered to be the first significant American contribution to the knowledge of differential equations in mathematics.

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Robert Daniel Carmichael'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

On the Numerical Factors of the Arithmetic Forms α n ± β n (348)
Introduction to the theory of groups of finite order (209)
The General Theory of Linear q-Difference Equations (1912) (203)
Note on a new number theory function (1910) (139)
On Composite Numbers P Which Satisfy the Fermat Congruence a P-1 ≡1 mod P (1912) (94)
Group Theory: 15 (1906) (93)
Mathematical tables and formulae (1929) (90)
The Theory of Functions of a Real Variable and the Theory of Fourier's Series (1928) (75)
Expansions of Arithmetical Functions in Infinite Series (1932) (62)
Linear differential equations of infinite order (1936) (37)
Theory of numbers (33)
On Euler's $\phi$-function (1907) (25)
Note on the roots of algebraic equations (1914) (24)
On the Theory of Linear Difference Equations (1913) (23)
Note on Euler's $\varphi$-function (1922) (23)
Review: A. S. Eddington, The Mathematical Theory of Relativity (1925) (20)
On Certain Functional Equations (1909) (19)
On the Numerical Factors of Certain Arithmetic Forms (1909) (19)
Tactical Configurations of Rank Two (1931) (18)
The Principles of Natural Knowledge (1921) (16)
History of the Theory of Numbers (13)
Textbooks in mathematics (1931) (12)
Boundary Value and Expansion Problems: Algebraic Basis of the Theory (1921) (11)
The Pell Equation (1913) (10)
Systems of linear difference equations and expansions in series of exponential functions (1933) (9)
Brief analytic geometry (1935) (8)
Algebras of Certain Doubly Transitive Groups (1931) (8)
Théorie des nombres (8)
Multiply Perfect Numbers of Three Different Primes (1906) (7)
A table of multiply perfect numbers (1907) (7)
A Simple Principle of Unification in the Elementary Theory of Numbers (1929) (7)
Elementary inequalities for the roots of an algebraic equation (1918) (7)
Review: Frédéric Riesz, Les Systèmes d'Équations linéaires a une Infinité d'Inconnues (1914) (6)
Summation of Functions of a Complex Variable (1933) (6)
The Logic of Discovery. (1931) (6)
The Theory of Relativity. (1914) (5)
On Non-Homogeneous Linear Differential Equations of Infinite Order With Constant Coefficients (1936) (5)
THE MEANING OF GRADUATE STUDY. (1913) (5)
Note on Fermat's last theorem (1913) (5)
The Present State of the Difference Calculus and the Prospect for the Future (1924) (4)
Boundary Value and Expansion Problems: Oscillation, Comparison and Expansion Theorems (1922) (4)
Multiply Perfect Odd Numbers with Three Prime Factors (1906) (4)
General aspects of the theory of summable series (1918) (4)
Boundary Value and Expansion Problems; Formulation of Various Transcendental Problems (1921) (3)
Conditions Necessary and Sufficient for the Existence of a Stieltjes Integral. (1919) (3)
On Certain Diophantine Equations having Multiple Parameter Solutions (1913) (3)
On a Certain Class of Curves Given by Transcendental Equations (1906) (3)
A Debate on the Theory of Relativity. (3)
On Certain Transcendental Functions Defined by a Symbolic Equation (1908) (3)
On the Character of Primitive Human Progress (3)
THE OUTLOOK FOR SCIENCE. (1914) (3)
On r-Fold Symmetry of Plane Algebraic Curves (1910) (3)
Book Review: The Mathematical Theory of Relativity (3)
Transformations Leaving Invariant Certain Partial Differential Equations of Physics (3)
On the Theory of Relativity: Analysis of the Postulates (1912) (2)
Notes on the simplex theory of numbers (1909) (2)
ON EXPANSIONS OF ARITHMETICAL FUNCTIONS. (1930) (2)
The Song of Fire (1921) (2)
The Larger Human Worth of Mathematics (1922) (2)
On transcendentally transcendental functions (1913) (2)
Fermat Numbers F n = 2 2n + 1 (1919) (2)
