Mathematics (Bookshelf)
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<<Science
Mathematics (colloquially, maths, or math in North American English) is the body of knowledge centered on concepts such as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions". Steen and Devlin have argued that mathematics is the science of pattern and that mathematicians seek out patterns whether found in numbers, space, science, computers, or in imaginary abstractions.
—Excerpted from Mathematics on Wikipedia, the Free Encyclopedia.
History
- Walter William Rouse Ball, A Short Account of the History of Mathematics
(English)
- Florian Cajori, A History of Mathematics (English)
- John Casey, The First Six Books of the Elements of Euclid (English)
- Levi Leonard Conant, The Number Concept: Its Origin and Development (English)
- Jacomy-Régnier, Histoire des Nombres et de la Numération Mécanique (French)
- Louis Charles Karpinski and David Eugene Smith, The Hindu-Arabic Numerals (English)
- Felix Klein, The Evanston Colloquium (English)
- Alexander Macfarlane, Lectures on Ten British Mathematicians (English)
- Isaac Newton, Philosophiae Naturalis Principia Mathematica (Latin)
- David Eugene Smith, History of Modern Mathematics (English)
- Robert Steele (ed.), The Earliest Arthmetics in English (English)
- Emil Weyr, Über die Geometrie der alten Ägypter (German)
Logic and Philosophy
- George Boole, An Investigation of the Laws of Thought (English)
- George Boole, The Mathematical Analysis of Logic (English)
- Isidore Auguste Marie François Xavier Comte, The Philosophy of Mathematics (English)
- Louis Couturat, The Algebra of Logic (English)
- Carveth Read, Logic: Deductive and Inductive (English)
- Bertrand Russell, Introduction to Mathematical Philosophy (English)
- St. George William Joseph Stock, Deductive Logic (English)
- Alfred North Whitehead, An Introduction to Mathematics (English)
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus (English)
Constants and Numerical Sequences
See also Amusements, Arithmetics, Recreations.
- A List of Factorial Math Constants (English)
- Miscellaneous Mathematical Constants ed. Simon Plouffe (English)
- Jerry Bonnell and Robert Nemiroff, The Square Root of 2 (English)
- Jerry Bonnell and Robert Nemiroff, The Square Root of 3 (English)
- Jerry Bonnell and Robert Nemiroff, The Square Root of 5 (English)
- Jerry Bonnell and Robert Nemiroff, The Square Root of 6 (English)
- Jerry Bonnell and Robert Nemiroff, The Square Root of 7 (English)
- Jerry Bonnell and Robert Nemiroff, The Square Root of 8 (English)
- Jerry Bonnell and Robert Nemiroff, The Square Root of 10 (English)
- Jerry Bonnell and Robert Nemiroff, The Golden Mean (English)
- Jerry Bonnell and Robert Nemiroff, The Number "e" (English)
- Greg Fee, Catalan's Constant: Ramanujan's Formula (English)
- Scott Hemphill, Pi (English)
- Michael Husted, The Fibonacci Number Series (English)
- Yasumasa Kanada, One Divided By pi (to 1 million digits) (English)
- Stan Kerr, The Square Root of 2 (English)
- Simon Plouffe, The First 1000 Euler Numbers (English)
- Simon Plouffe, The First 1001 Fibonacci Numbers (English)
- Simon Plouffe, The First 498 Bernoulli Numbers (English)
- Simon Plouffe, Miscellaneous Mathematical Constants (English)
- Simon Plouffe, The Value of zeta(3) to 1,000,000 places (English)
- David Slowinski, The 32nd Mersenne Prime (English)
Amusements, Arithmetics, Recreations
- Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions (English)
- Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions (Illustrated) (English)
- William Walter Rouse Ball, Mathematical Recreations and Essays (English)
- Mary Everest Boole, Philosophy and Fun of Algebra (English)
- Lewis Carroll, A Tangled Tale (English)
- Archie Frederick Collins, Short Cuts in Figures (English)
- Norman L. De Forest, The Square Root of 4 to a Million Places (English)
- P. Hampson, The Romance of Mathematics: Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion. (English)
- Petrus Ramus, The Way To Geometry (Middle English)
