Metadata
Mathematics Graduate Understand Medium
View More
Metadata

  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Understand

  • Difficulty estimate

    Medium

  • Tags

    Hilbert spaces, weak convergence, strong convergence, functional analysis, sequences, inner product

  • 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

    Assess graduate students' understanding of weak versus strong (norm) convergence in Hilbert spaces: include precise definitions, the inner-product characterization of weak convergence, examples distinguishing weak but not strong convergence, basic properties (uniqueness of limits, boundedness, subsequential weak compactness in Hilbert spaces, lower semicontinuity of the norm), and short proofs or counterexamples demonstrating relationships between weak and strong convergence and behavior of norms and orthonormal bases.
Use
Remix
Export
Review & Revise
Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.