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AIMS Sénégal
BIBLIOTHEQUE SELECTIVE
DE
MATHEMATIQUES
Juin
2011
Publiée avec le soutien de l'Université Paris 6
1
Avertissement
En 1992, Jean-Michel Lemaire m'avait demandé d'élaborer une bibliothèque virtuelle de
mathématiques pour le Cimpa, son but étant ``de diffuser une liste d'ouvrages fondamentaux
couvrant l'ensemble des mathématiques, à l'intention des mathématiciens exerçant dans les pays en
voie de développement et désireux de constituer une bibliothèque "minimale" de référence''.
Notons que cette bibliothèque prenait la suite d'un premier travail effectué par Jean Dieudonné en
1985-86.
L'ouverture de l'AIMS-Sénégal m'a naturellement amené à mettre à jour cette liste.
Ce travail a été possible grâce à la collaboration de nombreux collègues dont en
particulier:
Moussa Balde, Jean Bertoin, Olivier Biquard, Louis Boutet de Monvel, Jean-Benoît Bost, Antoine,
Chambert-Loir, Albert Cohen, Fabienne Comte, Guiseppe Dito, Jacques Faraut, Jacques Féjoz,
Christian Gilain, Grégory Ginot, Gilles Godefroy, Catherine Goldstein, Vincent Humilière, Max
Karoubi, Bernhard Keller, Pierre-Vincent Koseleff, Nicolas Lerner, François Loeser, Ayman Moussa,
François Murat, Jan Nekovar, Frédéric Paugam, Gilles Pisier, Patrick Polo, Geogres Skandalis, Sylvain
Sorin, Michel Waldschmidt.
Et aussi grâce à l'excellent travail technique de Lauranne Chaignon et l'appui de la Bibliothèque
Mathématique-Informatique Recherche de Jussieu.
Que toutes et tous en soient remerciés ici.
Lors de cette mise à jour j'ai appris que le Cimpa avait de son coté réactualisé le travail de 92 dans un
document consultable à:
http://www.cimpa-icpam.org/spip.php?article284&lang=fr
Nous proposons ici une autre mise à jour de la liste de 92, sans doute complémentaire à celle du
Cimpa, de nombreux titres étant évidemment communs à ces deux listes.
La liste présentée ici est le résultat de choix quelque peu arbitraires, tant par l'organisation des
thèmes que les personnes interrogées et la sélection finale. La responsabilité en incombe
uniquement à l'auteur de ces lignes.
Pierre Schapira
Coordinateur Aims-Sénégal/UPMC
2
Sommaire
LOGIQUE ...................................................................................................................................................5
COMBINATOIRE ........................................................................................................................................7
CALCUL FORMEL .......................................................................................................................................9
CATEGORIES, FAISCEAUX, ALGEBRE HOMOTOPIQUE ........................................................................... 11
TOPOLOGIE ALGEBRIQUE, TOPOLOGIE DIFFERENTIELLE ...................................................................... 13
K-THEORIE ............................................................................................................................................. 16
ALGEBRE ................................................................................................................................................ 17
THEORIE DES NOMBRES ........................................................................................................................ 18
GEOMETRIE ALGEBRIQUE ..................................................................................................................... 23
GROUPES ET ALGEBRES DE LIE .............................................................................................................. 26
C*- ALGEBRES, ALGEBRES D’OPERATEURS ............................................................................................ 29
GEOMETRIE DIFFERENTIELLE................................................................................................................. 31
SYSTEMES DYNAMIQUES ET GEOMETRIE SYMPLECTIQUE ................................................................... 34
ANALYSE COMPLEXE, GEOMETRIE ANALYTIQUE, SINGULARITES ......................................................... 37
EQUATIONS AUX DERIVEES PARTIELLES LINEAIRES, D-MODULES ........................................................ 40
ANALYSE REELLE, ANALYSE HARMONIQUE ........................................................................................... 42
EQUATION DIFFERENTIELLE ORDINAIRE, FONCTIONS SPECIALES ........................................................ 45
ANALYSE FONCTIONNELLE .................................................................................................................... 46
EQUATIONS AUX DERIVEES PARTIELLES NON LINEAIRES...................................................................... 48
PHYSIQUE MATHEMATIQUE.................................................................................................................. 49
ANALYSE NUMERIQUE........................................................................................................................... 51
PROBABILITES ........................................................................................................................................ 53
STATISTIQUE .......................................................................................................................................... 56
3
THEORIE DES JEUX, MATHEMATIQUES ECONOMIQUES, OPTIMISATION, CONTRÔLE ......................... 59
HISTOIRE DES MATHEMATIQUES .......................................................................................................... 63
CRYPTOGRAPHIE-CODAGE .................................................................................................................... 65
LOGIQUE
BARR, M. ; WELLS, C.
