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Principles of Mathematics for Economics

Autor Simone Cerreia-Vioglio, Massimo Marinacci, Elena Vigna
en Limba Engleză Paperback – 8 aug 2024
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.
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Specificații

ISBN-13: 9783319447131
ISBN-10: 3319447130
Pagini: 1505
Ilustrații: XXV, 1505 p. 234 illus., 43 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:1st ed. 2024
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică


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.

Textul de pe ultima copertă

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.  


Caracteristici

Presents mathematical concepts from an economic viewpoint Allows students of Economics or Business/Finance to broaden their mathematical knowledge Provides tools to learn how to construct mathematical proofs Useful for students continuing their studies in Economics or Finance at the postgraduate level Shows various economic and financial applications with mathematical rigor Useful for teachers of mathematics courses within an Economics or Business/Finance curriculum Covers topics for mathematics courses at undergraduate levels Recommendable for self-study