Lectures related to Projectively extended real line

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

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

Covers the basics of real analysis, including limits, sequences, and continuous functions.

Explores Sobolev spaces, unitary groups, Laplacian properties, and translation groups in L^2.

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

Explores complex numbers, operations, absolute value, and polar form, along with the analysis and graphic representation of complex numbers.

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

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

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.

Covers the concept of universal covering and its properties, including examples and monodromy action.

Discusses the binary representation of real numbers and the precision errors involved.

Covers functions of real numbers, graphing, and affine functions.

Explores inequalities on real numbers, including real intervals and comparison properties.

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.

Delves into cell attachment, exploring its implications for different cell dimensions.

Discusses Cauchy sequences, sub-sequences, and numerical series with parameters.

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

Covers the definition and basic properties of the absolute value function for real numbers.

Covers the definition of continuity at a point using epsilon and delta.

Covers absolute value, density of rationals, and real line topology.