Counting with Recurrence Relations: Fibonacci Sequence and Bit Strings

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

Fibonacci numbers and the golden ratio

Explores the Fibonacci sequence, identities, golden ratio, and explicit formulas.

Linear Recurrence Relations

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

Linear Recurrence Relations: Solving Techniques

Explores linear homogeneous recurrence relations, solving techniques, characteristic equations, and examples like Fibonacci numbers.

Number Sequences: Guessing, Fibonacci, Recurrence Relations

Covers the identification of number sequences and solving recurrence relations.

Matrix Recurrence Relations

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

Number Sequences: Guessing, Modeling, and Solving Recurrence Relations

Covers the identification of number sequences, modeling population growth, and solving recurrence relations.

Advanced Counting: Quiz

Covers advanced counting techniques and includes a quiz session.

Sequences: Induction Method

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

Recursive Sequences: Convergence and Limits

Covers the study of recursive sequences, focusing on convergence and limits.