Toposes, triples, and theories, Grundlehren der
Mathematischen Wissenschaften, 278. SpringerVerlag, 1985.
BARWISE, J.
Handbook of Mathematical logic, Studies in Logic
and the Foundations of Mathematics n°90, North
Holland, 1977.
BARWISE, J.
Admissible Sets and Structures - an Approach to
Definability Theory, Persp. In Math. Logic,
Springer-Verlag, 1975.
BARWISE, J. ; FEFERMAN, S.
Model-theoretic logics, Persp. In Math. Logic,
Springer-Verlag, 1985.
CHANG, C. C. ; KEISLER, H.J.
Model Theory, North Holland, 1973.
COHEN, P. J.
Set Theory and the Continuum Hypothesis, W. A.
Benjamin, 1966.
CORI, R. ; LASCAR, D.
Logique mathématique t1 & 2, Masson, 1993.
EBBINGHAUS, H. D. ; FLUM, J. ; THOMAS, W.
Mathematical Logic, UTM, Springer-Verlag, 1984.
GIRARD, J. Y. ; LAFONT, Y. ; TAYLOR, P.
Proofs and types, Cambridge Tracts in Theoretical
Computer Science n°7, Cambridge University
Press, 1989.
GÖDEL, K.
Collected works, Vol. I-II, Oxford University Press
1986, 1990.
HINDLEY, J. R. ; SELDIN, J-P.
Introduction to Combinatorics and [lambda]calculus, Students texts 1, London Math. Society,
1986.
JECH, T. J.
Set Theory, Pure & Appl. Math., Academic Press,
1978.
KRIVINE, J-L.
Lambda-calcul, types et modèles, Masson, Paris
1990.
KRIVINE, J-L.
Théorie axiomatique des ensembles, Presses
Universitaires de France, 1969.
KUNEN, K.
Set Theory, North Holland, 1980.
MANIN, Y.
A course in mathematical logic, Springer GTM,
53, Springer, 1977.
MARKER, D.
Model Theory : An Introduction, Springer-Verlag,
2002.
MINSKY, M.
Computation : Finite and Infinite Machines,
Series in Automatic Computation, Prentice Hall,
1967.
MOSCHOVAKIS, Y. N.
Descriptive Set Theory, Studies in Logic and the
Foundations of Mathematics n°100, North
Holland, 1980.
PILLAY, A.
An Introduction to Stability Theory, Oxford U.
Press, 1983.
POIZAT, B.
A Course in Model Theory : An Introduction to
Contemporary Mathematical Logic, Springer,
2000.
ROBINSON, J. A.
Logic: Form and Function, the Mechanization of
Deductive Rasoning, University Press of
Edinburgh, 1979.
ROGERS, H. Jr.
Theory of Recursive Functions and Effective
Computability, McGraw Hill, 1967.
SCHUTTE, K.
Proof Theory, GMW 225, Springer-Verlag, 1977.
SOARE, R. I.
Recursively Enumerable Sets and Degrees,
Springer-Verlag, 1987.
STERN, J.
Fondements mathématiques de l'informatique,
McGraw Hill, 1990.
TARSKI, A.
Logic, Semantics, Metamathematics, Clarendon
Press, 1956.
VAN HEIJENOORT, J.
From Frege to Gödel, a Source Book in
Mathematical Logic, 1879-1931, Harvard
University Press, 1967.
COMBINATOIRE
AIGNER, M.
A Course in Enumeration, Springer GTM 238,
2007.
ALON, N. ; SPENCER, J.
The Probabilistic Method, Wiley, 2000.
ANDREWS, C.E.
The Theory of Partitions and its Applications,
Addison-Wesley., 1976.
BERGE, C.
Graphes et Hypergraphes, Dunod, Paris 1973.
BIGGS, N.
Algebraic Graph Theory (2nd edition), Cambridge
University Press, 2010.
BONDY, J. ; MURTY, U.S.R.
Graph Theory, Graduate Texts in Mathematics,
Vol. 244, Springer, 2008.
COMTET, L.
Analyse combinatoire, 2 vol., "Le Mathématicien"
n°4 et 5, PUF, Paris 1978.
DIESTEL, R.
Graph Theory, Springer, 2010.
FLAJOLET, Ph. ; SEDGEWICK, R.
