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Also see:
General
- Alfred Wrigley and William H. Johnstone: Examples and Problems in Pure and Applied Mathematics (1845)
- A. Geary, H.V. Lowry and H.A. Hayden: Advanced Mathematics for Technical Students, Part I (1945)
- Lilian R. Lieber: Modern Mathematics for T. C. Mits (1946)
- H.V. Lowry and H.A. Hayden: Advanced Mathematics for Technical Students, Part II (1950)
- R. Wesley: Mathematics For All (1954)
- Margaret M. Gow: A Course in Pure Mathematics (1960)
- Patrick J. Murphy and Albert F. Kempf: The New Mathematics Made Simple (1966)
- A.J.M. Spencer: Engineering Mathematics Volume I (1977) (with others)
- David Acheson: 1089 and all that (2002)
- Rob Eastaway and Jeremy Wyndham: How Long is a Piece of String? (2002)
Geometry
Euclidean Geometry
- Euclid: The Elements (c. 300 BCE)
- René Descartes: La Géométrie (1637)
- André VandenBroeck: Philosophical Geometry (1972)
Algebraic Geometry
Solid Geometry
- Robert J.T. Bell: Coordinate Solid Geometry (1938) (reprint of chapters I to IX of An Elementary Treatise on Coordinate Geometry of Three Dimensions from 1911)
- William H. McCrea: Analytical Geometry of Three Dimensions (1942)
Projective Geometry
- E.A. Maxwell: The Methods of Plane Projective Geometry based on the use of General Homogeneous Coordinates (1946)
- Klaus Metsch: Linear Spaces with Few Lines (1991)
Differential Geometry
- C.E. Weatherburn: Differential Geometry of Three Dimensions: Volume I (1927)
- T.J. Willmore: An Introduction to Differential Geometry (1959)
Logic
- George Boole: An Investigation of the Laws of Thought (1854)
- Irving M. Copi: Symbolic Logic (1954)
- Willard Van Orman Quine: Set Theory and Its Logic (1963)
- Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning (1964)
- E.J. Lemmon: Beginning Logic (1965)
- William Warren Bartley, III (ed.): Lewis Carroll's Symbolic Logic (1977)
- Alan G. Hamilton: Logic for Mathematicians (1978)
- Irving M. Copi: Symbolic Logic: 5th Edition (1979)
- D.J. O'Connor and Betty Powell: Elementary Logic (1980)
- Michael R. Genesereth and Nils J. Nilsson: Logical Foundations of Artificial Intelligence (1987)
- Merrilee H. Salmon: Introduction to Logic and Critical Thinking (1995)
Boolean Algebra
Mathematical Logic
- George S. Boolos and Richard C. Jeffrey: Computability and Logic (1974)
- Alan G. Hamilton: Logic for Mathematicians (1978)
- Douglas R. Hofstadter: Gödel, Escher, Bach: an Eternal Golden Braid (1979)
- M. Ben-Ari: Mathematical Logic for Computer Science (1993)
- H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability (1996)
- Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems (2000)
Metamathematics
Set Theory
- Paul Isaac Bernays: Axiomatic Set Theory (1958)
- Paul R. Halmos: Naive Set Theory (1960)
- Willard Van Orman Quine: Set Theory and Its Logic (1963)
- Nicolas Bourbaki: Theory of Sets (1968)
- Gaisi Takeuti: Introduction to Axiomatic Set Theory (1971)
- T.S. Blyth: Set Theory and Abstract Algebra (1975)
- Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (1993)
Abstract Algebra
- Nathan Jacobson: Lectures in Abstract Algebra: I. Basic Concepts (1951)
- W.E. Deskins: Abstract Algebra (1964)
- J.A. Green: Sets and Groups (1965)
- Seth Warner: Modern Algebra (1965)
- Richard A. Dean: Elements of Abstract Algebra (1966)
- C.R.J. Clapham: Introduction to Abstract Algebra (1969)
- B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra (1970)
- Allan Clark: Elements of Abstract Algebra (1971)
- T.S. Blyth: Set Theory and Abstract Algebra (1975)
- John B. Fraleigh: A First Course in Abstract Algebra (1975)
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)
