Lectures related to Information Representation: conventions and basics

Explores number representation, algorithms, recursion, and probabilities in decimal and binary.

Binary Numbers: Representation and Complexity

Explores binary and decimal number representation complexity and conversion.

Number Systems: Fixed and Floating-Point Representations

Discusses fixed-point and floating-point representations in digital systems, covering key concepts like precision, accuracy, and the IEEE 754 standard.

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Nonlinear Equations: Representation of Real Numbers

Discusses the representation of real numbers in various bases and the implications of floating-point arithmetic.

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Number Systems: Fixed and Floating-Point Representations

Provides an overview of fixed-point and floating-point number representations in digital systems.

Kirillov Paradigm for Heisenberg Group

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Floating Point Numbers: Representation and Errors

Covers the representation of floating point numbers and the importance of uniform relative error.

Counting on Fingers

Compares various finger counting systems and introduces binary representation.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Symmetry and Group Theory: Exercise Set 4

Explores symmetry operations, isomorphic representations, and three-dimensional group representations.

Complex Gaussian Signals

Delves into complex Gaussian signals and their properties in communication systems.

Structure of Algebras

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Lie Algebras and Representations

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Subrepresentations of the regular representation

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.

Group Algebra: Maschke's Theorem

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Representation of Groups

Explores the theory of representation of groups and the concept of complete reducibility.