- Lyon Des Roys, La Géométrie en Vers Techniques (French)
- Hermann Schubert, Mathematical Essays and Recreations (English)
- Hermann Schubert, Elementare Arithmetik und Algebra (German)
- William Frank White, A Scrap-Book of Elementary Mathematics (English)
Algebra
- Wallace Clarke Boyden, A First Book in Algebra (English)
- William Burnside Theory of Groups of Finite Order (English)
- Augustus De Morgan, On the Study and Difficulties of Mathematics (English)
- Theodore Despeyrous, Mémoire sur les Équations Résolubles Algébriquement (French)
- Leonard Eugene Dickson, First Course in the Theory of Equations (English)
- Charles Lutwidge Dodgson (AKA Lewis Carroll), Condensation of Determinants, Being a New and Brief Method for Computing their Arithmetical Values (English)
- Henry Burchard Fine, The Number-System of Algebra (2nd edition) (English)
- Évariste Galois, Oeuvres Mathématiques d'Évariste Galois (French)
- Oliver Glenn, A Treatise on the Theory of Invariants (English)
- Joseph Louis Lagrange, Lectures on Elementary Mathematics (English)
- Lewis Irving Neikirk, Groups of the Order p^m (English)
- Romeyn Henry Rivenburg, A Review of Algebra (English)
- Richard Donald Schafer, An Introduction to Nonassociative Algebras (1961) (English)
- Hermann Schubert, Elementare Arithmetik und Algebra (German)
- George Albert Wentworth, The First Steps in Algebra (English)
Number Theory
See also Complex Analysis
- Robert Daniel Carmichael, The Theory Of Numbers (English)
- Robert Daniel Carmichael, Diophantine Analysis (English)
- Richard Dedekind, Essays on the Theory of Numbers (English)
- Godfrey Harold Hardy, Some Famous Problems of the Theory of Numbers and in particular Waring's Problem (English)
- Kurt Hensel, Zahlentheorie (German)
Combinatorics
- John W. Moon, Topics on Tournaments (English) (Under copyright; free for non-commercial use)
Calculus, Real Analysis, Fourier Series
- William Elwood Byerly, An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics. With Applications to Problems in Mathematical Physics (English)
- Augustus De Morgan, Elementary Illustrations of the Differential and Integral Calculus (English)
- David Bierens de Haan, Note sur une Méthode pour la Réduction d'Intégrales Définies
et sur son Application à Quelques Formules Spécials (French)
- Godfrey Harold Hardy, A Course of Pure Mathematics (English)
- Godfrey Harold Hardy, The Integration of Functions of a Single Variable (English)
- Godfrey Harold Hardy, Orders of Infinity: The Infinitärcalcül of Paul Du Bois-Reymond (English)
- Nels Johann Lennes and Oswald Veblen, Introduction to Infinitesimal Analysis. Functions of One Real Variable (English)
- James McMahon, Hyperbolic Functions (English)
- Sylvanus Phillips Thompson, Calculus Made Easy (English)
Differential Equations
- Gaston Floquet, Sur la Théorie des Équations Différentielles Linéaires (French)
- Jacques Hadamard, Four Lectures on Mathematics. Delivered at Columbia University in 1911
- Horace Bryon Heywood and Maurice Fréchet, L'Équation de Fredholm (French)
- Walle Abraham Hurwitz, Randwertaufgaben bei Systemen von linearen partiellen Differentialgleichungen erster Ordnung (German)
- Sophus Lie, Über Integralinvarianten und Differentialgleichungen (German)
- François De Salvert, Étude sur le Mouvement Permanent des Fluides (French)
- Vito Volterra, Leçons sur l'Intégration des Équations Différentielles aux Dérivées Partielles (French)
Complex Analysis, Elliptic Functions
- Arthur Baker, Elliptic Functions (English)
- Karl Bobek, Einleitung in die Theorie der Elliptischen Funktionen (German)
- Otto Bohler, Über die Picard'schen Gruppen aus dem Zahlkörper der dritten und der vierten Einheitswurzel (German)
- Jean Claude Bouquet and Charles Briot, Théorie des Fonctions Elliptiques (French)
- Maurice Godefroy, La Fonction Gamma. Théorie, Histoire, Bibliographie (French)
- Charles Henry, Abrégé de la Theorie des Fonctions Elliptiques (French)
- Charles Hermite, Sur Quelques Applications des Fonctions Elliptiques (French)
- Felix Klein, Ueber Riemann's Theorie der Algebraischen Functionen (German)
