Lectures related to Fibonacci Numbers: Recursion and Induction

Recursively Defined Sets and Structures

Explores recursively defined sets, natural numbers, strings, functions, string concatenation, and well-formed formulae.

Induction and Recursion: Summary

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

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Cartesian Product and Induction

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

Recursively Defined Sets and Structures

Explores recursively defined sets, natural numbers, strings, functions, and propositional logic formulae.

Mathematical Induction: Basics and Applications

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

Recursively Defined Functions

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

Recursively Defined Functions

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

Course Overview: Teaser on Course Contents

Offers an overview of propositional and predicate logic, sets, functions, relations, algorithms, Swiss cities, sorting tables, Covid infections, poker hands, and prime numbers.

Discrete Mathematics: Logic, Structures, Algorithms

Covers the basics of discrete mathematics, focusing on logic, structures, and algorithms for computer systems.

Discrete Mathematics: Logic, Structures, Algorithms

Covers the basics of discrete mathematics, including logic, structures, and algorithms.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Introduction to Analysis: Understanding Real Numbers and Proofs

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Linear Algebra: Sets and Propositional Language

Covers sets, propositional language, reading, writing, containment, and cardinality.

Recursion and Induction: Proving Algorithms Correctly

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

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Proofs and Logic: Introduction

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

Recursion and Induction: Understanding Mathematical Proofs

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

Sets and Proofs

Introduces sets in discrete mathematics and explores proof techniques like direct and indirect proofs.