Recurrence Demonstrations: Principle and Examples

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Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Proofs by Induction: Principles and Examples

Explains the induction principle and proofs by induction with examples like 1 + 3 + 5 + ... + (2n-1) = n².

Linear Algebra: Propositions and Sets

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.

Geometric Series: Convergence and Applications

Explores the convergence of geometric series and their applications in real-world problems.

Strong Induction: The Power of Mathematical Proof

Explores strong induction as a powerful proof method with advantages over mathematical induction, demonstrated through a theorem about expressing integers as sums of powers of two.

Recursion and Induction: Understanding Mathematical Proofs

Explores recursion and induction for mathematical proofs through recursive algorithms and functions.

Mathematical Recursion: Induction and Recursion

Explains mathematical induction for proving propositions true for all positive integers.

Mathematical Recursion: Induction and Recursion

Covers the principle of mathematical induction for proving propositions true for all positive integers.

Rigorous Proof of Differential Equations

Covers the rigorous proof of differential equations, emphasizing accuracy and precision.

Limits of Sequences: Induction, Bernoulli's Inequality, and Algebra

Explores induction, Bernoulli's inequality, and algebraic limits in sequences with examples and computations.