Metadata
Mathematics Graduate Understand Easy
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Metadata

  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Understand

  • Difficulty estimate

    Easy

  • Tags

    Hilbert spaces, weak convergence, strong convergence, inner product, orthonormal sequences

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Test understanding of definitions of strong (norm) and weak convergence in Hilbert spaces, basic relationships and properties (uniqueness of limits, norm lower semicontinuity), characterization via inner products, and simple examples/counterexamples such as orthonormal sequences, bounded sequences without strong limits, and convergence in finite-dimensional subspaces. Scope: definitions, elementary proofs, and example analysis.
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Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.