Lectures related to Inverse Operations

Place-Valued Arithmetic: Addition and Subtraction

Explores place-valued arithmetic, covering addition, subtraction, and limitations of digital systems.

Covers the basic concepts of rational numbers and algebraic operations, including addition, subtraction, multiplication, and division.

Modular Arithmetic: Introducing Z/mZ

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Complex Numbers: Operations and Applications

Covers the properties and operations of complex numbers and their applications.

Logic Systems: Representations and Arithmetic

Explores logic system representations, place-value notation, addition, subtraction, and digital system limitations, culminating in a multifunction alarm watch project.

Modular Arithmetic: Operations and Polynomials

Covers modular arithmetic operations and polynomial calculations modulo N with various examples.

Geometry: Euclidean Elements & Vitruvius

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

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.

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Subtraction: Properties and Definitions

Covers the properties and definitions of subtraction using addition and multiplication as a basis.

Modular Arithmetic: Inverses and Equations

Explores modular arithmetic, emphasizing inverses and equations in Z/mZ, with practical examples and exercises.

Group Theory: Basics

Covers the basics of group theory, including definitions, examples, and isometries.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Mathematical Equation Rule

Covers the process of converting handwritten entries into text and sharing mathematical equation rules.

Trivial Group: Properties and Notation

Covers properties and notation of the trivial group and discusses the uniqueness of elements.

Division in Rational Numbers

Explores division in rational numbers and the extension of addition from integers.

Number Theory: Operations and Equivalence

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Rational Numbers: Definitions and Operations

Covers the definition and operations involving rational numbers.

General Integrals: Notation and Equations

Covers the general concept of integrals, focusing on notation and equations.

Mapping Functions and Surjections

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