Lectures related to Setting up arithmetic

Linear Equations and Matrices: Solution Methods, Elementary Operations

Explores solution methods and elementary operations for linear equations and matrices, demonstrating techniques to simplify systems and obtain solutions.

Definition of Complex Numbers Field

Introduces complex numbers and defines their field, emphasizing properties and operations.

Different Infinities: Cantor's Theorem

Explains Cantor's theorem comparing cardinalities of different number sets.

Cardinality of Sets: Countable and Uncountable

Explores countable and uncountable sets, demonstrating how to determine the cardinality of different sets through listing elements in a sequence.

Complex Numbers: Introduction and Properties

Introduces complex numbers to solve unsolvable equations, exploring their properties and relationship with real numbers.

Selected Topics in Mathematics

Covers selected topics in mathematics, including Taylor approximations and algebraic structures of Z and K[X].

Limits of Sequences

Explores the concept of limits of sequences and their convergence towards infinity or negative infinity.

Relations, Sequences, Summation: Cantor Diagonalization

Covers countable and uncountable sets, sequences, summation, and Cantor's Diagonalization proof.

Properties of Real Numbers: Bounds, Density, Absolute Value

Covers the properties of real numbers, including bounds, density, and absolute value.

Real Numbers: Sets and Operations

Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.

Real Numbers Sequences

Explores real number sequences, convergence, limits, boundedness, and monotonicity.

Vector Spaces: Definitions and Examples

Covers the definition and examples of vector spaces, including subspaces and linear transformations.

Prelude: Linking Mathematics and Course Content

Introduces the course content by linking familiar mathematics with upcoming topics.

Additional Properties of Real Numbers

Explores the countability of subsets of real numbers and demonstrates that the set of real numbers is uncountable.

Real Numbers: Sets and Operations

Covers the fundamental concepts related to real numbers, including sets, notations, and operations.

Divergent Sequences

Explains divergent sequences and limits at infinity with examples.

Complexity of Algorithms: Proofs of Time Complexity

Covers the analysis of worst time complexity for algorithms and time complexity with real numbers and integers.

Roots of Real Numbers

Explores the properties and applications of roots of real numbers through practical examples.

Determinant Calculation

Explains the step-by-step process of calculating determinants using elementary row operations.

Integers Representation: Sign vs. Two's Complement

Explores integer representation methods, comparing sign-and-magnitude with two's complement, and introduces fixed-point and floating-point representations.