Analytic Combinatorics, Addison Wesley, 2009.
GODSIL, C. ; ROYLE, G.
Algebraic Graph Theory, Springer, 2001.
KORTE, B. ; VYGEN, J.
Combinatorial Optimization : Theory and
Algorithms, Springer, 2008.
LOTHAIRE, M.
Combinatorics on Words, Encyclopedia of
Mathematics and its Applications n°17, AddisonWesley, 1983.
MACDONALD, I.G.
Symmetric Functions and Hall Polynomials,
Clarendon Press, 1979.
OXLEY, J.
Matroid Theory, OUP, 2011.
SCHRIJVER, A.
Combinatorial Optimization : Polyhedra and
Efficiency, Springer, 2003.
STANLEY, R.
Enumerative Combinatorics (volumes 1 & 2),
Cambridge, 2001.
TUTTE, W.T.
Graph Theory, Encycl. Of Math. And its Appl.
N°21, Addison-Wesley, 1984.
CALCUL FORMEL
BASU, S. ; POLLACK, R. ; ROY, M.-F
Algorithms in Real Algebraic Geometry, SpringerVerlag, 2008
BORWEIN, JM. ; BAILEY, D.
Mathematics by experiment, A.K Peters, 2008.
BURGISSER, P ; CLAUSEN, M ; SHOKROLLAHI, M A
Algebraic complexity theory, Grundlehren der
Mathematischen Wissenschaften, 315. SpringerVerlag, 1997.
COX ; LITTLE ; O'SHEA
Ideals, Varieties and Algorithms, Springer, 1993
COX ; LITTLE ; O'SHEA
Using Algebraic Geometry, Springer, 2004
DAVENPORT, J. ; SIRET, Y. ; TOURNIER, E.
Calcul formel, systèmes et algorithmes de
manipulations algébriques, Masson, Paris 1987
DEMAZURE, M.
Cours d'algèbre, Nouvelle Bibliothèque
Mathématique, Cassini, 2008.
GEDDES, K. ; CZAPOR, S. ; LABAHN, G.
Algorithms for Computer Algebra, Kluwer
Academic Publishers, 1992
GRAHAM, R.L. ; KNUTH, D.E. ; PATASHNIK, O.
Concrete Mathematics, a Foundation for
Computer Science, dedicated to L. Euler (17011783), Addison-Wesley, 1983
KNUTH, D.E.
The Art of Computer Programming, Vol 1, 2, 3,
Addison-Wesley, 1981.
MIGNOTTE, M.
Mathématiques pour le calcul formel, PUF, Paris
1989 (à paraître en anglais chez Springer)
NAUDIN, P. ; QUITTE, CL.
Algorithmique algébrique, Masson, 1992
SEDGEWICK, R.
Algorithms, Addison-Wesley, 1988
SHOUP, V.
A Computational Introduction to Number Theory
and Algebra, Cambridge University Press, 2005
VON ZUR GATHEN, J. ; GERHARD, J.
Modern Computer Algebra, Cambridge UP, 2003
CATEGORIES, FAISCEAUX, ALGEBRE HOMOTOPIQUE
ADAMEK, J. ; ROSICKY, J.
Locally presentable and accessible categories, London
Mathematical Society Lecture Note Series, 189.
Cambridge University Press, 1994.
ADAMS, J.F.
Stable Homotopy and Generalized Homology, Chicago
Lectures in Mathematics, University of Chicago Press,
1974
BORCEUX, F.
Handbook of categorical algebra, Vol 1-3, CUP, 1994.
BOUSFIELD, A. ; KAN, D
Homotopy Limits, Completions and Localizations, LNM
304 Springer-Verlag, 1972.
CARTAN H., EILENBERG S.
Homological Algebra, Math. Series Vol. 19, Princeton
University Press, 1956
FELIX, Y. ; HALPERIN, S. ; THOMAS, J-C.
Rational homotopy theory, Graduate
Mathematics, 205, Springer-Verlag, 2001
FRANJOU, V. ET AL.
Rational Representations, the Steenrod Algebra
and Functor Homology, Panoramas et Synthèses 16, Soc.
Math. France, 2003.
FRESSE, B.
Modules over Operads and Functors, Lecture Notes in
Mathematics, Vol. 1967, 2009
GABRIEL, P. ; ZISMAN, M.
Calculus of Fractions and Homotopy Theory, EMG 35,
Springer-Verlag, 1967
GODEMENT, R.
