Lectures related to Selected Topics in Mathematics

Covers strings, countable sets, cardinality, and the concept of countability, exploring the countability of various sets and Cantor diagonalization.

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

Covers selected topics in mathematics for students interested in foundational concepts and challenges.

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

Covers selected mathematical topics including numbers, approximations, algebraic structures, limits, and series.

Explores cardinality, countable sets, and examples of countable and uncountable sets.

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

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Covers countability and bijections between sets, demonstrating the uncountability of real numbers.

Covers the concept of total order relation and properties of real numbers.

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

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

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

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

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

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

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

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

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.