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Advanced Calculus: An Introduction to Linear Analysis

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  • Posted April 6, 2013

    This is another example of someone who either refuses to or simp

    This is another example of someone who either refuses to or simply cannot write clearly.

    Just to focus on 1.7, the Heine-Borel Covering Theorem which is representative. His opening is to say the least baffling to someone without at least some introduction to topology and this is made worse by the deliberate absence of meaningful examples of open and closed sets. His exposition on Theorem 1.7.1, that the union of open sets is an open set is just as baffling, as he refers the reader to a later exercise and then starts the proof in medias res. This is simply bad teaching, bad presentation. In Definition 1.7.2, he defines an open cover in as incomprehensibly a way as possible and then makes matters worse by providing no meaningful example. When he finally gets to the-Borel Covering Theorem, as he does not clearly explain what it stands for, his proof comes out as a pile of gibberish. There is simply no excuse for this.

    Many of the problems do not clearly follow from the exposition and there are far too many of the "give an example" type. Richardson is the professor; he should be providing the examples; he should be facilitating comprehension, not deliberately obviating it.

    Why Richardson and others take the byzantine approach to composing mathematics texts, as opposed to the down-to-earth approach, is beyond me. Are they fearful that too many people will grasp the subject too quickly? Are they afraid that if they write in an immediately comprehensible manner that students will simply read their books, not attend class and put them out of a job?

    I have no idea why Richardson even wrote this book (except for the obvious and vulgar reason)for it is no better--and in some ways, it is considerably worse--than the texts out there. This book is beyond disappointing and I resent having paid nearly $100.00 for it and gotten next to nothing out of it. Richardson should be ashamed for even writing it. This is another example of someone who either refuses to or simply cannot write clearly.

    Just to focus on 1.7, the Heine-Borel Covering Theorem which is representative. His opening is to say the least baffling to someone without at least some introduction to topology and this is made worse by the deliberate absence of meaningful examples of open and closed sets. His exposition on Theorem 1.7.1, that the union of open sets is an open set is just as baffling, as he refers the reader to a later exercise and then starts the proof in medias res. This is simply bad teaching, bad presentation. In Definition 1.7.2, he defines an open cover in as incomprehensibly a way as possible and then makes matters worse by providing no meaningful example. When he finally gets to the-Borel Covering Theorem, as he does not clearly explain what it stands for, his proof comes out as a pile of gibberish. There is simply no excuse for this.

    Many of the problems do not clearly follow from the exposition and there are far too many of the "give an example" type. Richardson is the professor; he should be providing the examples; he should be facilitating comprehension, not deliberately obviating it.

    Why Richardson and others take the byzantine approach to composing mathematics texts, as opposed to the down-to-earth approach, is beyond me. Are they fearful that too many people will grasp the subject too quickly? Are they afraid that if they write in an immediately comprehensible manner that students will simply read their books, not attend class and put them out of a job?

    I have no idea why Richardson even wrote this book (except for the obvious and vulgar reason)for it is no better--and in some ways, it is considerably worse--than the texts out there. This book is beyond disappointing and I resent having paid nearly $100.00 for it and gotten next to nothing out of it. Richardson should be ashamed for even writing it.

    Was this review helpful? Yes  No   Report this review
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