Stochastic Calculus: Foundations and Applications

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Explores broken and emerging symmetries in turbulent states, discussing energy cascades, lack of scale invariance, and potential conformal invariance.

Stochastic Integration

Covers stochastic integration and exchange mobility for mathematics students.

Calculus Applications: Lengths and Surfaces of Revolution

Discusses the applications of calculus in calculating lengths and surfaces of revolution, emphasizing integral calculus and geometric interpretations.

Fourier Transform and Spectral Densities

Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.

Interest Rate Models: Introduction

Covers the fundamentals of interest rates and stochastic models in finance.

Advanced Analysis II: Riemann Integrability and Jordan Measure

Explores Riemann integrability and Jordan measure, discussing the conditions for a set to be negligible.

Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Multivariable Integral Calculus

Delves into multivariable integral calculus, covering topics like volume calculations and finding extrema under constraints.

Fundamental Theorem of Integral Calculus

Explores the Fundamental Theorem of Analysis for continuous functions on closed intervals, illustrated with examples like integrating cos(x).

Asset Pricing Theory: Dynamic Arbitrage Pricing

Covers the first theorem of asset pricing, self-financing portfolios, replication, Kolmogorov equations, and pricing strategies.