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Principles of Mathematics for Economics, 1st ed. 2024

Langue : Anglais

Auteurs :

Couverture de l’ouvrage Principles of Mathematics for Economics

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.

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.

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

Date de parution :

Ouvrage de 1505 p.

15.5x23.5 cm

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36,91 €

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