I'm a retired high school / community college math teacher in SoCal and kind of tripped onto your youtube videos. They are very good. I like how you take your time explaining the concepts. Also, you have a great speaking voice. Little unusual to be in a nice suite. Reminds me of films of Los Angeles in the 1940s and 50s. Everyone dressed up. Have you seen Gilbert Strang's "Introduction to Linear Algebra?" He gives an excellent excellent explanation to linear dependence and independence.
Thank you! Yes, I have seen many of Strang's Linear Algebra videos, and enjoy them! I often share them with students in Linear Algebra if they need any supplementary material, especially from someone who was so experienced as Professor Strang. Thank you for your compliment as well! I sort of grew up a lot around people who were of the WWII, aka "greatest generation", so I think that might have had some influence on many of my values. I learned a lot from that generation!
I like your lectures very much. Thank you for making these videos. One thing puzzles me though. You have quoted the Bible -- the truth shall set you free -- and have suggested that mathematics is an expression of truth. But is mathematics not tautology? Can tautology be the kind of truth the Bible is talking about?
Thank you for your comment! Mathematics may indeed appear tautological on the surface-built as it is on axioms and logical deductions-but its beauty lies in how those 'tautologies' can illuminate truths about the world in ways far beyond their humble beginnings. As for the Bible's 'the truth shall set you free,' consider this: if mathematics, through its tautologies, gives us the tools to launch rockets, cure diseases, or even uncover the fabric of the cosmos, then it seems that freedom and truth are hand in hand here. Maybe the Bible was hinting at a broader truth, one that encompasses the profound clarity mathematics brings to our understanding of reality. Or perhaps the Bible and math are like an unlikely duet-each singing their own version of truth. One shows us the stars, the other tells us why to marvel at them.
I'm a retired high school / community college math teacher in SoCal and kind of tripped onto your youtube videos.
They are very good. I like how you take your time explaining the concepts. Also, you have a great speaking voice. Little unusual to be in a nice suite. Reminds me of films of Los Angeles in the 1940s and 50s. Everyone dressed up.
Have you seen Gilbert Strang's "Introduction to Linear Algebra?" He gives an excellent excellent explanation to linear dependence and independence.
Thank you! Yes, I have seen many of Strang's Linear Algebra videos, and enjoy them! I often share them with students in Linear Algebra if they need any supplementary material, especially from someone who was so experienced as Professor Strang.
Thank you for your compliment as well! I sort of grew up a lot around people who were of the WWII, aka "greatest generation", so I think that might have had some influence on many of my values. I learned a lot from that generation!
Please more videos! They are actually really good😊
Thank you! I plan to do so!
I like your lectures very much. Thank you for making these videos. One thing puzzles me though. You have quoted the Bible -- the truth shall set you free -- and have suggested that mathematics is an expression of truth. But is mathematics not tautology? Can tautology be the kind of truth the Bible is talking about?
Thank you for your comment! Mathematics may indeed appear tautological on the surface-built as it is on axioms and logical deductions-but its beauty lies in how those 'tautologies' can illuminate truths about the world in ways far beyond their humble beginnings.
As for the Bible's 'the truth shall set you free,' consider this: if mathematics, through its tautologies, gives us the tools to launch rockets, cure diseases, or even uncover the fabric of the cosmos, then it seems that freedom and truth are hand in hand here. Maybe the Bible was hinting at a broader truth, one that encompasses the profound clarity mathematics brings to our understanding of reality. Or perhaps the Bible and math are like an unlikely duet-each singing their own version of truth. One shows us the stars, the other tells us why to marvel at them.
@citytutoring Thank you for your message. I really appreciate your patience and mindfulness.