Lectures related to Mathematical Recursion: Induction and Recursion

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.

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

Strong Induction: Proof Method and Application

Explores strong induction as a proof method and demonstrates its application in proving a theorem about positive integers.

Integers: Elementary Concepts

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

Complexity & Induction: Algorithms & Proofs

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

Mathematical Induction: Basics and Applications

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

Proofs: Logic, Mathematics & Algorithms

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

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.

Subtraction: Absolute Value and Opposite

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

Complexity & Induction: Algorithms & Proofs

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

Holomorphic Functions: Taylor Series Expansion

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

Cartesian Product in Linear Algebra

Explores the Cartesian product in linear algebra and the method of induction for proving propositions.

Extrema and Lagrange Multipliers

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

Proofs and Sets: Applications

Covers the basics of proofs, defining sets, and applications between sets.

Proofs: Rules and Applications

Explores rules of inference, quantified statements, and proof methods in logic and mathematics.

Basic Properties

Covers basic properties of natural numbers, including order relations and inverses.

Integers and Rings

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

Algebra: Integer Numbers and Principles

Introduces integer numbers, well-ordering, induction principles, GCD, LCM, and Bezout's theorem.

Proofs: Contraposition vs. Contradiction

Covers the concepts of contraposition and contradiction in proofs.