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Principles of Mathematics for Economics

Author(s):
Publisher:

Springer

Pages: 1505
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Recommend to library

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Paperback - 9783319447131

06 September 2019

$44.99

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Ebook - 9783319447155

06 September 2019

$34.99

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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...

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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.

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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


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.
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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.

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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.

Show Less

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