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Space Identification: SO(3)
Explores the identification of the space SO(3) and the topology of SS-space of R₃(R).
Advanced Physics I: Trajectory and Velocity
Explores trajectory, velocity, and acceleration in advanced physics, emphasizing rectilinear motion and the importance of instantaneous velocity.
Homotopy Categories: Model Structures
Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.
Equivalence Relations: Relations, Sequences and Summations
Explores equivalence relations, functions, subsets, and De Morgan's laws.
Mathematical Analysis: Functions and Composition
Covers the analysis of functions, composition, and mathematical induction.
Frames of Reference: Physics 1
Covers frames of reference in physics, emphasizing the importance of choosing a reference frame and the laws of physics in different frames.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Dynamics on Homogeneous Spaces and Interactions with Number Theory
Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.
Analytic Continuation of Zeta Function
Explores the analytic continuation of the zeta function and its relation to holomorphic functions and natural numbers.
Equivalence Relations and Partitions
Discusses equivalence relations, partitions, reflexivity, symmetry, transitivity, and set cardinality.