Lectures related to Fibonacci numbers and the golden ratio

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.

Counting with Recurrence Relations: Fibonacci Sequence and Bit Strings

Covers the definition of recurrence relations and their application in counting problems.

Matrix Recurrence Relations

Explores matrix recurrence relations, eigenvalues, Fibonacci sequence, and the golden ratio in linear algebra.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Sequences: Induction Method

Covers sequences, induction method, Fibonacci, Bernoulli's inequality, and binomial formula.

Real Analysis: Sequences and Limits

Covers real sequences, induction, limits, and convergence in mathematical analysis.

Convergence of Sequences in Multivariable Analysis

Covers the convergence of sequences in multivariable analysis, including definitions, properties, and examples in higher dimensions.

Linear Algebra: Injective Functions

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Real Analysis: Basics and Sequences

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

Improper Integrals: Fundamental Concepts and Examples

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Limits and Continuity: Analysis 1

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

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