Lectures related to Data Abstraction: Rational Numbers

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

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.

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

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.

Introduction to Analysis

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

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.

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.

Division and Multiplication in Rational Numbers

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

Rational Numbers Operations

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

Rational Numbers Construction

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

Decimal Expansion: Division and Periodicity

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

Real Analysis: Basics and Sequences

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

Real Numbers: Structure and Properties

Covers the structure and properties of real numbers, including the introduction to the axiomatic system and the implications of Archimedean property.

Continuity of a Function

Explores the conditions for continuity of a function on real numbers.

Introduction to Analysis: Understanding Real Numbers and Proofs

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

Decimal Development

Delves into infinite decimal numbers, exploring convergence and divergence, and showcasing examples of rational and irrational numbers.

Norms and Valuations on Fields

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

Rational Numbers: Definitions and Operations

Covers the definition and operations involving rational numbers.