Contents -- 1 Monte Carlo methods -- 1.1 Popular games in Monaco -- 1.1.1 Direct sampling -- 1.1.2 Markov-chain sampling -- 1.1.3 Historical origins -- 1.1.4 Detailed balance -- 1.1.5 The Metropolis algorithm -- 1.1.6 A priori probabilities, triangle algorithm -- 1.1.7 Perfect sampling with Markov chains -- 1.2 Basic sampling -- 1.2.1 Real random numbers -- 1.2.2 Random integers, permutations, and combinations -- 1.2.3 Finite distributions -- 1.2.4 Continuous distributions and sample transformation -- 1.2.5 Gaussians -- 1.2.6 Random points in/on a sphere -- 1.3 Statistical data analysis -- 1.3.1 Sum of random variables, convolution -- 1.3.2 Mean value and variance -- 1.3.3 The central limit theorem -- 1.3.4 Data analysis for independent variables -- 1.3.5 Error estimates for Markov chains -- 1.4 Computing -- 1.4.1 Ergodicity -- 1.4.2 Importance sampling -- 1.4.3 Monte Carlo quality control -- 1.4.4 Stable distributions -- 1.4.5 Minimum number of samples -- Exercises -- References -- 2 Hard disks and spheres -- 2.1 Newtonian deterministic mechanics -- 2.1.1 Pair collisions and wall collisions -- 2.1.2 Chaotic dynamics -- 2.1.3 Observables -- 2.1.4 Periodic boundary conditions -- 2.2 Boltzmann's statistical mechanics -- 2.2.1 Direct disk sampling -- 2.2.2 Partition function for hard disks -- 2.2.3 Markov-chain hard-sphere algorithm -- 2.2.4 Velocities: the Maxwell distribution -- 2.2.5 Hydrodynamics: long-time tails -- 2.3 Pressure and the Boltzmann distribution -- 2.3.1 Bath-and-plate system -- 2.3.2 Piston-and-plate system -- 2.3.3 Ideal gas at constant pressure -- 2.3.4 Constant-pressure simulation of hard spheres -- 2.4 Large hard-sphere systems -- 2.4.1 Grid/cell schemes -- 2.4.2 Liquid-solid transitions -- 2.5 Cluster algorithms -- 2.5.1 Avalanches and independent sets -- 2.5.2 Hard-sphere cluster algorithm -- Exercises -- References.

3 Density matrices and path integrals -- 3.1 Density matrices -- 3.1.1 The quantum harmonic oscillator -- 3.1.2 Free density matrix -- 3.1.3 Density matrices for a box -- 3.1.4 Density matrix in a rotating box -- 3.2 Matrix squaring -- 3.2.1 High-temperature limit, convolution -- 3.2.2 Harmonic oscillator (exact solution) -- 3.2.3 Infinitesimal matrix products -- 3.3 The Feynman path integral -- 3.3.1 Naive path sampling -- 3.3.2 Direct path sampling and the Lévy construction -- 3.3.3 Periodic boundary conditions, paths in a box -- 3.4 Pairdensity matrices -- 3.4.1 Two quantum hard spheres -- 3.4.2 Perfect pair action -- 3.4.3 Many-particle density matrix -- 3.5 Geometry of paths -- 3.5.1 Paths in Fourier space -- 3.5.2 Pathmaxima, correlation functions -- 3.5.3 Classical random paths -- Exercises -- References -- 4 Bosons -- 4.1 Ideal bosons (energy levels) -- 4.1.1 Single-particle density of states -- 4.1.2 Trapped bosons (canonical ensemble) -- 4.1.3 Trapped bosons (grand canonical ensemble) -- 4.1.4 Large-N limit in the grand canonical ensemble -- 4.1.5 Differences between ensembles-.uctuations -- 4.1.6 Homogeneous Bose gas -- 4.2 The ideal Bose gas (density matrices) -- 4.2.1 Bosonic density matrix -- 4.2.2 Recursive counting of permutations -- 4.2.3 Canonical partition function of ideal bosons -- 4.2.4 Cycle-length distribution, condensate fraction -- 4.2.5 Direct-sampling algorithm for ideal bosons -- 4.2.6 Homogeneous Bose gas, winding numbers -- 4.2.7 Interacting bosons -- Exercises -- References -- 5 Order and disorder in spin systems -- 5.1 The Ising model-exact computations -- 5.1.1 Listing spin configurations -- 5.1.2 Thermodynamics, specific heat capacity, and magnetization -- 5.1.3 Listing loop configurations -- 5.1.4 Counting (not listing) loops in two dimensions -- 5.1.5 Density of states from thermodynamics.

5.2 The Ising model-Monte Carlo algorithms -- 5.2.1 Local sampling methods -- 5.2.2 Heat bath and perfect sampling -- 5.2.3 Cluster algorithms -- 5.3 Generalized Ising models -- 5.3.1 The two-dimensional spin glass -- 5.3.2 Liquids as Ising-spin-glass models -- Exercises -- References -- 6 Entropic forces -- 6.1 Entropic continuum models and mixtures -- 6.1.1 Random clothes-pins -- 6.1.2 The Asakura-Oosawa depletion interaction -- 6.1.3 Binary mixtures -- 6.2 Entropic lattice model: dimers -- 6.2.1 Basic enumeration -- 6.2.2 Breadth-.rst and depth-first enumeration -- 6.2.3 Pfaffian dimer enumerations -- 6.2.4 Monte Carlo algorithms for the monomer-dimer problem -- 6.2.5 Monomer-dimer partition function -- Exercises -- References -- 7 Dynamic Monte Carlo methods -- 7.1 Random sequential deposition -- 7.1.1 Faster-than-the-clock algorithms -- 7.2 Dynamic spin algorithms -- 7.2.1 Spin-flips and dice throws -- 7.2.2 Accelerated algorithms for discrete systems -- 7.2.3 Futility -- 7.3 Disks on the unit sphere -- 7.3.1 Simulated annealing -- 7.3.2 Asymptotic densities and paper-cutting -- 7.3.3 Polydisperse disks and the glass transition -- 7.3.4 Jamming and planar graphs -- Exercises -- References -- Acknowledgements -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- O -- P -- R -- S -- T -- U -- V -- W -- Y -- Z.