Linear Mixed Equations and Their Analytic Solutions (1913) (2)
Review: Thomas M. Macrobert, Functions of a Complex Variable (1919) (2)
Even multiply perfect numbers of five different prime factors (1908) (2)
NATIONAL TEMPERAMENT IN SCIENTIFIC INVESTIGATIONS. (2)
On the Impossibility of Certain Diophantine Equations and Systems of Equations (1913) (2)
Review: Werner Gent, Die Raum-Zeit-Philosophie des 19. Jahrhunderts (1932) (2)
Algebraic guides to transcendental problems (1922) (2)
On a general class of integrals of the form (1919) (1)
THE PROSPECT OF HUMAN PROGRESS. (1914) (1)
Book Review: The Algebraic Theory of Modular Systems (1919) (1)
Repeated Solutions of a Certain Class of Linear Functional Equations (1)
On the Geometric Properties of Quartic Curves Possessing Fourfold Symmetry with Respect to a Point (1)
On the Theory of Relativity: Mass, Force and Energy (1913) (1)
Review: G. H. Hardy, Some famous problems of the theory of numbers and in particular Waring's problem (1921) (1)
Watson on Bessel Functions (1924) (1)
A Generalization of Cauchy's Functional Equations (1911) (1)
Second note on Fermat's last theorem (1913) (1)
Some Recent Researches in the Theory of Numbers (1932) (1)
A Table of the Values of m Corresponding to Given Values of φ(m) (1908) (1)
Review: L. R. Ingersoll and O. J. Zobel, An Introduction to the Mathematical Theory of Heat Conduction with Engineering and Geological Applications (1915) (1)
Note on Multiply Perfect Numbers (1906) (1)
Number Theory: 211-214 (1914) (1)
Algebra: 398-400 (1)
Note on triple systems (1932) (1)
On a General Class of Integrals of the Form i nfty 0 φ(t) g (x + t) dt (1919) (1)
On a classification of integral functions by means of certain invariant point properties (1936) (1)
THE NEW VOLUMES OF THE ENCYCLOPAEDIA BRITANNICA (1923) (1)
Number Theory and Diophantine Analysis: 185 (1911) (1)
On the Solutions of Linear Homogeneous Difference Equations (1916) (1)
Note on a Recent Problem in the American Mathematical Monthly (1)
THE PROVISION MADE BY MATHEMATICS FOR THE NEEDS OF SCIENCE. (1917) (1)
Functions of exponential type (1934) (1)
A LESSON FROM THE HISTORY OF NUMBERS (1913) (1)
On the Classification of Plane Algebraic Curves Possessing Fourfold Symmetry with Respect to a Point (1)
Note on certain inverse problems in the simplex theory of numbers (1907) (1)
Public ownership - the alternatives [Book Review] (1962) (1)
The Outlook of Science (1)
Meaning in the Case of Mathematical Postulates (1925) (1)
Review: E. Rutherford, Radioactive Substances and their Radiations (1)
Review: Emanuel Czuber, Wahrscheinlichkeitsrechnung und ihre Anwendung auf Fehlerausgleichung, Statistik und Lebensversicherung (1916) (1)
Book Review: Sophus Lie's Gesammelte Abhandlungen (Samlede Avhandlinger) (1923) (1)
On the Expansion of Certain Analytic Functions in Series (1920) (0)
Nörlund on Finite Differences (0)
Birkhoff on Relativity (1926) (0)
Number Theory and Diophantine Analysis: 149-150 (1907) (0)
On a Certain Quartic Curve which May Degenerate into an Ellipse (1907) (0)
Book Review: Oeuvres de G. H. Halphen (0)
Note on a certain equation involving the function $E\left( x \right)$ (1908) (0)
Book Review: The Logic of Science (1932) (0)
Review: H. Latzin, Analysis des Unendlichen im Psychischen und Physischen (1932) (0)
Review: Harold T. Davis, Philosophy and Modern Science (1932) (0)
Note on Some Polynomials Related to Legendre's Coefficients (1909) (0)
Number Theory and Diophantine Analysis: 155-156 (1908) (0)
On the Convergence of Certain Classes of Series of Functions (1920) (0)
Miscellaneous: 163-167 (1906) (0)
Geometry: 257-259 (1905) (0)
Chapter III: Equations of the third degree (0)
Algebra: 253-255 (0)
Calculus: 196-197,189 (1905) (0)
Geometry: 427-430 (0)
Review: F. S. C. Northrop, Science and First Principles (1932) (0)
