UID:
almafu_9958094963602883
Umfang:
1 online resource (301 p.)
ISBN:
1-281-76339-X
,
9786611763398
,
0-08-087413-4
Serie:
Pure and applied mathematics ; 97
Originaltitel:
Panorama des mathématiques pures.
Inhalt:
A panorama of pure mathematics, as seen by N. Bourbaki
Anmerkung:
Translation of: Panorama des mathématiques pures.
,
Front Cover; A Panorama of Pure Mathematics; Cpyright Page; Contents; Introduction; Chapter A I. Algebraic and differential topology; 1. Techniques; 2. Results; 3. Connections with the natural sciences; 4. The originators; References; Chapter A II. Differential manifolds. Differential geometry; 1. The general theory; 2. G-structures; 3. The topology of differential manifolds; 4. Infinite-dimensional differential manifolds; 5. Connections with the natural sciences; 6. The originators; References; Chapter A III. Ordinary differential equations; 1. The algebraic theory
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2. Ordinary differential equations in the complex domain3. The qualitative study of ordinary differential equations; 4. The classification problem; 5. Boundary-value problems; 6. Connections with the natural sciences; 7. The originators; References; Chapter A IV. Ergodic theory; 1. The ergodic theorem; 2. Classification problems; 3. Connections with the natural sciences; 4. The originators; References; Chapter A V. Partial differential equations; 1. The local study of differential systems; 2. Completely integrable systems and foliations
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3. Linear partial differential equations: general theory4. Equations with constant coefficients; 5. Boundary-value problems for linear equations: I. General theory; 6. Boundary-value problems for linear equations: II. Spectral theory of elliptic operators; 7. Boundary-value problems for linear equations: III. Equations of evolution; 8. Pseudodifferential operators on compact manifolds; 9. Nonlinear partial differential equations; 10. Connections with the natural sciences; 11. The originators; References; Chapter A VI. Noncommutative harmonic analysis
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1. Elementary cases: compact groups and abelian groups2. The fundamental problems; 3. Harmonic analysis on real reductive Lie groups; 4. Harmonic analysis on reductive p-adic groups; 5. Harmonic analysis on nilpotent and solvable Lie groups; 6. Representations of group extensions; 7. Connections with the natural sciences; 8. The originators; References; Chapter A VII. Automorphic forms and modular forms; 1. The analytic aspect; 2. The intervention of Lie groups; 3. The intervention of adèle groups; 4. Applications to number theory; 5. Automorphic forms, abelian varieties, and class fields
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6. Relations with the arithmetic theory of quadratic forms7. Connections with the natural sciences; 8. The originators; References; Chapter A VIII. Analytic geometry; 1. Functions of several complex variables and analytic spaces; 2. Compact analytic spaces; Kähler manifolds; 3. Variations of complex structures and infinite-dimensional manifolds; 4. Real and p-adic analytic spaces; 5. Connections with the natural sciences; 6. The originators; References; Chapter A IX. Algebraic geometry; 1. The modem framework of algebraic geometry; 2. The fundamental notions of the theory of schemes
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3. The study of singularities
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English
Weitere Ausg.:
ISBN 0-12-215560-2
Sprache:
Englisch
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