Lectures related to Strong Induction: Proof Method and Application

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

Mathematical Recursion: Induction and Recursion

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

Mathematical Recursion: Induction and Recursion

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

Covers fundamental concepts related to integers, including properties of well-ordered sets and the principle of induction.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Mathematical Induction: Basics and Applications

Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.

Complexity & Induction: Algorithms & Proofs

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

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.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Complexity & Induction: Algorithms & Proofs

Explores worst-case complexity, mathematical induction, and algorithms like binary search and insertion sort.

Newtonian Potential: Bounded Domains

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Extrema and Lagrange Multipliers

Explores Lagrange multipliers for finding extrema under constraints and various proof methods.

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Subtraction: Absolute Value and Opposite

Covers absolute value, subtraction in integers, and comparisons between integers.

Integers and Rings

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Linear Algebra: Reciprocity and Equivalence

Explores reciprocity, equivalence, and proof techniques in linear algebra, emphasizing logical reasoning and mathematical rigor.

Proof Techniques: Examples

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

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