- Stanley Burris and H. P. Sankappanavar: A Course in Universal Algebra (1981)
- Alan G. Hamilton: Numbers, Sets and Axioms (1982)
- R.B.J.T. Allenby: Rings, Fields and Groups: An Introduction to Abstract Algebra (1991)
- Joseph A. Gallian: Contemporary Abstract Algebra (1994)
- J.C. Rosales and P.A. García-Sánchez: Finitely Generated Commutative Monoids (1999)
- John H. Conway and Derek A. Smith: On Quaternions And Octonions (2003)
Group Theory
- Walter Ledermann: Introduction to the Theory of Finite Groups (1949)
- Ian D. Macdonald: The Theory of Groups (1968)
- Robert Gilmore: Lie Groups, Lie Algebras and Some of Their Applications (1974)
- John F. Humphreys: A Course in Group Theory (1996)
- David Joyner: Adventures in Group Theory (2002)
Field Theory
Galois Theory
Category Theory
Discrete Mathematics
- Ronald L. Graham, Donald E. Knuth and Oren Patashnik: Concrete Mathematics: A Foundation for Computer Science (1989)
- Steven G. Krantz: Discrete Mathematics Demystified (2009)
Graph Theory
Design Theory
Cellular Automata
Communication Theory
Linear Algebra
- Nathan Jacobson: Lectures in Abstract Algebra: II. Linear Algebra (1953)
- L. Mirsky: An Introduction to Linear Algebra (1955)
- M.A. Akivis and V.V. Goldberg: An Introduction to Linear Algebra & Tensors (1972) (translated by Richard A. Silverman)
- A.O. Morris: Linear Algebra: An Introduction (1978)
- John B. Fraleigh and Raymond A. Beauregard: Linear Algebra: Third Edition (1995)
Vector Analysis
- C.E. Weatherburn: Elementary Vector Analysis (1921)
- C.E. Weatherburn: Advanced Vector Analysis (1924)
- B. Hague and D. Martin: An Introduction to Vector Analysis (1939, 1970)
- D.E. Rutherford: Vector Methods (1939)
Number Theory
- G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (1938)
- Helmut Hasse: Zahlentheorie (1949) (Number Theory) (3 editions: 1949, 1962, 1969; English translation 1980 by Horst-Günter Zimmer)
- H. Davenport: The Higher Arithmetic (1952)
- Harvey Cohn: Advanced Number Theory (1962)
- C. Stanley Ogilvy and John T. Anderson: Excursions in Number Theory (1966)
- George E. Andrews: Number Theory (1971)
- Tom M. Apostol: Introduction to Analytic Number Theory (1976)
- Alan Baker: A Concise Introduction to the Theory of Numbers (1984)
- Melvyn B. Nathanson: Additive Number Theory: The Classical Bases (1996)
- Gary Cornell, Joseph H. Silverman and Glenn Stevens: Modular Forms and Fermat's Last Theorem (1997)
Analysis
- Hermann Weyl: The Continuum: A Critical Examination of the Foundation of Analysis (1918)
- George Pólya and Gábor Szegő: Problems and Theorems in Analysis I (1925) (translated by Dorothée Aeppli)
- James M. Hyslop: Infinite Series (1942)
- Tom M. Apostol: Mathematical Analysis (1957)
- J.C. Burkill and H. Burkill: A Second Course in Mathematical Analysis (1970)
Analytical Geometry
- Elias Loomis: Elements of Analytical Geometry and of the Differential and Integral Calculus (1851)
- D.M.Y. Sommerville: Analytical Conics (1924)
Real Analysis
- G.H. Hardy: A Course of Pure Mathematics (1908)
- E.G. Phillips: A Course of Analysis (1930)
- Walter Rudin: Principles of Mathematical Analysis (1953)
- William K. Smith: Limits and Continuity (1964)
- A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis (1968) (translated by Richard A. Silverman)
- C.R.J. Clapham: Introduction to Mathematical Analysis (1973)
- K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)
- Elon Lages Lima: Análise Real 1 (1989)
Calculus
- David V. Widder: Advanced Calculus (1947)
- J.C. Burkill: The Lebesgue Integral (1951)
- P.J. Hilton: Partial Derivatives (1960)
- Roland E. Larson and Robert P. Hostetler: Calculus (1978)
- Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards and David E. Heyd: Calculus: 7th Edition (2001)
- Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards: Calculus: 8th Edition (2005)
- Roland E. Larson and Bruce H. Edwards: Calculus: 9th Edition (2009)
Complex Analysis
- E.T. Copson: An Introduction to the Theory of Functions of a Complex Variable (1935)
- E.G. Phillips: Functions of a Complex Variable (1940)
- Murray R. Spiegel: Theory and Problems of Complex Variables (1964)
- Ian Stewart and David Tall: Complex Analysis (The Hitchhiker's Guide to the Plane) (1983)
- Hilary A. Priestley: Introduction to Complex Analysis (1985)
Trigonometrical Series
- Antoni Zygmund: Trigonometrical Series (1935)
- I.N. Sneddon: Fourier Series (1961)
- H.J. Nussbaumer: Fast Fourier Transform and Convolution Algorithms (1981)
Functional Analysis
Measure Theory
Special Functions
- Andrew Gray and G.B. Mathews: A Treatise on Bessel Functions (1895) (second edition 1922 with T.M. MacRobert)
- F.E. Relton: Applied Bessel Functions (1946)
- Aleksandar Ivić: The Riemann Zeta-Function (1985)
- Larry C. Andrews: Special Functions of Mathematics for Engineers (1992) (second edition of Special Functions for Engineers and Applied Mathematicians from 1985)
Differential Equations
- E.L. Ince: Integration of Ordinary Differential Equations (1939)
- J.C. Burkill: The Theory of Ordinary Differential Equations (1956)
- G.E.H. Reuter: Elementary Differential Equations & Operators (1958)
- Morris Tenenbaum: Ordinary Differential Equations (1963)
- George F. Simmons: Differential Equations (1972)
- Erich Müller-Pfeiffer: Spectral Theory of Ordinary Differential Operators (1981)
Partial Differential Equations
- G. Stephenson: An Introduction to Partial Differential Equations for Science Students (1968)
- Arne Broman: Introduction to Partial Differential Equations (1970)
- D.L. Colton: Partial Differential Equations in the Complex Domain (1976)
Laplace's Equation
Topology
- Stephen Barr: Experiments in Topology (1964)
- Steven A. Gaal: Point Set Topology (1964)
- George McCarty: Topology: An Introduction with Application to Topological Groups (1967)
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)
- W.A. Sutherland: Introduction to Metric and Topological Spaces (1975)
- Donald W. Blackett: Elementary Topology: A Combinatorial and Algebraic Approach (1982)
- Gerard Buskes and Arnoud van Rooij: Topological Systems: From Distance to Neighborhood (1997)
Knot Theory
Probability and Statistics
- Alexander M. Mood and Franklin A. Graybill: Introduction to the Theory of Statistics (1950)
- P.A.P. Moran: The Theory of Storage (1959)
- Murray R. Spiegel: Theory and Problems of Statistics (1961)
- D.R. Cox and H.D. Miller: The Theory of Stochastic Processes (1965)
- A.A. Sveshnikov: Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions (1965)
- Michael C. Gemignani: Calculus and Statistics (1970) $\S 1.3$
- Geoffrey Keppel: Design and Analysis: A Researcher's Handbook (1973)
- Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction (1986)
- Merrilee H. Salmon: Introduction to Logic and Critical Thinking (1995) $\S 6.1$
- Stephen Bernstein and Ruth Bernstein: Elements of Statistics II: Inferential Statistics (1999)
- Michael A. Bean: Probability: The Science of Uncertainty (2001) $\S 1.2$
Catastrophe Theory
Chaos Theory
- James Gleick: Chaos: Making a New Science (1987)
- Ian Stewart: Does God Play Dice? (1989)
- Brian H. Kaye: A Random Walk through Fractal Dimensions (1989)
Computer Science
- R.W. Hamming: Numerical Methods for Scientists and Engineers (1962)
- John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation (1969)
- D.C. Ince: An Introduction to Discrete Mathematics and Formal System Specification (1988)
