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Mathmos6
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Hello everyone - I'm a third year student at Cambridge university, and I've recently started taking a course on Riemann surfaces along with a number of other pure courses this year.
The problem is, the lecturer of the course is of a rather sub-par standard - whilst I don't doubt he's probably exceptional in his field, he often struggles for clarity, and the work we have to do ourselves is often barely, if it all, linked to the material on the lectures, or indeed quite often tenuously so at best.
The following - http://www.dpmms.cam.ac.uk/study/II/Riemann/2010-2011/RS10.2.pdf - is an example of one of the problem sheets I'm currently working on, and http://www.dpmms.cam.ac.uk/study/II/Riemann/2009-2010/RS09.3.pdf is last year's version of the work I will have to do in a few weeks' time. The small majority of the questions I -can- do are Algebraic Topology which I've taught myself - in general I'm really struggling to find ways to utilise the lecture notes effectively to understand a lot of this, and so I'm looking for a book which might help me get to grips with some of the concepts I might need to answer questions like those in the above PDFs. From your experience, is there anything at all you might be able to recommend which you yourself used, a book which looks like it might be relevant for some or all of the above problems?
I'm well aware there may be no such book, but I thought I would ask anyway in case you had something which you found extremely useful in getting the hang of a lot of the relevant concepts, and which might enlighten me on how one might approach a few questions like those above. We do have a recommended book list, but it is evident the lecturer is unaware of the chasms between his lectures and his worksheets, so I don't have a lot of faith in them, but I'd be very glad to look into anything relevant you PF users have read in the past! As I said, this is with an eye primarily to solving problems like the above - in terms of learning about what a Riemann surface is etc., I'm happy with the lecture notes, it's applying the results to the above problems where I come undone. Any thoughts? Thanks very much for the help, any suggestions welcome! (And indeed multiple such suggestions, assuming no one book will cover all of the above) - Mathmos6
The problem is, the lecturer of the course is of a rather sub-par standard - whilst I don't doubt he's probably exceptional in his field, he often struggles for clarity, and the work we have to do ourselves is often barely, if it all, linked to the material on the lectures, or indeed quite often tenuously so at best.
The following - http://www.dpmms.cam.ac.uk/study/II/Riemann/2010-2011/RS10.2.pdf - is an example of one of the problem sheets I'm currently working on, and http://www.dpmms.cam.ac.uk/study/II/Riemann/2009-2010/RS09.3.pdf is last year's version of the work I will have to do in a few weeks' time. The small majority of the questions I -can- do are Algebraic Topology which I've taught myself - in general I'm really struggling to find ways to utilise the lecture notes effectively to understand a lot of this, and so I'm looking for a book which might help me get to grips with some of the concepts I might need to answer questions like those in the above PDFs. From your experience, is there anything at all you might be able to recommend which you yourself used, a book which looks like it might be relevant for some or all of the above problems?
I'm well aware there may be no such book, but I thought I would ask anyway in case you had something which you found extremely useful in getting the hang of a lot of the relevant concepts, and which might enlighten me on how one might approach a few questions like those above. We do have a recommended book list, but it is evident the lecturer is unaware of the chasms between his lectures and his worksheets, so I don't have a lot of faith in them, but I'd be very glad to look into anything relevant you PF users have read in the past! As I said, this is with an eye primarily to solving problems like the above - in terms of learning about what a Riemann surface is etc., I'm happy with the lecture notes, it's applying the results to the above problems where I come undone. Any thoughts? Thanks very much for the help, any suggestions welcome! (And indeed multiple such suggestions, assuming no one book will cover all of the above) - Mathmos6
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