Lectures related to Gaussian rational

Explores Dedekind cuts in rational numbers, essential for constructing real numbers.

Covers data abstraction in rational numbers, including client's view, self-reference, preconditions, assertions, constructors, and end markers.

Algebraic Operations

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

Fermat's Equation: Integral Solutions and Gaussian Integers

Discusses Fermat's equation and Gaussian integers' properties.

Simplex: Implementation and Methods

Covers the implementation of the Simplex algorithm and its methods.

Mathematical Notations: Recap and Rational Numbers

Covers a recap on mathematical notations and introduces rational numbers and basic algebraic operations.

Complex Numbers: Gauss Numbers

Explores Gaussian integers, prime factorization, and number theory concepts related to prime numbers.

Square Roots and Irrationality

Explores even squares, irrationality of √2, gaps in rational numbers, and minorants in Q.

Rational Numbers: Definitions and Operations

Covers the definition and operations involving rational numbers.

Rational Numbers Operations

Explains the properties of addition and multiplication in Q with illustrative examples.

Division and Multiplication in Rational Numbers

Explores division and multiplication in rational numbers, emphasizing the concept of multiplying by the inverse.

Rational Numbers Construction

Explores the construction of rational numbers, irreducible fractions, equivalence, and simplification rules.

Norms and Valuations on Fields

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Q is a Field

Covers the properties of rational numbers and introduces the concept of an ordered field in Q.

Decimal Expansion: Division and Periodicity

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Complex Numbers: Introduction and Operations

Introduces complex numbers and their forms, including Cartesian, polar, and exponential forms, and explains how to find the argument of a complex number.

Organization, Numbers: Real Numbers and Equations

Introduces real numbers, including equations like x²=2 with no rational solutions.

Construction of Real Numbers

Discusses the construction and uniqueness of real numbers from rational numbers.

Complex Numbers: Algebraic Structures and Applications

Covers algebraic structures, real numbers, fields, and the applications of complex numbers in science and engineering.

More Results on Inf/Sup, Density of Q in R

Covers inf/sup, integral part of real numbers, and density of rational numbers.