### Outcome 1

Use probability density functions to describe a system, and recognize simple probability functions and their properties including Gaussian (normal), binomial (or multinomial), and Poisson distributions.

### Outcome 2

Use combinatorics to define probabilities in simple systems.

### Outcome 3

Describe how to choose a Gibbsian ensemble for calculation of system properties. Be able to recognize when the following ensembles are appropriate: microcanonical (*N,V,E*), canonical (*N,V,T*), grand canonical (*V,T,**m*), isobaric-isothermal (*N,T,P*). Know how to construct the partition function in each case.

### Outcome 4

Calculate average system quantities and thermodynamic variables using the appropriate partition function.

### Outcome 5

Calculate the size of fluctuations of system properties and relate them to the number of particles in a system.

### Outcome 6

Use proper statistics for classical particles and for quantum particles (bosons or fermions).

### Outcome 7

Calculate canonical partition functions for translation, rotation, and harmonic vibration. Use them for applications and know when they don't apply.

### Outcome 8

Explain the meaning, significance and range of applicability of these fundamentals: ergodic hypothesis, equipartition theorem, and Bose-Einstein condensation.

### Outcome 9

Use statistical mechanical principles to describe chemical equilibrium constants.

### Outcome 10

Apply statistical mechanical principles to simple crystals, blackbody radiation and imperfect gases.

### Outcome 11

Use the Metropolis Monte Carlo method to calculate statistical averages for a system. Know how to choose an efficient sampling method.

### Outcome 12

Show how to use molecular dynamics to calculate statistical averages for a molecular system. Know when molecular dynamics is more appropriate than Monte Carlo methods. Know the advantages and disadvantages of common trajectory propagation algorithms.

### Outcome 13

Obtain the radial distribution from the probability function for a system, from Monte Carlo calculations or molecular dynamics trajectories and evaluate system properties from the radial distribution function.

### Outcome 14

Use Monte Carlo and transfer matrix methods to study a system of interacting spins as a model of phase transitions.