Lectures related to Ordered field

Dedekind Cuts: Rational Numbers

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

Complex Numbers and 2x2 Matrices

Covers complex numbers, quadratic equations, solutions in C, and 2x2 matrices.

Q is a Field

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

Properties of Real Numbers

Explains the properties of subsets of real numbers, including Supremum, Infimum, intervals, open sets, and closed sets.

Rational Numbers Operations

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

Real Analysis: Sequences and Limits

Covers real sequences, induction, limits, and convergence in mathematical analysis.

Finite Fields and Vector Spaces

Explores finite fields, vector spaces, commutative groups, and field properties, highlighting their significance in coding theory and algebraic computations.

Completion of a Field: Algebraic Closure

Covers the completion of a field, focusing on algebraic closure and function convergence.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, cyclic unit groups, and field construction.

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