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Viser: Principles of Mathematics for Economics
Principles of Mathematics for Economics
Simone Cerreia-Vioglio, Massimo Marinacci og Elena Vigna
(2024)
Sprog: Engelsk
Springer International Publishing AG
387,00 kr.
Denne bog er endnu ikke udgivet. Den forventes Aug 2024.
Detaljer om varen
- Paperback
- Udgiver: Springer International Publishing AG (August 2024)
- Forfattere: Simone Cerreia-Vioglio, Massimo Marinacci og Elena Vigna
- ISBN: 9783319447131
This textbook provides a comprehensive and rigorous introduction to various mathematical topics that play a key role in economics and finance. Motivated by economic applications, the authors introduce students to key mathematical ideas through an economic viewpoint, starting from the real line and moving to n-dimensional spaces, with a special emphasis on global optimization. Additionally, the text helps unacquainted, but intellectually curious, students become familiar with mathematical proofs.
The book is suitable for both self-study and rigorous introductory mathematics courses for undergraduate students majoring in economics or finance.
Part I Structures.- 1 Sets and Numbers: An Intuitive Introduction.- 2 Cartesian Structure and R^n.- 3 Linear Structure.- 4 Euclidean Structure.- 5 Topological Structure.- 6 Functions.- 7 Cardinality.-
Part II Discrete Analysis.- 8 Sequences.- 9 Series.- 10 Discrete Calculus.-
Part III Continuity.- 11 Limits of Functions.- 12 Continuous Functions.-
Part IV Linear and Nonlinear Analysis.- 13 Linear Functions and Operators.- 14 Concave Functions.- 15 Homogeneous Functions.- 16 Lipschitz Functions.- 17 Supermodular Functions.-
Part V Optima.- 18 Optimization Problems.- 19 Semicontinuous optimization.- 20 Projections and Approximations.- 21 Forms and spectra.-
Part VI Differential Calculus.- 22 Derivatives.- 23 Differential Calculus in Several Variables.- 24 Differential Methods.- 25 Approximation.- 26 Concavity and Differentiability.- 27 Nonlinear Riesz's Theorems.- 28 Implicit Functions.- 29 Inverse Functions.- 30 Study of Functions.-
Part VII Differential Optimization.- 31 Unconstrained Optimization.- 32 Equality Constraints.- 33 Inequality Constraints.- 34 General Constraints.- 35 Intermezzo: Correspondences.- 36 Parametric Optimization Problems.- 37 Interdependent Optimization.-
Part VIII Integration.- 38 The Riemann Integral.- 39 Improper Riemann integrals.- 40 Parametric Riemann integrals.- 41 Stieltjes' Integral.- 42 Moments.-
Part IX Appendices.- A Binary Relations.- B Permutations.- C Notions of Trigonometry.- D Elements of Intuitive Logic.- E Mathematical Induction.- F Cast of Characters.
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