Review: W. Ahrens, Mathematische Spiele (1919) (0)
Review: A. Voss, Ueber das Wesen der Mathematik (1915) (0)
Calculus: 232-233 (1906) (0)
Functions of Two Complex Variables (1918) (0)
Chapter II: Problems involving a multiplicative domain (0)
Average and Probability: 192 (1907) (0)
On the Representation of the Trigonometric Functions by Lines (1908) (0)
Points of View of Cauchy and Weierstrass in the Theory of Functions (1919) (0)
Algebra: 326-328 (1909) (0)
Note on the Theory of Integral Functions of the first Class (0)
On The Theory of Functions of a Triple Variable (1909) (0)
Algebra: 313-316 (1909) (0)
Algebra: 413-417 (1914) (0)
On Plane Algebraic Curves Symmetrical With Respect to Each of Two Rectangular Axes (1908) (0)
Calculus: 284-286 (1909) (0)
Note on the Maximum Indicator of Certain Odd Numbers (1906) (0)
Review: Charles Marquis Smith, Electric and Magnetic Measurements (1918) (0)
Finite Geometries and the Theory of Groups (1930) (0)
Book Review: The Emergence of Life (1932) (0)
Average and Probability: 193-194 (0)
Number Theory: 218-219 (1914) (0)
Calculus: 255-256 (1908) (0)
On a Certain Class of Quartic Curves (0)
IV. On the singular solutions of differential equations (0)
Additive Functions of a Point Set (1918) (0)
On the n-Section of an Angle (1906) (0)
A THREAD OF MATHEMATICAL HISTORY, AND SOME LESSONS1 (1913) (0)
Answers to Queries (1909) (0)
Number Theory and Diophantine Analysis: 148 (1907) (0)
Review: C. Jordan, H. Poincaré, É. Picard and E. Vessiot, Oeuvres de G. H. Halphen (1922) (0)
Miscellaneous: 155-156 (1905) (0)
BOOK AND FILM REVIEWS: Mathematical Tables & Formulas (1963) (0)
Average and Probability: 163-164 (1905) (0)
Geometry: 290-294 (1906) (0)
Correction: Note on Prime Numbers (1920) (0)
Calculus: 347-349 (1913) (0)
MATHEMATICS AND LIFE-THE VITALIZING OF SECONDARY MATHEMATICS (1915) (0)
Number Theory and Diophantine Analysis: 163-164 (1909) (0)
Review: H. Bateman, The Mathematical Analysis of Electrical and Optical Wave-Motion on the Basis of Maxwell's Equations (0)
Book Review: The Atom and the Bohr Theory of its Structure (1924) (0)
Geometry: 251-253 (1905) (0)
The New Mechanics (1930) (0)
Book Review: Einführung in die Wellenmechanik (1930) (0)
The System of Animate Nature (1921) (0)
Number and Clear Thinking (1935) (0)
Another Proof of a Theorem in Multiply Perfect Numbers (1908) (0)
Review: Edward V. Huntington, The Continuum and Other Types of Serial Order (1918) (0)
History of the Theory of Numbers@@@History of the Theory of Numbers. (1921) (0)
The Calculus of Probability (1919) (0)
Review: Max Planck, Where Is Science Going? (1933) (0)
Review: Otto Stolz und J. A. Gmeiner, Theoretische Arithmetik (1921) (0)
The Meaning of Relativity (1923) (0)
Calculus: 242-244 (1907) (0)
Calculus: 217-219 (1906) (0)
Book Review: Die Raum-Zeit-Philosophie des 19. Jahrhunderts (1932) (0)
Average and Probability: 174-175 (1905) (0)
Chapter V: Equations of the degree higher than the fourth. The Fermat problem (0)
Book Review: Analysis des Unendlichen im Psychischen und Physischen (1932) (0)
Book Review: The Mathematical Analysis of Electrical and Optical Wave-Motion on the Basis of Maxwell's Equations (0)
Algebra: 275-277 (1906) (0)
Review: Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers (1916) (0)
Number Theory and Diophantine Analysis: 168-169 (1909) (0)
On Numbers of the Form a 2 + αb 2 (1937) (0)
Calculus: 267-268 (1908) (0)
Number Theory and Diophantine Analysis: 147 (1907) (0)
Calculus: 221-224 (1906) (0)
Book Review: Das Problem der Kreisteilung. Ein Beitrag zur Geschichte seiner Entwicklung (1914) (0)
Chapter I: Introduction. Rational triangles. Method of infinite descent (0)
Note on convergence tests for series and on Stieltjes integration by parts (1919) (0)
Review: M. Pasch, Veränderliche und Funktion (1915) (0)
Mechanics: 205-206 (1907) (0)