Topologie algébrique et théorie des faisceaux, Hermann,
Paris, 1964
GOERSS, P. ; JARDINE, J.,
Simplicial Homotopy Theory, Progress in Mathematics,
174. Birkhäuser, 1999.
HILTON, P.J. ; STAMMBACH, U.
A Course in Homological Algebra, GTM 4, SpringerVerlag, 1971
HOVEY, M.
Model categories, Mathematical Surveys and
Monographs, 63. American Mathematical Society, 1999.
HU, S.T.
Homotopy theory, Academic Press, 1959
KASHIWARA, M. ; SCHAPIRA, P.
Sheaves on Manifolds, GMW 292, Springer-Verlag, 1990
Texts
in
KASHIWARA, M. ; SCHAPIRA, P.
Categories and sheaves, GMW 332, Springer-Verlag,
2006
KASSEL, C. ; ROSSO, M. ; TURAEV, V.
Quantum Groups and Knot Invariants, Panoramas et
Synthèses 5, Soc. Math. France, 1997.
LURIE, J.
Higher topos theory, Annals of Mathematics Studies,
170. Princeton University Press, 2009.
MAC LANE, S.
Categories for the Working Mathematician, GTM 5,
Springer-Verlag, 1971
NEEMAN, A.
Triangulated categories, Princeton University Press, 2001
QUILLEN, D.
Homotopical algebra, Lecture Notes in Mathematics, No.
43. Springer-Verlag, 1967.
RAVENEL, D.C.
Complex cobordism and stable homotopy groups of
spheres, Academic Press, 1986
WEIBEL, C.A.
An introduction to homological algebra, CUP, 1994.
TOPOLOGIE ALGEBRIQUE, TOPOLOGIE DIFFERENTIELLE
ADAMS, J.F.
Algebraic Topology, a student's guide, London
Mathematical Society lecture Notes n°4, Cambridge
University Press 1972
ADAMS, J.F.
Algebraic topology, A student guide, Cambridge
University Press, 1972
BOTT, R. ; TU, L.
Differential Forms in Algebraic Topology, GTM 82,
Springer-Verlag, 1982
BREDON, G.
Geometry and Topology, Graduate Texts in
Mathematics, 139. Springer-Verlag, 1993.
BROWDER, W.
Surgery of Simply Connected Manifolds, EMG 65,
Springer-Verlag, 1972
BRYLINSKI, J.-L.
Loop spaces, characteristic classes and geometric
quantization, Birkhäuser, 1993.
DOLD, A.
Lectures on Algebraic Topology, Springer, 1972
DONALDSON, S.K. ; KRONHEIMER, P.B.
The geometry of four-manifolds, OUP, 1990.
EILENBERG, S. ; STEENROD, E.
Foundations of Algebraic Topology, Princeton,1952
FOMENKO, A. T. ; FUCHS, D. B.
A Course in Homotopic Topology, "Nauka," 1989
GRAY, B.
Homotopy theory, Academic Press, 1975
GREENBERG, M. ; HARPER, J.
Algebraic Topology: A First Course, Addison-Wesley,
1981
HATCHER, A.
Algebraic Topology, Cambridge University Press, 2002.
Disponible gratuitement sur ce site :
http://www.math.cornell.edu/~hatcher/AT/ATpage.html
HATCHER, A.
Algebraic Topology, Cambridge University Press, 2002.
HIRSCH, M.
Differential Topology, Springer-Verlag, 1997.
HIRZEBRUCH, F.
Topological Methods in Algebraic Geometry, SpringerVerlag, 1995
HUSEMOLLER, D.
Fiber bundles, Mc Graw Hill, 1964
KAROUBI, M. ; LERUSTE, C.
Differential methods in Algebraic Topology, Cambridge
University Press, 1987
MADSEN, I. ; MILGRAM, R.
Classifying Spaces for Surgery and Cobordism of
Manifolds, AMS n°92, Princeton University Press, 1979
MASSEY, W.
A Basic Course in Algebraic Topology, Springer-Verlag,
1993
MAY, J. P.
A Concise Course in Algebraic Topology, University
Chicago Press, 1999
MILNOR, J.
Lectures on the h-Cobordism Theorem, Princeton
University Press, 1974
MILNOR, J.
Topology from the Differentiable Viewpoint, University
Press of Virginia, 1965
MILNOR, J.
Morse theory, Ann. of Math Studies 51, Princeton
University Press,1965
MILNOR, J. ; STASHEFF, J.
Lectures on characteristic classes, Ann. of Math. Studies
197, Princeton University Press, 1968
MILNOR, J. ; STASHEFF, J.D.
Charasteristic Classes, AMS n°76, Princeton University
Press, 1974.
