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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.
List of contents
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.
About the author
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.
