Notes & Coursework

Estimation of Location & Scale, Regression

Image Segmentation with Spatial Priors · Weekly Reading Reports

Gradient Descent and Variants

Statistical Depths for Multivariate and Functional Data with Applications

Monte Carlo Integration, Gibbs Sampling

Characters, Representations of Symmetric Groups

An Introduction to Statistical Depth Functions

Characteristic Curves, Heat & Light Equations

Regression · Hypothesis Testing, Density Estimation

The Three Classical Problems

Existence & Stability of Solutions of ODEs

Sequences & Series of Random Variables

Rank Deficient Designs, Simultaneous Confidence Intervals · Cross Validation & Outlier Detection · Generalized Linear Models, Model Selection

Normed Linear Spaces

Signed, Complex, and Radon Measures

Fundamental Groups

Linear Regression, Least Squares & Ridge · Model Selection

The Hyperbolic plane as the Universal Cover of the Double Torus

Topology

Rings & Modules

Measure Theory

Curves & Surfaces in Euclidean Spaces

Centrality, Dispersion, Correlation, and Sampling · Rejection Sampling

Multivariable Calculus · Spivak's Calculus on Manifolds

Group Theory

Graph Theory & Combinatorics

Linear Operators & Inner Product Spaces

Root Finding, Interpolation, Numerical Integration, and ODEs · Trapezoidal method for solving ODEs

The Stone-Weierstrass Theorem · Rudin's Principles of Mathematical Analysis · Armstrong's Groups and Symemtry · Artin's Algebra

Sequences & Series of Functions · Differentiation · Integration

Introduction to Probability · Conditional Probability · Random Variables · Random Vectors · Markov Chains

Quantum Mechanics

Kinetic Theory of Gases

Seismic Waves

Gaussian Plume Model

Real Numbers · Point Set Topology on R · Sequences & series

Fields & Vector Spaces · Linear Maps · Change of Basis · Eigenvectors & Eigenvalues, Inner Products · Term Presentation

Partial Differential Equations · Laplace's Equation · Heat Flow & Schrodinger Equations · Wave Equation · Fourier Series · Sine/Cosine & Complex Exponential Series · Probability & Statistics

Waves and Optics

Special Relativity

Diffraction and Interference · Electron Diffraction · Interferometry and Coherence · Velocity of Light · Quantum Nature of Atoms · Polarization of Light · Quantization of Light

Ground Based Observations of Noctilucent Cloud Brightness and Frequency

Tectonic Plate Buoyancy · Bouguer Gravity Anomaly

The Liquid State · Chemical Kinetics

Isoelectronic Point of Glycine · pK of Bromocresol Green · Iodine Clock Reaction

Global Energy Balance · Atmospheric Circulation · Oceanic Circulation · Formation of the Earth · Formation of the Atmosphere · Early Earth and Climate Regulation

Sequences · Series · Integration · Linear Algebra · Countability · Linear Algebra & Analytical Geometry

Second Order ODE's · Series Solution of ODES's · Complex Analysis

The Elements, Waves and Particles · Quantum Mechanics - Wavefunctions and Electrons · Quantum Mechanics - the Shape of Wavefunctions

Earth's Structure & Seismology · Supercontinents & Superplumes in the Precambrian

Set Theory · Relations · Functions · Induction · Number Systems · Limits · Continuity & Differentiability · Inequalities · Cubic Equations

Diversity (birdlife) · Diversity (treelife) · Photospectrometry