On the Remainder Term in a Certain Development of f(a + x) (0)
On the Asymptotic Character of Functions Defined by Series of the Form Σc n g(x + n) (1917) (0)
Review: H. A. Kramers and Helge Holst, The Atom and the Bohr Theory of its Structure (1924) (0)
Diophantine Analysis: 132-133 (1906) (0)
Book Review: Tratado Elemental de Goniometria (1919) (0)
Calculus: 237-238 (1907) (0)
THE INTERNATIONAL WORK OF SCIENTIFIC SYNTHESIS. (1923) (0)
Number Theory and Diophantine Analysis: 160-162 (1909) (0)
Review: Paul R. Heyl, The Fundamental Concepts of Physics in the Light of Modern Discovery (1927) (0)
Book Review: Elementary Theory of Equations (1915) (0)
Individuality in Research (1919) (0)
Introduction to the theory group of finite order / Robert D. Carmichael (1956) (0)
Review: A. R. Forsyth, Lehrbuch der Differentialgleichungen (1913) (0)
Note on a physical interpretation of Stieltjes integrals (1919) (0)
Review: Friedrich Engel and Poul Heegaard, Sophus Lie's Gesammelte Abhandlungen (Samlede Avhandlinger) (1930) (0)
Average and Probability: 165-167 (1905) (0)
ON THE NATURE OF MATHEMATICAL AND SCIENTIFIC DEMONSTRATION. (1913) (0)
Geometry: 274-276 (1905) (0)
Comparison Theorems for Homogeneous Linear Differential Equations of General Order (1918) (0)
On the Theory of Relativity: Philosophical' Aspects (1913) (0)
Some theorems on the convergence of series (1914) (0)
Number Theory and Diophantine Analysis: 181-182,148,153,157,161,162,166, 167 (1911) (0)
Geometry: 260-262 (1905) (0)
Book Review: Mathematische Spiele (1919) (0)
Algebra: 273-274 (1906) (0)
On Series of Iterated Linear Fractional Functions (1914) (0)
Review: Arthur Mitzscherling, Das Problem der Kreisteilung. Ein Beitrag zur Geschichte seiner Entwicklung (1914) (0)
Review: Abraham Edel, Aristotle's Theory of the Infinite (1936) (0)
Review: Andreas Voigt, Theorie der Zahlenreihen und der Reihengleichungen (0)
On the General Tangent to Plane Curves (1908) (0)
NATIONAL TEMPERAMENT IN SCIENTIFIC INVESTIGATIONS. (1921) (0)
Calculus: 247-249 (1907) (0)
Chapter IV: Equations of the fourth degree (0)
Volume III of Lie's Memoirs (1923) (0)
On Constructing a Cube having a given Ratio to a given Cube (1907) (0)
Diophantine Analysis: 139-141 (1906) (0)
Average and Probability: 185 (1906) (0)
Book Review: Aristotle's Theory of the Infinite (1936) (0)
Book Review: Wahrscheinlichkeitsrechnung und ihre Anwendung auf Fehlerausgleichung, Statistik und Lebensversicherung (1916) (0)
Theory of numbers and Diophatine analysis (1959) (0)
Algebra: 262-264 (1906) (0)
On Dividing an Angle into Parts having the Ratios of any given Straight Lines (1907) (0)
Book Review: Monographs on Topics of Modern Mathematics Relevant to the Elementary Field (0)
Number Theory and Diophantine Analysis: 203-204 (0)
Geometry: 313-315 (1907) (0)
Algebra: 318-320 (1909) (0)
Geometry: 299-302 (1906) (0)
Proof that every positive integer is a sum of four integral squares (1936) (0)
Average and Probability: 200-203 (1908) (0)
Number Theory and Diophantine Analysis: 199-202 (1913) (0)
Hobson's Second Volume (0)
Number Theory: 208-210 (1914) (0)
Average and Probability: 190 (1907) (0)
Calculus: 250-251 (1907) (0)
The Order of Nature (1921) (0)
Number Theory and Diophantine Analysis: 165-167 (1909) (0)
L'unité de la Science (1921) (0)
Review: Émile Borel, Leçons sur la Théorie de la Croissance (1911) (0)
Book Review: Calcul des Probabilités (1913) (0)
Book Review: Calcul numérique (1915) (0)
Review: O. D. Chwolson, Traité de Physique. Tome supplémentaire: La Physique de 1914 à 1926, première partie, and Albert Einstein, Investigations on the Theory of the Brownian Movement, and A. Sommerfeld, Three Lectures on Atomic Physics (1927) (0)
Review: E. Fabry, Démonstration du Théorème de Fermat (1914) (0)
Review: Emile Borel, Leons sur la Thorie des Fonctions (0)
