By William M. Boothby
Nice introductory differential geometry textual content! I used this booklet to aid me go my qualifying examination. Yay Boothby!
Read Online or Download An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) PDF
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Additional resources for An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics)
For example, in [this question] proof by contradiction was desirable – but not explicitly requested – as was an argument within the context of matrix operations. Few student responses though matched the question setter's intentions. Instead of this neatly contextualised Method-Context (1: Contradiction - Matrix operations), the majority of students made a 'reductive' choice of another Method-Context (2: 'straight' deduction - Arithmetic of Determinants). (p59) CHAPTER 3: MATHEMATICAL REASONING 43 Student W Student WD (To start with M offers a critique of the question and its proposed answer as follows: 44 CHAPTER 3: MATHEMATICAL REASONING M: I like the lecturer’s part (iii): none of this sentences nonsense...
I have failed to locate the origin – so, with apologies, could the owner, if any, please stand up?! – but it seems to encapsulate my thinking and soul-searching at the time with regard to the direction this work was going to take. So I feel it is worth mentioning here. 16 Except Datasets 3 and 4 for which there were five Examples. CHAPTER 2: METHODOLOGY • • 25 a mini literature review and bibliography on the theme of the Dataset concluding page with thanks to the participants (and, in the case of UEA interviews, arrangements for the next interview) In the five ‘mathematical’ Datasets there were twenty two Examples and in the one ‘meta-mathematical’ Dataset there were three.
RME: Most students too did just that in fact. M: And most probably paid little attention to how this part connects with whatever you have proved in parts (i) and (ii), right? It would be interesting to ask this question with (iii) and (i) transposed. That would put the student in the A-is-notthe-zero-matrix frame of mind. In a sense there is a problem with the language of the question: the first line needs a lot of unpacking and it may even be interpreted as if the brackets referred to A. It could have been interpreted as A is in fact the nxn zero matrix.
An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) by William M. Boothby