Lectures related to Dynamics on homogeneous spaces and interactions with number theory

Natural Logarithm: Definition and Properties

Explores the definition, properties, and limits of the natural logarithm function.

Generalized Powers: Derivatives and Exponentials

Covers properties of logarithms, derivatives, exponentials, and sine-cosine functions.

Power Functions: Properties and Derivatives

Covers properties of logarithms, power functions, and their derivatives, with examples illustrating key concepts.

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Natural Logarithm: Graph

Explores the properties and graph of the natural logarithm function, emphasizing its bijectivity and the Euler's number 'e'.

Logarithmic Functions: Properties and Applications

Explores the properties and applications of natural logarithmic functions, including area invariance and harmonic series divergence.

Natural Logarithm: Properties and Inequalities

Covers properties and inequalities of the natural logarithm function, including solving related inequalities.

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Convergence in Law: Theorem and Proof

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Natural Logarithm: Definition and Properties

Delves into the definition, geometric interpretation, and properties of the natural logarithm, including its continuity and behavior as x approaches infinity or zero.

Exponential Function: Properties and Definitions

Explores the properties and definitions of the exponential function and its relation to the natural logarithm.

Abel Summation and Prime Number Theory

Introduces the Abel summation formula and its application in establishing various equivalent formulations of the Prime Number Theory.

Exponential Functions: Properties and Logarithms

Explores exponential functions, their properties, and the relationship with logarithmic functions.

Properties of Natural Logarithm

Explores the properties of the natural logarithm function and its graphical representation.

Taylor Polynomials: Approximating Functions with Taylor Polynomials

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.

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Entropy and the Second Law of Thermodynamics

Covers entropy, its definition, and its implications in thermodynamics.

Complexity of Algorithms: Advanced Big-O Facts

Covers big-O estimates for factorial function and combinations of functions.

Limits and Exponential Functions

Explores limits, exponential functions, and logarithms properties.