Book proposals

Mathematical preparations -- Optimization problems and existence of optimal solutions -- Necessary and sufficient conditions of optimal solutions -- Problems with convexity and quasi-convexity conditions -- Linear programming

What is numerical analysis? -- Understanding error -- Direct methods for linear systems -- Least squares problems -- Iterative methods for linear systems -- Eigenvalue problems -- Polynomial interpolation -- Approximation of functions -- Dierentiation and integration -- Zeros of nonlinear functions -- Optimization -- Initial value problems -- Two-point boundary value problems -- Partial dierential equations

2. Probabilistic Numerical Methods2.1 [...]

1.3.5 Expectation estimates1.3.6 Proof of Theorem 1.3.7; 1.3.7 Back to graphical indexation; 1.4 General Stein's estimates: proofs; 1.4.1 Proof of Theorem 1.2.1; 1.4.2 Proof of Theorem 1.2.2; 1.5 Stein's method for diffusion approximations; 1.5.1 A functional CLT via Stein's method; 1.5.2 Finite dimensional convergence rate; 1.6 A nonconventional functional CLT; 1.7 Extensions to nonlinear indexes; 1.7.1 Preliminaries; 1.7.2 Another example with nonlinear indexes; 2. Local limit theorem; 2.1 Introduction; 2.2 Local central limit theorem via Fourier analysis

A collection of problems and solutions in differential geometry, with applications