Principles of Mathematics for Economics

ISBN-13: 9783319447131 / Angielski / Miękka / 2024 / 1505 str.

Elena Vigna

Opis

This textbook provides a comprehensive general introduction to various mathematical tools in the context of their applications in economics and finance.
It approaches topics like mathematical structures and functions, linear and non-linear analysis, differential calculus and integration by starting from the real line and moving to n-dimensional spaces. Additionally, a special emphasis is placed on global optimization, bringing it closer to real economic applications.

The book is suitable for both self-study and as supplementary material for an introductory mathematics course taken by university students majoring in economics and business/finance. The rigorous style helps inexperienced students to familiarize themselves with the concept of mathematical proofs and also shows tools to prove new findings. This makes the book ideal for students undertaking further studies in economics and finance, and eventually planning an academic or professional career.

Spis treści

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.

O autorze

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.

Blurb

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.