End of Jan 2011 Update.

January 24, 2011

It’s almost the end of the month, and I haven’t been posting as much as I’d like.  I’ve just started the spring semester, and I’m getting used to juggling my schedule. 

In addition, as it stands, my homology primer has been bothering me; it’s not rigorous enough to be lecture notes and it’s not simplistic enough for it do be of any more use than, say, Hatcher.  This is a significant problem: I set out to compute the cellular homology for certain structures, but without the notion of singular homology (which I don’t even mention!) it’s difficult to justify certain notions and to define new ways of computing and it feels sort of cheap to just say, "it works because it does — trust me." 

I’m not sure when I’ll have a chance to revamp the homology primer, but what I may do is just handwrite a bunch of examples (it’s much faster) and upload them.  The upshot to this is that it’s really quick for me.  The downshot is that any typos will be much harder to fix.  C’est la vie. 

 

Either way, I will be posting again soon. 

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7 Responses to “End of Jan 2011 Update.”

  1. Daniel said

    Wow, I just found your Homology primer and it is amazing as an introduction. It might not be rigorous but it definately showed me exactly what is going on intuitively when we calculate these groups (something which seems to be lost in many other books on the subject). I wish you could write about all of the topics I have never had motivated.

    I have literally just started a course on this stuff and for the introduction the lecturer ignored all of the intuitions, started by defining chain complexes and the homology groups then expected us to understand it straight off.

    As with 99% of people in that situation, I tried to find somewhere that would show me the significance of this stuff and i’m glad I found this…my thirst has certainly been satisfied!

    I can’t wait to hear more. Carry on writing about it the way you do, it really helps. Don’t compare yourself to others, write things up how you think about them, it is obviously working so far.

    • Leonie said

      I am in a similar situation to Daniel. I have just started algebraic homology and have been struggling with the terminology and stuff and your page has explained in words I can understand. I would like the next page that you were talking about doing. The one that you would call “Homology Primer 4”. I think I can now move onto Hatcher, etc, (and my lecturer) and have some idea of what they are talking about.
      Never underestimate your comtribution to us strugglers!
      Thanks

    • James said

      Thank you, both of you! It’s nice to know that my primer is being used, at least. I’ve got a rough draft for my next updates, so expect them soon!

      • Daniel said

        The way I see it, everything in maths has a meaning or a reason to be.

        Unfortunately a great many lecturers seem to have lost this philosophy and see fit to give out scraps of information along with formal definitions, leading to a dry exposition of the maths.

        I am a number theorist/algebraist at heart, I know and understand nearly everything I come across in these areas. As soon as I come across any analysis/topology, it makes no sense to me because I have only ever had it taught badly, in an entirely formal fashion.

        Sites like yours help me to grasp the concepts and intuition that get missed in lectures.

        Many thanks.

  2. Nathan said

    You are my hero right now as I am reading your homology primer. Thank you

  3. Michael said

    My entire algebraic topology class read this thread in order to get some insight into homology groups, and we all found it very helpful. Admittedly there are only 8 of us, but seriously, thank you.

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