{"product_id":"mathematical-methods-and-quantum-mathematics-for-economics-and-finance-9789811566134","title":"Mathematical Methods and Quantum Mathematics for Economics and Finance","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eGiven the rapid pace of development in economics and finance, a concise and up-to-date introduction to mathematical methods has become a prerequisite for all graduate students, even those not specializing in quantitative finance. This book offers an introductory text on mathematical methods for graduate students of economics and finance–and leading to the more advanced subject of quantum mathematics. The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided – in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economics and finance.  In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton’s theory of corporate debt are among topics analyzed using quantum mathematics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePART I : INTRODUCTION \u003c\/p\u003e    \u003cp\u003e1 Introduction \u003c\/p\u003e  \u003cp\u003e1.1 Introduction \u003c\/p\u003e  \u003cp\u003e1.2 Elementary Algebra \u003c\/p\u003e  \u003cp\u003e1.2.1 Quadratic polynomial \u003c\/p\u003e  \u003cp\u003e1.3 Finite Series \u003c\/p\u003e  \u003cp\u003e1.4 Infinite Series \u003c\/p\u003e  \u003cp\u003e1.4.1 Cauchy convergence \u003c\/p\u003e  \u003cp\u003e1.5 Problems \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003e2 Functions \u003c\/p\u003e  \u003cp\u003e2.1 Introduction \u003c\/p\u003e  \u003cp\u003e2.2 Exponential function \u003c\/p\u003e  \u003cp\u003e2.3 Demand and supply function \u003c\/p\u003e  2.4 Option theory payoff \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e2.5 Interest rates; bonds \u003c\/p\u003e  \u003cp\u003e2.6 Problems \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  PART II : LINEAR ALGEBRA \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e3 Simultaneous linear equations \u003c\/p\u003e  \u003cp\u003e3.1 Introduction \u003c\/p\u003e  \u003cp\u003e3.2 Two commodities \u003c\/p\u003e  \u003cp\u003e3.3 Vectors \u003cbr\u003e 3.4 Basis vectors \u003cbr\u003e 3.4.1 Scalar product \u003cbr\u003e 3.5 Linear transformations; matrices \u003c\/p\u003e  \u003cp\u003e3.6 EN: N-dimensional linear vector space \u003c\/p\u003e  \u003cp\u003e3.7 Linear transformations of EN\u003c\/p\u003e  \u003cp\u003e3.8 Problems \u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e4 Matrices \u003c\/p\u003e  \u003cp\u003e4.1 Introduction \u003c\/p\u003e  \u003cp\u003e4.2 Matrix multiplication \u003c\/p\u003e  \u003cp\u003e4.3 Properties of N × N matrices \u003c\/p\u003e  \u003cp\u003e4.4 System of linear equations \u003c\/p\u003e  \u003cp\u003e4.5 Determinant: 2 × 2 case \u003c\/p\u003e  \u003cp\u003e4.6 Inverse of a 2 × 2 matrix \u003c\/p\u003e  \u003cp\u003e4.7 Outer product; transpose \u003c\/p\u003e  \u003cp\u003e4.7.1 Transpose \u003c\/p\u003e  \u003cp\u003e4.8 Eigenvalues and eigenvectors \u003c\/p\u003e  \u003cp\u003e4.8.1 Spectral decomposition \u003c\/p\u003e  \u003cp\u003e4.9 Problems \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003e5 Square matrices \u003c\/p\u003e  \u003cp\u003e5.1 Determinant: 3 × 3 case \u003c\/p\u003e  \u003cp\u003e5.2 Properties of determinants \u003c\/p\u003e  \u003cp\u003e5.3 N × N determinant \u003c\/p\u003e  \u003cp\u003e5.3.1 Inverse of a N × N matrix \u003c\/p\u003e  \u003cp\u003e5.4 Leontief input-output model \u003c\/p\u003e  \u003cp\u003e5.4.1 Hawkins-Simon condition \u003c\/p\u003e  \u003cp\u003e5.5 Symmetric matrices \u003c\/p\u003e  5.6 Symmetric matrix: diagonalization \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e5.6.1 Functions of a symmetric matrix \u003c\/p\u003e  \u003cp\u003e5.7 Hermitian matrices \u003c\/p\u003e  \u003cp\u003e5.8 Diagonalizable matrices \u003c\/p\u003e  \u003cp\u003e5.8.1 Non-symmetric matrix \u003c\/p\u003e  \u003cp\u003e5.9 Change of Basis states \u003c\/p\u003e  \u003cp\u003e5.9.1 Symmetric matrix: change of basis \u003c\/p\u003e  \u003cp\u003e5.9.2 Hermitian matrix: change of basis \u003c\/p\u003e  \u003cp\u003e5.10 Problems \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003ePART III : CALCULUS \u003c\/p\u003e  6 Integration \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.1 Introduction \u003c\/p\u003e  \u003cp\u003e6.2 Sums leading to integrals \u003c\/p\u003e  \u003cp\u003e6.3 Definite and indefinite integrals \u003c\/p\u003e  \u003cp\u003e6.4 Applications in economics\u003c\/p\u003e  \u003cp\u003e6.5 Multiple Integrals \u003c\/p\u003e  \u003cp\u003e6.5.1 Change of variables \u003c\/p\u003e  \u003cp\u003e6.6 Gaussian integration \u003c\/p\u003e  \u003cp\u003e6.6.1 N-dimensional Gaussian integration \u003c\/p\u003e  \u003cp\u003e6.7 Problems \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003e7 Differentiation \u003c\/p\u003e  \u003cp\u003e7.1 Introduction \u003c\/p\u003e  \u003cp\u003e7.2 Inverse of Integration \u003c\/p\u003e  7.3 Rules of differentiation \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e7.4 Integration by parts \u003c\/p\u003e  \u003cp\u003e7.5 Taylor expansion \u003c\/p\u003e  \u003cp\u003e7.6 Minimum and maximum \u003c\/p\u003e  7.6.1 Maximizing profit \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e7.7 Integration; change of variable \u003c\/p\u003e  \u003cp\u003e7.8 Partial derivatives \u003c\/p\u003e  \u003cp\u003e7.8.1 Chain rule; Jacobian \u003c\/p\u003e  7.8.2 Polar coordinates; Gaussian integration\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e7.9 Hessian matrix: critical points \u003c\/p\u003e  \u003cp\u003e7.10 Constrained optimization: Lagrange multiplier \u003c\/p\u003e  \u003cp\u003e7.10.1 Interpretation of λc\u003c\/p\u003e  \u003cp\u003e7.11 Line integral; Exact and inexact differentials \u003c\/p\u003e  \u003cp\u003e7.12 Problems\u003c\/p\u003e   \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e8 Functional analysis\u003c\/p\u003e  \u003cp\u003e8.1 Dirac bracket and vector notation\u003c\/p\u003e  \u003cp\u003e8.2 Continuous basis states \u003c\/p\u003e  \u003cp\u003e8.3 Dirac delta function \u003c\/p\u003e  \u003cp\u003e8.4 Basis states for function space \u003c\/p\u003e  \u003cp\u003e8.5 Operators on function space \u003c\/p\u003e  \u003cp\u003e8.6 Gaussian kernel \u003c\/p\u003e  \u003cp\u003e8.7 Fourier Transform \u003c\/p\u003e  \u003cp\u003e8.8 Taylor expansion \u003c\/p\u003e  \u003cp\u003e8.9 Gaussian functional integration \u003c\/p\u003e  \u003cp\u003e8.10 Problems \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003e9 Ordinary Differential Equations \u003c\/p\u003e  \u003cp\u003e9.1 Introduction \u003c\/p\u003e  9.2 Separable differential equations \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e9.3 Linear differential equations \u003c\/p\u003e  \u003cp\u003e9.4 Bernoulli differential equation \u003c\/p\u003e  \u003cp\u003e9.5 Homegeneous differential equation \u003c\/p\u003e  \u003cp\u003e9.6 Second order linear differential equations \u003c\/p\u003e  \u003cp\u003e9.6.1 Single eigenvalue \u003c\/p\u003e  \u003cp\u003e9.7 Ricatti differential equation \u003c\/p\u003e  \u003cp\u003e9.8 Inhomogeneous second order differential equations\u003c\/p\u003e  \u003cp\u003e9.8.1 Green’s function \u003c\/p\u003e  \u003cp\u003e9.9 System of linear differential equations \u003c\/p\u003e  \u003cp\u003e9.10 Strum-Louisville theorem; special functions \u003c\/p\u003e  9.11 Problems \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003ePART IV : PROBABILITY THEORY \u003c\/p\u003e  \u003cp\u003e10 Random variables \u003c\/p\u003e  \u003cp\u003e10.1 Introduction: Risk \u003c\/p\u003e  \u003cp\u003e10.1.1 Example \u003c\/p\u003e  \u003cp\u003e10.2 Key ideas of probability \u003c\/p\u003e  \u003cp\u003e10.3 Discrete random variables \u003c\/p\u003e  \u003cp\u003e10.3.1 Bernoulli random variable \u003c\/p\u003e  \u003cp\u003e10.3.2 Binomial random variable \u003c\/p\u003e  \u003cp\u003e10.3.3 Poisson random variable \u003c\/p\u003e  \u003cp\u003e10.4 Continuous random variables\u003c\/p\u003e  \u003cp\u003e10.4.1 Uniform random variable \u003c\/p\u003e  \u003cp\u003e10.4.2 Exponential random variable \u003c\/p\u003e  \u003cp\u003e10.4.3 Normal (Gaussian) random variable \u003c\/p\u003e  \u003cp\u003e10.5 Problems \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003e11 Probability distribution functions \u003c\/p\u003e  \u003cp\u003e11.0.1 Cumulative density \u003c\/p\u003e  11.1 Axioms of probability theory \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e11.2 Joint probability density \u003c\/p\u003e  \u003cp\u003e11.3 Independent random variables \u003c\/p\u003e  \u003cp\u003e11.3.1 Law of large numbers \u003c\/p\u003e  \u003cp\u003e11.4 Correlated random variables \u003c\/p\u003e  \u003cp\u003e11.5 Marginal probability density \u003c\/p\u003e  \u003cp\u003e11.6 Conditional expectation value \u003c\/p\u003e  \u003cp\u003e11.6.1 Discrete random variable \u003c\/p\u003e  \u003cp\u003e11.6.2 Continuous random variables \u003c\/p\u003e  11.7 Problems \u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e12 Stochastic processes \u0026amp; Option pricing \u003c\/p\u003e  \u003cp\u003e12.1 Gaussian white noise \u003c\/p\u003e  \u003cp\u003e12.1.1 Integrals of White Noise \u003c\/p\u003e  \u003cp\u003e12.2 Ito Calculus \u003c\/p\u003e  \u003cp\u003e12.3 Lognormal Stock Price \u003c\/p\u003e  \u003cp\u003e12.4 Black-Scholes Equation; Hedged Portfolio \u003c\/p\u003e  \u003cp\u003e12.4.1 Assumptions in the Derivation of Black-Scholes\u003c\/p\u003e  \u003cp\u003e12.5 Risk-Neutral Martingale Solution of the Black-Scholes Equation\u003c\/p\u003e  \u003cp\u003e12.6 Black-Scholes-Schrodinger equation \u003c\/p\u003e  \u003cp\u003e12.7 Linear Langevin Equation \u003c\/p\u003e  \u003cp\u003e12.7.1 Random Paths \u003c\/p\u003e  \u003cp\u003e12.8 Problems \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003e13 Appendix \u003c\/p\u003e  \u003cp\u003e13.1 Introduction \u003c\/p\u003e  \u003cp\u003e13.2 Integers \u003c\/p\u003e  \u003cp\u003e13.3 Real numbers \u003c\/p\u003e  \u003cp\u003e13.4 Cantor’s Diagonal Argument \u003c\/p\u003e  \u003cp\u003e13.5 Higher Order Infinities \u003c\/p\u003e  13.6 Mathematical Logic\u003cp\u003e\u003c\/p\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":51743213879639,"sku":"9789811566134","price":62.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811566134.jpg?v=1758389503","url":"https:\/\/bookcurl.com\/products\/mathematical-methods-and-quantum-mathematics-for-economics-and-finance-9789811566134","provider":"Book Curl","version":"1.0","type":"link"}