Review: Clément Laurès, Les Bases de la Géométrie et de la Physique. L'Invariance de L'Espace Euclidien (1928) (0)
Review: R. de Montessus et R. d'Adhémar, Calcul numérique (1915) (0)
Review: Georges Giraud, Leçons sur les Fonctions automorphes (1921) (0)
Review: Pierre Duhem, Le Système du Monde. Histoire des Doctrines cosmologiques de Platon à Copernic. Tome premier (1915) (0)
Diophantine Analysis: 137 (1906) (0)
Book Review: Le Systme du Monde. Histoire des Doctrines cosmologiques de Platon Copernic. (1915) (0)
Book Review: Les Sciences Mathématiques en France depuis un Demi-Siècle (0)
Book Review: Leçons sur la Théorie de la Croissance (1911) (0)
Analyse indéterminée, triangles rationnels-équations du second degré equations des 3e et 4e degré et d'un degré supérieur au 4e dernier théoréme de fermat-equations fonctionnelles (0)
Book Review: Les Bases de la Gomtrie et de la Physique. L'Invariance de L'Espace Euclidien (0)
Concerning quasi-$k$-fold transitivity of permutation groups (1930) (0)
Review: H. Poincaré, Calcul des Probabilités (1913) (0)
Book Review: Vorlesungen ber Differenzenrechnung (0)
Response : National Temperament in Scientific Investigations (1921) (0)
Concerning the Postulational Treatment of Empirical Truth (1923) (0)
The Secret (Poem) (0)
The International Work of Scientific Synthesis (1923) (0)
Review: L. E. Dickson, Elementary Theory of Equations (1915) (0)
Book Review: Theoretische Arithmetik (0)
Book Review: Ueber das Wesen der Mathematik (1915) (0)
Book Review: Science and First Principles (1932) (0)
Review: John Butler Burke, The Emergence of Life (1932) (0)
Review: Krise und Neuaufbau in den exakten Wissenschaften (0)
Review: Harold R. Smart, The Logic of Science (1932) (0)
Review: Arthur Eddington, The Expanding Universe (1934) (0)
The Domain of Natural Science (1924) (0)
Review: Horace Lamb, Hydrodynamics (1925) (0)
Book Review: Where Is Science Going? (1933) (0)
Book Review: The Expanding Universe (0)
Book Review: Philosophy and Modern Science (1932) (0)
Book Review: Le Hasard (1915) (0)
The Domain of Natural Science . The Gifford Lectures delivered in the University of Aberdeen in 1921 and 1922. By E. W. Hobson. The Macmillan Company, 1923. xvi + 510 pages. (1924) (0)
Review: W. Ahrens, Mathematiker Anekdoten (1921) (0)
Review: Oeuvres de G. H. Halphen (1925) (0)
The Structure of Exact Thought (0)
Review: Harris Hancock, Elliptic Integrals (1918) (0)
Review: Leonard Eugene Dickson, Algebraic Invariants (0)
Criticisms and Discussions: Carmichael's Reply to Klyce (1925) (0)
ON A QUESTION RELATED TO WARING'S PROBLEM (1931) (0)
A Half Century of French Mathematics (0)
Empirical Results in the Theory of Numbers (1921) (0)
What is man? : a poem (1950) (0)
Examples of a remarkable class of series (1917) (0)
Note on a Transformation of Series similar to the Principle of Inversion in the Theory of Numbers (0)
Number Theory: 205-207 (1914) (0)
Book Review: The Fundamental Concepts of Physics in the Light of Modern Discovery (0)
Review: A. N. Whitehead, An Enquiry Concerning the Principles of Natural Knowledge (1920) (0)
The Mathematical Work of Thomas Jan Stieltjes (0)
Review: H. Bateman, Differential Equations (1920) (0)
On Non-Homogeneous Equations with an Infinite Number of Variables (0)
Average and Probability: 167 (1905) (0)
Review: Max Planck, The Universe in the Light of Modern Physics (1932) (0)
Six Propositions on Prime Numbers (1905) (0)
Calculus: 252-253 (0)
Nörlund on Calculus of Differences (1925) (0)
Average and Probability: 199 (1908) (0)
Geometry: 263-267 (1905) (0)
Book Review: Elements of Optics for the Use of Schools and Colleges (1919) (0)
Chapter VI: The method of functional equations (0)
Review: Emile Borel, Le Hasard (1915) (0)
Average and Probability: 196-197 (1908) (0)
Lie's Works, Volume VI (1928) (0)

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