Lectures related to Induction and Recursion: Quiz

Complexity & Induction: Algorithms & Proofs

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

Complexity & Induction: Algorithms & Proofs

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

Introduces recursively defined functions and demonstrates how to compute values and prove properties using mathematical induction.

Fibonacci Numbers: Recursion and Induction

Explores Fibonacci numbers, rabbit population growth, and recursively defined functions.

Recursion and Induction: Understanding Mathematical Proofs

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

Induction and Recursion: Summary

Covers mathematical induction, recursively defined functions, and iterative algorithms for problem-solving.

Recursively Defined Functions

Introduces recursively defined functions, showcasing examples like the Fibonacci numbers.

Cartesian Product and Induction

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

Induction and Recursion: Mathematical and Strong Induction - An Example

Covers the concepts of mathematical and strong induction through an example.

Introduction to Coq: Arithmetic Expressions and Evaluators

Covers the basics of Coq, focusing on arithmetic expressions, evaluation, and proof techniques.

Structural Induction

Introduces structural induction, a method to prove properties of elements in recursively defined sets.

Structural Induction

Introduces structural induction, a method to prove properties of elements in recursively defined sets.

Logical Formulas and Types: Understanding the Kerry Howard Isomorphism

Explores the Kerry Howard Isomorphism, translating logical propositions into types and terms, with a focus on proof by induction and exam preparation.

Recursion and Induction: Proving Algorithms Correctly

Explains recursion, induction, and proving algorithm correctness through mathematical induction.

Proofs by Induction: Principles and Examples

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

Big-step semantics: Defining arithmetic expressions and commands

Covers the definition of a simple programming language and its big-step semantics, including arithmetic expressions and imperative commands.

Least Mean Squares with Features

Covers the concept of Least Mean Squares (LMs) with features and iterative updates.

Dynamic Programming: Solving Sequential Problems Efficiently

Explores dynamic programming for efficient problem-solving, illustrated with binomial coefficients and Pascal's triangle.

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.

Recurrence: Induction

Covers the principle of induction for natural numbers and the importance of caution in its application.