Lectures related to Stirling's formula: Euler's integral and Gaussian integral

Complexity of Algorithms: Advanced Big-O Facts

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

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

Natural Logarithm: Definition and Properties

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

Binary Search: Logarithm Function

Explains binary search, the logarithm function, and recursive algorithms for factorial and Fibonacci sequences.

Limit Properties: Exponential and Logarithmic Functions

Covers the properties of limits related to exponential and logarithmic functions.

Complexity of Algorithms: Advanced Big-O Facts

Explores advanced big-O facts for powers, logarithms, factorials, and function combinations.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

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.

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.

Algebraic Identities and Trigonometry

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

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.

Taylor Polynomials: Examples and Convergence

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Exponential Function: Properties and Definitions

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

Combinatorics: Counting Methods

Introduces combinatorics and counting methods for determining possible outcomes in various scenarios, illustrated with examples.

Enumeration: Counting Subsets

Covers the concept of enumeration and counting subsets of a finite set with examples and factorial notation.

Exponential Functions and Logarithms

Explores exponential and logarithmic functions, their properties, relations, and graphs, including different bases and commonly used logarithms.

Dynamics on homogeneous spaces and interactions with number theory

Explores dynamics on homogeneous spaces, Khintchine theorem, Sullivan's logarithm law, and interactions with number theory.