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.
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.
