User:Nonabelian/Reading List

=A-Level=

Decision Mathmatics


=Pre-reading=

Mathematical Adventures & Recreational

 * Problem Solving Through Recreational Mathematics Bonnie Averbach & Orin Chein (Dover 2000)
 * Game, Set and Math. I. Stewart (Penguin, 1997)
 * Does God Play Dice? I. Stewart (Penguin, 1990)
 * To Infinity and Beyond Eli Maor (Princeton, 1991)
 * e The Story of a Number Eli Maor Princeton (1994)
 * Cakes, Custard and Category Theory: Easy recipes for understanding complex maths Eugenia Cheng (Profile Books Ltd, 2015)
 * A Mathematical Mosaic Ravi Vakil (Brendan Kelly, 2008)
 * To Infinity and Beyond Eli Maor (Princeton, 1991)
 * e The Story of a Number Eli Maor Princeton (1994)
 * Cakes, Custard and Category Theory: Easy recipes for understanding complex maths Eugenia Cheng (Profile Books Ltd, 2015)
 * A Mathematical Mosaic Ravi Vakil (Brendan Kelly, 2008)

Readable Mathematics

 * The MαTH βOOK Clifford A Pickover (Sterling, 2009)
 * The Mathematical Experience P.J. Davis & R. Hersh (Penguin, 1990)
 * Mathematics: a very short introduction Timothy Gowers (OUP, 2002)
 * Solving Mathematical Problems Terence Tao (OUP, 2006)
 * Archimedes’ Revenge P. Hoffman (Penguin, 1991)
 * The Pleasures of Counting T.W. Korner (CUP, 1996)
 * Calculus for the Ambitious T.W. Korner (CUP, 2014)
 * Logical Labyrinths Raymond S. Smullyan (CRC Press, 2008)
 * Luck, Logic, and White Lies: The Mathematics of Games J¨org Bewersdorff (A K Peters Ltd, 2004)
 * Insights into Game Theory: An Alternative Mathematical Experience Ein-Ya Gura & Michael M. Maschler (CUP, 2008)
 * What is Mathematics? R. Courant & H. Robbins (OUP, 1996)
 * Beyond Numeracy J. A. Paulos (Penguin, 1991)
 * Neural Networks and Deep Learning Michael Nielsen (Determination Press, 2015, available in web-only format at http://neuralnetworksanddeeplearning.com.)
 * From Here to Infinity Ian Stewart (OUP, 1996)
 * What’s Happening in the Mathematical Sciences D. MacKenzie and B. Cipra (AMS, biennial publication, since 1993)
 * The Penguin Dictionary of Curious and Interesting Numbers D. Wells (Penguin,1997)
 * Wells’s The Penguin Dictionary of Curious and Interesting Geometry (Penguin, 1991)
 * Historical, Beautiful, and Romantic Julian Havil (Princeton University Press, 2019)
 * 50 Visions of Mathematics Sam Parc (ed.) (OUP, 2014)
 * Reaching for Infinity S. Gibilisco (Tab/McGraw-Hill, 1990)
 * The Computational Beauty of Nature: Computer Explorations of Fractals,
 * Chaos, Complex Systems, and Adaptation Gary W Flake (MIT Press, 2000)
 * Chaos J. Gleick (Minerva/Random House, 1997)
 * Chaos and Fractals: An Elementary Introduction David P. Feldman (OUP, 2012)
 * Algorithms Unlocked Thomas H. Cormen (MIT, 2013)

Readable Physics

 * A Short History of Nearly Everything Bill Bryson (Black Swan 2004)
 * The Strangest Man: The Hidden Life of Paul Dirac Graham Farmelo (Faber and Faber 2009)
 * Black Hole Blues Janna Levin (Vintage 2016)
 * The Particle at the End of the Universe Sean Carroll (Oneworld Publications 2013)
 * The New Quantum Universe T. Hey & P. Walters (CUP, 2003)
 * A Brief History of Time Stephen Hawking (Bantam Publishing 1988)

Textbooks
=Cambridge=
 * Mathematical Methods for Physics and Engineering K F Riley, M P Hobson &S J Bence (Cambridge University Press 1998)
 * A Concise Introduction to Pure Mathematics Martin Liebeck (Chapman& Hall/CRCMathematic, 2010)
 * What is Mathematical Analysis? John Baylis (MacMillan, 1991)
 * Groups: A Path to Geometry R.P. Burn (CUP, 1987)
 * Yet Another Introduction to Analysis V. Bryant (CUP, 1990)
 * A First Course in Mechanics Mary Lunn (OUP, 1991)
 * Understanding Probability Henk Tijm (CUP, 2012)
 * What is Mathematical Analysis? John Baylis (MacMillan, 1991)
 * Groups: A Path to Geometry R.P. Burn (CUP, 1987)
 * Yet Another Introduction to Analysis V. Bryant (CUP, 1990)
 * A First Course in Mechanics Mary Lunn (OUP, 1991)
 * Understanding Probability Henk Tijm (CUP, 2012)

Differential Equations

 * J. Robinson An introduction to Differential Equations. Cambridge University Press, 2004
 * W.E. Boyce and R.C. DiPrima Elementary Differential Equations and Boundary-Value Problems (and associated web site: google Boyce DiPrima). Wiley, 2004
 * G.F.Simmons Differential Equations (with applications and historical notes). McGraw-Hill 1991
 * D.G. Zill and M.R. Cullen Differential Equations with Boundary Value Problems. Brooks/Cole 2001