- Thomas H. Cormen, Charles E. Leiserson and Ronald L. Rivest: Introduction to Algorithms (1990)
- Bruce W. Watson: Taxonomies and Toolkits of Regular Language Algorithms (1995)
- Douglas Hofstadter: Fluid Concepts and Creative Analogies (1995)
Game Theory
- Steven Vajda: Theory of Games and Linear Programming (1956)
- R. Duncan Luce and Howard Raiffa: Games and Decisions (1957)
- John H. Conway: On Numbers And Games (1976)
- Elwyn Berlekamp: The Dots-and-Boxes Game (2000)
Numerical Analysis
- B. Noble: Numerical Methods 1: Iteration, Programming and Algebraic Equations (1964)
- B. Noble: Numerical Methods 2: Differences, Integration and Differential Equations (1964)
- James G. Simmonds and James E. Mann, Jr.: A First Look at Perturbation Theory (1986)
Applied Mathematics
- George Arfken: Mathematical Methods for Physicists (1970)
- K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists (1976) (translated into English 1986 by J. Grosjean and P. Schuster)
- Kurt Arbenz and Alfred Wohlhauser: Advanced Mathematics for Practicing Engineers (1986)
- Fayssal Benkhaldoun and Roland Vilsmeier: Finite Volumes for Complex Applications (1996)
- Roland Vilsmeier, Fayssal Benkhaldoun and Dieter Hänel: Finite Volumes for Complex Applications II (1999)
Mechanics
Wave Mechanics
Fluid Mechanics
Physics
- Arthur Beiser: Concepts of Modern Physics (1963)
- Isaac Asimov: Understanding Physics (1966)
- Frederick W. Byron, Jr. and Robert W. Fuller: Mathematics of Classical and Quantum Physics: Volume One (1969)
- Frederick W. Byron, Jr. and Robert W. Fuller: Mathematics of Classical and Quantum Physics: Volume Two (1970)
- Roger Penrose: The Emperor's New Mind (1989)
- Frederick W. Byron, Jr. and Robert W. Fuller: Mathematics of Classical and Quantum Physics (1992) (republication of Mathematics of Classical and Quantum Physics: Volume One and Mathematics of Classical and Quantum Physics: Volume Two in one volume)
- Roger Penrose: The Road to Reality: A Complete Guide to the Laws of the Universe (2004)
- Roger Penrose: Cycles of Time: An Extraordinary New View of the Universe (2010)
Electromagnetism
Atomic Physics
- L.R.B. Elton: Introductory Nuclear Theory (1959)
- M. Russell Wehr, James A. Richards, Jr. and Thomas W. Adair, III: Physics of the Atom (1967)
Quantum Mechanics
- A.P. French and Edwin F. Taylor: An Introduction to Quantum Physics (1978)
- Anthony Sudbery: Quantum Mechanics and the Particles of Nature (1986)
- Yoav Peleg, Reuven Pnini and Elyahu Zaarur: Quantum Mechanics (1998)
General Reference
- Peter Barlow: New Mathematical Tables (1814)
- Milton Abramowitz and Irene Stegun: Handbook of Mathematical Functions (1964)
- Murray R. Spiegel: Mathematical Handbook of Formulas and Tables (1968)
- Henry R. Neave: Elementary Statistics Tables (1981)
- David Wells: Curious and Interesting Numbers (1986)
- Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics (1989)
- David Wells: Curious and Interesting Geometry (1991)
History of Mathematics
- Eric Temple Bell: Men of Mathematics (1937)
- Bharati Krishna Tirthaji: Vedic Mathematics (1965)
- Carl B. Boyer: A History of Mathematics (1968)
- R.L. Wilder: Evolution of Mathematical Concepts (1968)
- Morris Kline: Mathematical Thought From Ancient to Modern Times (1972)
- Ian Stewart: The Problems of Mathematics (1987)
- Carl B. Boyer and Uta C. Merzbach: A History of Mathematics: Second Edition (1991)
- George F. Simmons: Calculus Gems (1992)
- Simon Singh: Fermat's Last Theorem (1997)
- Robert Kaplan: The Nothing That Is (1999)
- Keith Devlin: The Millennium Problems (2002)
- Karl Sabbagh: Dr. Riemann's Zeros (2002)
- Brian Clegg: A Brief History of Infinity (2003)
- John Derbyshire: Prime Obsession (2003)
- Marcus du Sautoy: The Music of the Primes (2003)
