- Free online algebra computer system I asked Bard a simple question and got a simple answer. I now know of at least one website that will do my algebra for me at no cost.
- Heisenberg's quantum mechanics The textbooks tell us that Quantum Mechanics was co-invented by two people, and then proceed to explain only the origin of the wave equation. The matrix theory seems to come from nowhere, and Heisenberg's paper seems impossible to follow (even for someone who knows the matrix theory.) The chat was curious because Bard was very graceful when it was corrected.
- Lumped mass vibrational modes Sometimes talking about a mathematical problem helps me see the solution myself. The chat ended with me making a snarky remark that drew a rebuke from Bard.
- Matrix versus tensor I had feeling that the two words are essentially synonyms, but with subtle differences in what properties are more essential to the conversation. Bard confirmed that opinion.
- Teaching the discrete Fourier transform to beginners Bard came up with a lot of useful ideas. I knew about most of them before the conversation, but Bard seemed to understand the question and gave me new insights that I plan to use in Eigenvalues and eigenvectors.|}
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