Lectures related to Strong Induction: The Power of Mathematical Proof

Cartesian Product and Induction

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

Proofs: Logic, Mathematics & Algorithms

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

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.

Strong Induction: Proof Method and Application

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

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.

Holomorphic Functions: Taylor Series Expansion

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

Inductive Propositions: Reasoning and Evaluation Techniques

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

Proofs and Logic: Introduction

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Proofs: Contraposition vs. Contradiction

Covers the concepts of contraposition and contradiction in proofs.

Complexity & Induction: Algorithms & Proofs

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

Subtraction: Absolute Value and Opposite

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

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Elementary Algebra: Numeric Sets

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

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.

The Languages of Isabelle: Isar, ML, and Scala

Explores the languages of Isabelle, focusing on Isar, ML, and Scala, covering proof schemes, Natural Deduction rules, inductive definitions, and the LCF approach.

Extrema and Lagrange Multipliers

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

Integers: Elementary Concepts

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