- Stephen Hawking: God Created the Integers (2005)
- Mark Ronan: Symmetry and the Monster (2006)
- Ian Stewart: Taming the Infinite (2008)
Recreational Mathematics
- Maurice Kraitchik: Mathematical Recreations (1942)
- Malba Tahan: O Homem que Calculava (1949) (translated 1993 by Leslie Clark and Alastair Reid as The Man Who Counted)
- Martin Gardner: Mathematics, Magic and Mystery (1956)
- Martin Gardner: The Scientific American Book of Mathematical Puzzles and Diversions (1959)
- A.P. Domoryad: Mathematical Games and Pastimes (1961) (translated 1964 by Halina Moss)
- Martin Gardner: The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds (1964)
- Martin Gardner: Unexpected Hangings, and Other Mathematical Diversions (1969)
- Martin Gardner: Mathematical Carnival (1975)
- Martin Gardner: Mathematical Magic Show (1977)
- Martin Gardner: Further Mathematical Diversions (1977) (reprint of Unexpected Hangings, and Other Mathematical Diversions from 1969)
- Martin Gardner: Wheels, Life, and Other Mathematical Amusements (1983)
- Martin Gardner: Puzzles from Other Worlds (1984)
- Martin Gardner: Time Travel and Other Mathematical Bewilderments (1987)
- Martin Gardner: Hexaflexagons and Other Mathematical Diversions (1988) (expanded edition of The Scientific American Book of Mathematical Puzzles and Diversions from 1959)
- Martin Gardner: The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings (1990) (Revised edition of The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds from 1964)
- Martin Gardner: The Unexpected Hanging and Other Mathematical Diversions (1991) (updated edition of Unexpected Hangings, and Other Mathematical Diversions from 1969)
- Clifford A. Pickover: Computers and the Imagination (1991)
- David Wells: Curious and Interesting Puzzles (1992)
- Clifford A. Pickover: The Alien IQ Test (1997)
- Ian Stewart: Professor Stewart's Cabinet of Mathematical Curiosities (2008)
- Jeremy Stangroom: Einstein's Riddle (2009)
- Ian Stewart: Professor Stewart's Hoard of Mathematical Treasures (2009)
Philosophy
- Edwin A. Abbott: Flatland: a Romance of Many Dimensions (1884)
- G. Polya: How To Solve It (1945)
- W.W. Sawyer: A Path to Modern Mathematics (1966)
- D.E. Knuth: Surreal Numbers (1974)
- Ian Stewart: Concepts of Modern Mathematics (1975)
- Rudolf v.B. Rucker: Geometry, Relativity and the Fourth Dimension (1977)
- Rudy Rucker: Infinity and the Mind (1982)
- A.K. Dewdney: The Planiverse: Computer Contact with a Two-Dimensional World (1984)
- Rudy Rucker: The Fourth Dimension (1985)
- Rudy Rucker: Mind Tools (1987)
Other Science
- Martin Gardner: In the Name of Science (1952)
- Martin Gardner: Great Essays in Science (1957) (as editor)
- Martin Gardner: Fads and Fallacies in the Name of Science (1957) (expansion of In the Name of Science)
- Martin Gardner: The Sacred Beetle and Other Great Essays in Science (1984) (as editor: revised edition of Great Essays in Science from 1957)
- Martin Gardner: Did Adam and Eve Have Navels?: Debunking Pseudoscience (2001) (collection of Notes of a Fringe Watcher columns)
- Ben Goldacre: Bad Science (2008)
Entertainment
- Martin Gardner: The Annotated Alice (1960)
- Rudy Rucker: White Light (1980)
- Robert Ainsley: Bluff Your Way in Maths (1988)
- Martin Gardner: More Annotated Alice (1990) (a supplement to The Annotated Alice from 1960)
- Terry Wiley: Surreal School Stories (1995)
- Martin Gardner: The Annotated Alice: The Definitive Edition (1999) (new edition of The Annotated Alice from 1960)
- Ian Stewart: Flatterland (2001)
- Clifford A. Pickover: A Passion for Mathematics (2005)
- Colin C. Adams: Riot at the Calc Exam and Other Mathematically Bent Stories (2009)