- Felix Klein, On Riemann's Theory of Algebraic Functions and their Integrals (English)
- Leo Koenigsberger, Zur Geschichte der Theorie der elliptischen Transcendenten (German)
- Leo Koenigsberger, Vorlesungen ueber die Theorie der Hyperelliptischen Integrale (German)
- Ernest Leonard Lindelöf, Le Calcul des Résidus et ses Applications à la Théorie des Fonctions (French)
- Friedrich Schottky, Abriss einer Theorie der Abelschen Functionen von drei Variabeln (German)
- Karl Weierstrass, Theorie der Abel'schen Functionen (German)
Euclidean and Non-Euclidean Geometry
- Raymond Clare Archibald, Euclid's Book on Division of Figures (English)
- Archimedes, Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes (English)
- William Henry Besant, Conic Sections: Treated Geometrically (English)
- Julian Coolidge, The Elements of Non-Euclidean Geometry (English)
- René Descartes, La géométrie (French)
- George Whitehead Hearn, Researches on Curves of the Second Order (English)
- David Hilbert, The Foundations of Geometry (English)
- Hermann Laurent, Sur les Principes Fondamentaux de la Théorie des Nombres et de la Géométrie (French)
- Nels Johann Lennes and Herbert Ellsworth Slaught, Solid Geometry with Problems and Applications (Revised edition) (English)
- Henry Manning, Non-Euclidean Geometry (English)
- George Albert Wentworth, Plane Geometry (English)
Trigonometry, Technical Drawing
See also Euclidean and Non-Euclidean Geometry.
- Hugh Blackburn, Elements of Plane Trigonometry (English)
- Alfred Bray Kempe, How to Draw a Straight Line (English)
- Isaac Todhunter, Spherical Trigonometry (English)
Differential, Projective, and Synthetic Geometry
See also Euclidean and Non-Euclidean Geometry.
- Johannes Frischauf, Elemente der Absoluten Geometrie (German)
- Karl Friedrich Gauss, General Investigations of Curved Surfaces of 1827 and 1825 (English)
- Felix Klein, Vergleichende Betrachtungen über neuere geometrische Forschungen (German)
- Derrick Norman Lehmer, An Elementary Course in Synthetic Projective Geometry (English)
- Theodor Reye, Synthetische Geometrie der Kugeln und linearen Kugelsysteme (German)
- Albert Ribaucour, Étude des Élassoïdes ou Surfaces A Courbure Moyenne Nulle (French)
- Artur Schoenflies, Einführung in die Hauptgesetze der Zeichnerischen Darstellungsmethoden (German)
- Ernest Vessiot, Leçons de Géométrie Supérieure (French)
- Wolfgang Vogt, Synthetische Theorie der Cliffordschen Parallelen und der Linearen Linienörter des Elliptischen Raumes (German)
Mathematical Physics
See also Differential Equations and Quaternions.
- Rudolf Clausius, Die Potentialfunction und das Potential (German)
- Albert Einstein, The Meaning of Relativity -- Four lectures delivered at Princeton University, May, 1921 (English)
- James Clerk Maxwell, On a Dynamical Top, for exhibiting the phenomena of the motion of a system of invariable form about a fixed point, with some suggestions as to the Earth's motion (English)
- Max Planck, Vorlesungen über Thermodynamik (German)
- Henri Poincaré, Sechs Vorträge über ausgewählte Gegenstände aus der reinen Mathematik und mathematischen Physik (German/French)
- Hermann Sieveking, Moderne Probleme der Physik (German)
- Joseph John Thomson, Notes on Recent Researches in Electricity and Magnetism (English)
- Richard Chace Tolman, The Theory of the Relativity of Motion (English)
- Hermann Weyl, Space--Time--Matter (English)
Quaternions
- Arthur Hathaway, A Primer of Quaternions (English)
- Alexander Macaulay, Utility of Quaternions in Physics (English)
- Alexander Macfarlane, Vector Analysis and Quaternions (English)
Probability
- John Maynard Keynes, A Treatise on Probability (English)
- Richard Proctor, Chance and Luck (English)
- Heinrich Emil Timerding, Die Analyse des Zufalls (German)
Periodicals
- Joseph Liouville (ed.), Journal de Mathématiques Pures et Appliquées (1837) (French)
Miscellaneous
- Willis E. Johnson, Mathematical Geography (English)
- Henri Poincaré, Science and hypothesis (English)
- Phillip H. Wicksteed, The Alphabet of Economic Science (English)
