Simone Cerreia-Vioglio, Massimo Marinacci, Elena Vigna

Principles of Mathematics for Economics

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Egea / Springer / Springer Nature Switzerland / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-44713-1
• 1st ed. 2024
• Seitenzahl: 1505
• Erscheinungstermin: 4. Oktober 2026
• Englisch
• Abmessung: 235mm x 155mm
• ISBN-13: 9783319447131
• ISBN-10: 3319447130
• Artikelnr.: 45381849

Autorenporträt

Simone Cerreia-Vioglio is Associate Professor at the Department of Decision Sciences at Università Bocconi in Milan.
Massimo Marinacci holds the AXA-Bocconi Chair in Risk at the Department of Decision Sciences at Università Bocconi in Milan.
Elena Vigna is Associate Professor at the Department Esomas at the Università di Torino.

Inhaltsangabe

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 Rieszs 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.