MOSHER, R. ; TANGORA, M.
Cohomology Operations and Applications in Homotopy
Theory, Harper and Row, 1968
ROHLIN, V. ; FUCHS, D.
Premier cours de topologie, chapitres géométriques,
Editions MIR, Moscou, 1981
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Knots and Links, Math. Lect. Series 7, Publ. Or Perish,
1976
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On Thom Spectra, Orientability, and Cobordism, Springer
Monographs in Mathematics, Springer-Verlag, 1998.
SERRE, J-P
Algèbre locale - Multiplicités, LNM 11, Springer-Verlag,
1965
SPANIER, E.
Algebraic Topology, Mc Graw Hill, 1966
STEENROD, N.
The topology of fiber bundles, Princeton Mathematical
Series n°14, Princeton University Press, 1974
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1968
TURAEV, V.G.
Quantum invariants of knots and 3-manifolds, WDG,
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K-THEORIE
ATIYAH, M.
K-theory, Benjamin, 1967
BASS, H.
Algebraic K-theory, Math. Lectures Notes Series,
Benjamin, 1968
BASS, H.
"Classical" Algebraic K-theory and Connections
with Arithmetic, Seattle 1972, LNM 342,
Springer-Verlag, 1972
BASS, H.
Hermitian K-theory and Geometric Applications,
LNM 343, Springer-Verlag, 1973
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Higher K-theories, LNM 341, Springer-Verlag,
1973
BLACKADAR, B.
K-theory for operator algebras, Mathematical
Sciences Research Institute Publications, 5,
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FRIEDLANDER, E.M. ; GRAYSON, D.R.
Handbook of K-theory, Vol 1-2, Springer, 2005.
KAROUBI, M.
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MILNOR, J.
Introduction to Algebraic K-theory, AMS n° 72,
Princeton University Press, 1971
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An introduction to K-theory for C*-algebras,
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Algebraic K-theory and its applications, Springer,
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TAKESAKI, M.
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Operator Algebras and Non-commutative
Geometry, 8. Springer-Verlag, 2003.
ALGEBRE
ATIYAH M., MACDONALD I.
Introduction to Commutative Algebra, Series in
Mathematics, vol. 361, Addison-Wesley, 1969
BOURBAKI, N.
Algèbre commutative, Ch 1-9, Masson, Paris
1983, 85
EISENBUD, D.
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JACOBSON, N.
Basic algebra, I, II, 2nd edition, Freeman, 1980
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Algebra, Addison-Wesley, 1984
MATSUMURA, H.
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Noncommutative Noetherian Rings,
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Algèbre locale - Multiplicités, LNM 11, SpringerVerlag, 1965
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Commutative Algebra, Vol. 1-2. Van Norstrand,
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THEORIE DES NOMBRES
ABHYANKAR, S.
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Mathematical Surveys and Monographs, vol. 35,
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Automatic sequences, CUP, 2003.
BAKER, A.
Transcendental Number Theory, Cambridge
Mathematical Library, CUP, 1990
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Le grand crible dans la théorie analytique des
nombres, Astérique 17, Société Mathématique de
France, 1974
BOMBIERI, E. ; GUBLER, W.
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BOREL, A. ; CASSELMAN, W.
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ZAGIER, D.
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Summer School on Modular Forms and their
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Topics in Number Theory, The University Series in
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theory and complex multiplication, John Wiley &
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An Introduction to the Theory of Numbers,
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IGUSA, J-I.
An introduction to the theory of the local zeta
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p-adic numbers, p-adic analysis, and zetafunctions. Second edition. Graduate Texts in
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Mathematics, 112. Springer-Verlag, 1987
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Fundamental problems, ideas and theories,
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Algebraic number theory, Grundlehren der
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Co., 1970
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vol. 1, Jones and Bartlett, 1992.
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Automorphic Functions, Publ. Math. Soc. Japan
n°11, Princeton U. Press, 1971
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Texts in Mathematics, vol. 241, Springer-Verlag,
New York, 2007
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in Mathematics, 106. Springer, 2009
SILVERMAN, J.H.
Advanced topics in the arithmetic of elliptic
curves. Graduate Texts in Mathematics, 151.
Springer-Verlag,1994.
SILVERMAN, J.H. ; TATE, J.
Rational points on elliptic curves, Undergraduate
Texts in Mathematics. Springer-Verlag, 1992.
SOULE, C.
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Studies in Advanced Mathematics, vol. 33.
Cambridge University Press, 1992
TITCHMARSH, E. C.
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