Groups

 * M.A. Armstrong Groups and Symmetry. Springer–Verlag 1988
 * Alan F Beardon Algebra and Geometry. CUP 2005
 * R.P. Burn Groups, a Path to Geometry. Cambridge University Press 1987
 * J.A. Green Sets and Groups: a first course in Algebra. Chapman and Hall/CRC 1988
 * W. Lederman Introduction to Group Theory. Longman 1976
 * Nathan Carter Visual Group Theory. Mathematical Association of America Textbooks

Numbers and Sets

 * R.B.J.T. Allenby Numbers and Proofs. Butterworth-Heinemann 1997
 * R.P. Burn Numbers and Functions: steps into analysis. Cambridge University Press 2000
 * H. Davenport The Higher Arithmetic. Cambridge University Press 1999
 * A.G. Hamilton Numbers, sets and axioms: the apparatus of mathematics. Cambridge University Press 1983
 * C. Schumacher Chapter Zero: Fundamental Notions of Abstract Mathematics. Addison-Wesley 2001
 * I. Stewart and D. Tall The Foundations of Mathematics. Oxford University Press 1977

Vectors and Matrices

 * Alan F Beardon Algebra and Geometry. CUP 2005
 * Gilbert Strang Linear Algebra and Its Applications. Thomson Brooks/Cole, 2006
 * Richard Kaye and Robert Wilson Linear Algebra. Oxford science publications, 1998
 * D.E. Bourne and P.C. Kendall Vector Analysis and Cartesian Tensors. Nelson Thornes 1992
 * E. Sernesi Linear Algebra: A Geometric Approach. CRC Press 1993
 * James J. Callahan The Geometry of Spacetime: An Introduction to Special and General Relativity. Springer 2000

Mechanics (non-examinable)

 * Peter J O’Donnell Essential Dynamics and Relativity. CRC Press, 2014
 * J. Hebborn and J. Littlewood Mechanics 1, Mechanics 2 and Mechanics 3 (Edexel). Heinemann, 2000

Analysis I

 * T.M. Apostol Calculus, vol 1. Wiley 1967-69
 * J.C. Burkill A First Course in Mathematical Analysis. Cambridge University Press 1978
 * D.J.H.Garling A Course in Mathematical Analysis (Vol 1). Cambridge University Press 2013
 * J.B. Reade Introduction to Mathematical Analysis. Oxford University Press
 * M. Spivak Calculus. Addison–Wesley/Benjamin–Cummings 2006
 * David M. Bressoud A Radical Approach to Real Analysis. Mathematical Association of America Textbooks

Dynamics and Relativity

 * D. Gregory Classical Mechanics. Cambridge University Press 2006
 * G.F.R. Ellis and R.M. Williams Flat and Curved Space-times. Oxford University Press 2000
 * A.P. French and M.G. Ebison Introduction to Classical Mechanics. Kluwer 1986
 * T.W.B. Kibble and F.H. Berkshire Introduction to Classical Mechanics. Kluwer 1986
 * M.A. Lunn A First Course in Mechanics. Oxford University Press 1991
 * P.J. O’Donnell Essential Dynamics and Relativity. CRC Press 2015
 * W. Rindler Introduction to Special Relativity. Oxford University Press 1991
 * E.F. Taylor and J.A. Wheeler Spacetime Physics: introduction to special relativity. Freeman 1992

Probability

 * W. Feller An Introduction to Probability Theory and its Applications, Vol. I. Wiley 1968
 * G. Grimmett and D. Welsh Probability: An Introduction. Oxford University Press 2nd Edition 2014
 * S. Ross A First Course in Probability. Prentice Hall 2009
 * D.R. Stirzaker Elementary Probability. Cambridge University Press 1994/2003

Vector Calculus

 * H. Anton Calculus. Wiley Student Edition 2000
 * T.M. Apostol Calculus. Wiley Student Edition 1975
 * M.L. Boas Mathematical Methods in the Physical Sciences. Wiley 1983
 * D.E. Bourne and P.C. Kendall Vector Analysis and Cartesian Tensors. 3rd edition, Nelson Thornes 1999
 * E. Kreyszig Advanced Engineering Mathematics. Wiley International Edition 1999
 * J.E. Marsden and A.J.Tromba Vector Calculus. Freeman 1996
 * P.C. Matthews Vector Calculus. SUMS (Springer Undergraduate Mathematics Series) 1998
 * K. F. Riley, M.P. Hobson, and S.J. Bence Mathematical Methods for Physics and Engineering. Cambridge University Press 2002
 * H.M. Schey Div, grad, curl and all that: an informal text on vector calculus. Norton 1996
 * M.R. Spiegel Schaum’s outline of Vector Analysis. McGraw Hill 1974

Algebraic Topology

 * Bott, R. and Tu, L. Differential forms in algebraic topology. Springer, 1982.
 * Hatcher, A. Algebraic Topology. Cambridge Univ. Press, 2002.
 * May, P. A concise course in algebraic topology. Univ. of Chicago Press, 1999.
 * Sutherland, W. Introduction to metric and topological spaces. Oxford Univ. Press, 1999.

=Oxford=

Introduction to Complex Numbers

 * Jordan, D.W. and Smith, P. (2008) Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences. 4th ed. Oxford: Oxford University Press.

COD Dissertations on the History of Mathematics
=Durham=

Linear Algebra
Analysis