Lectures related to Mathematical Induction: Basics and Applications

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

Sets and Operations: Introduction to Mathematics

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

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

Introduction to Analysis: Understanding Real Numbers and Proofs

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

Complexity & Induction: Algorithms & Proofs

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

Linear Algebra: Reciprocity and Equivalence

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

Function Composition and Integers

Covers function composition and integers, including properties and examples.

Differential Forms Integration

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

Algebra: Integer Numbers and Principles

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

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Proofs and Logic: Introduction

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

Mapping Functions and Surjections

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

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.

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

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Fibonacci Numbers: Recursion and Induction

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

Linear Algebra: Sets and Propositional Language

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

Cartesian Product in Linear Algebra

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

Proofs: Logic, Mathematics & Algorithms

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

Sets and Proofs

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