The exhaustive list of topics in Random Walks and Diffusion in which we provide Help with Homework Assignment and Help with Project is as follows:

- Harmonic Measure, Hastings-Levitov Algorithm, Comparison of Discrete and Continuous Dynamics
- Chapman-Kolmogorov Equation, Kramers-Moyall Expansion, Fokker-Planck Equation
- Modified Kramers-MoyallCumulant Expansion for Identical Steps
- Flagellar Bacteria
- General Formulation in Higher Dimensions, Moments of First Passage Time, Eventual Hitting Probability, Electrostatic Analogy for Diffusion, First Passage to a Sphere
- Run and Tumble Motion, Chemotaxis
- Corrections to the CLT for Power-law Tails
- Polymer Models: Persistence and Self-avoidance
- I.C. First Passage and Exploration
- Application to Flagellar Bacteria
- Width of the Central Region when Third and Fourth Moments Exist
- Nonlinear Diffusion
- Arcsine Distribution
- Conformal Invariance
- General Formulation in One Dimension
- Return Probability on a Lattice
- Leaper Example: Polymer Surface Adsorption Sites and Cross-sections of a Random Walk
- Financial Time Series
- Weakly Non-identical Steps
- Infinite Man Waiting Time, Mittag-Leffler Decay of Fourier Modes, Time-delayed Flux, Fractional Diffusion Equation
- Levy Flights
- Fractional Diffusion Equations
- Multi-dimensional CLT for Sums of IID Random Vectors
- Surface Growth, Kardar-Parisi-Zhang Equation
- Stochastic Differentials, Wiener Process
- Power-law "Fat Tails"
- Non-separable Continuous-time Random Walks
- Nonlinear Drift
- Superdiffusion and Limiting Levy Distributions for Steps with Infinite Variance, Examples, Size of the Largest Step, Frechet Distribution
- Hughes' Leaper and Creeper Models
- Parabolic Cylinder Functions and Dawson's Integral
- First Passage to a Circle, Wedge/Corner,
- Probability Generating Functions on the Integers, First Passage and Return on a Lattice, Polya's Theorem
- From Random Walks to Diffusion
- Minimum First Passage Time of a Set of N Random Walkers
- Continuous-Time Random Walks
- Central Limit Theorem and the Diffusion Equation
- Normal vs. Anomalous Diffusion
- Laplace Transform
- Berry-Esseen Theorem
- Fat Tails and Riesz Fractional Derivatives
- Interacting Random Walkers, Concentration-dependent Drift
- Leapers and Creepers
- I.B. Nonlinear Diffusion
- Cole-Hopf Transformation, General Solution of Burgers Equation
- "Phase Diagram" for Anomalous Diffusion: Large Steps Versus Long Waiting Times
- Smirnov Density
- CLT for CTRW
- Applications of Conformal Mapping
- Asymptotics with Fat Tails
- Method of Steepest Descent (Saddle-Point Method) for Asymptotic Approximation of Integrals
- Power-law Tails, Diverging Moments and Singular Characteristic Functions
- Normal Diffusion
- Discrete Versus Continuous Stochastic Processes
- First Passage in the Continuum Limit
- Additive Versus Multiplicative Processes
- Asymptotic Shape of the Distribution
- Montroll-Weiss Formulation of CTRW
- Parabola. Continuous Laplacian Growth, Polubarinova-Galin Equation, Saffman-Taylor Fingers, Finite-time Singularities
- Renewal Theory
- Mechanisms for Anomalous Diffusion. Non-identical Steps
- Hitting Probabilities in Two Dimensions
- First Passage in Arbitrary Geometries
- Continuum Derivation Involving the Diffusion Equation
- Concentration-dependent Diffusion, Chemical Potential. Rechargeable Batteries, Steric Effects
- DNA Gel Electrophoresis
- Globally Valid Asymptotics
- Application to Random Walks
- Diffusion-limited Aggregation
- Moments, Cumulants, and Scaling
- Probability Flux
- Reflection Principle and Path Counting for Lattice Random Walks, Derivation of the Discrete Arcsine Distribution for the Fraction of Time Spent on One Side of the Origin, Continuum Limit
- Hughes' General Formulation of CTRW with Motion between "turning points"
- Potential Theory using Complex Analysis, Mobius Transformations, First Passage to a Line
- Mechanisms for Anomalous Diffusion
- Additivity of Tail Amplitudes
- Continuous-time Random Walks
- Corrections to the Diffusion Equation Approximating Discrete Random Walks with IID Steps
- Nonlinear Waves in Traffic Flow, Characteristics, Shocks, Burgers' Equation