Page 180, column 2, line 12, should read “pushes forward to a k-dimensional oriented manifold in Y” (not X).

]]>I’m hoping to start my own blog soon but I’m a little lost on everything. Would you suggest starting with a free platform like WordPress or go for a paid option? There are so many choices out there that I’m totally overwhelmed .. Any tips? Cheers! ]]>

I fall at the far (wrong) end of your target audience bell, but I can proofread. Your paragraph 3 above says that on page 24 of the PCM you claimed that

(T^i.R^j) (T^i’, R^j’) = (T^(i – i’), R^(j – j’))

(T^i.R^j) (T^i’, R^j’) = (T^(i – i’), R^(j + j’))

is the formula my copy shows. Perhaps this changes nothing.

]]>By itself, Section VI is an extremely poor way of correlating the mathematician’s lives: it is much too bulky to be useful.. Fortunately, the Table of Contents neatly resolves this deficiency. Proposal: Alphabetize Section VI. Relocate the chronological listing from the TOC (as a single page) at the beginning of Section VI, retaining the dates given in round brackets (I have always attributed the “mathematician’s” failure to use the established terms for parentheses, brackets, and braces as disinterest in their English classes, but there may be other reasons. The term “curly brackets” makes me wonder, however). Omit the subsection numbers and correct the page numbers. The TOC entry for Section VI would become the page number of the chronological list. All of the references to Section VI that appear throughout the entire book can be reduced to their existing names in small caps font: no section numbers. Names in normal font do not appear in Section VI.

I feel that I must comment on the notion that using the current organization is a “slight inconvenience” in return for learning “something small.” Without a formal proof, I suggest that the word “something” should be replaced with the word “infinitely,” whereas “pain in the ass” might be used to describe convenience (No offense intended). But, I am not a mathematician. Perhaps a poll would provide insight from the community at large.

George Powers, Arroyo Grande, CA

Long retired Electrical Engineer

See PCM errata II for a distillation of the errata pointed out here.

]]>Also, the unpacked definition (10) allows for m=1, which is not a prime.

I love this wonderful book.

Just to add my voice to Ivan’s earlier request to distill the listings on this page into an errata page, Roger Penrose established a convention for his book which seems to work.

I’ve been away from this for a while. My question is whether this is sufficient to guarantee actual “bundlesness”, i.e., local triviality so that for each point x in X there is a neighborhood U and a homeomorphism h:U x F –> p^-1(x) so p(h(x,y)) = x for all x in U and y in the vector space F. In other words, locally for X, p is just the projection.

]]>It’s not 100% clear but I’m pretty sure it should read “Two obvious conditions” at the bottom of the page, rather than “Three obvious..” ]]>

Perhaps the author meant to say “for every bounded infinite set” or “in every closed and bounded infinite set”. The limit point of course doesn’t have to be IN the set, as written.

]]>page 194 – the density factor “rho” has been left out (perhaps intentionally) of the NS equations, which kind of makes sense because the fluid is deemed incompressible, but makes the statement about the time derivative of momentum a bit confusing.

page 202ff – the discussion of FFT makes no mention of Cooley, Tukey. This seem not quite proper.

]]>p.314: Near the end of the Zermelo-Fraenkel entry, “when ones does includes” should be “when one does include.”

]]>p.756: This page says that Gauss found six proofs of quadratic reciprocity (his first, plus “five more”), whereas pages 104 and 719 reckon the total as eight. (I realise this might reflect some historical dispute as to the figure, with different authors taking different positions; I’ve seen both seven and eight quoted before; Wikipedia claims “He published six proofs, and two more were found in his posthumous papers.”. None of the statements in this book appear to be restricting consideration to proofs published in Gauss’s lifetime.)

p.813: The description of real closed fields as “fields with the property that -1 cannot be expressed as the sum of two squares” is neither an accurate characterisation of real closed fields nor helpful to give a feel for what such fields are. Perhaps a reference to IV.23 section 5, along with the example of the real numbers, would be better than trying to explain what real closed fields are in more detail here.

p.889: The description of CBC and OFB modes is oversimplified. Simplification is of course expected in this sort of exposition, but the CBC description gives the impression that two successive cleartext blocks are added before encryption (so a 128-bit repeat in cleartext would result in a 64-bit repeat in ciphertext, similar to the ECB problem described in the previous paragraph) when actually each cleartext block is added to the previous ciphertext block before encryption. In turn this reads like the description given of OFB mode; OFB does not feed the input cleartext through the block cipher at all, but starts with an initialization vector and repeatedly enciphers that to generate a keystream, that is then added mod 2 to the cleartext to generate a ciphertext.

p.909: “Becky has five siblings” should read “Desta has five siblings”.

p.919: “” (in the second paragraph of the first column) should read ““.

p.920: Both times the second column gives a probability density function for a normal distribution, there is a stray factor of 2 in the denominator inside exp (either this factor or the should be removed), and the “” in the square root should be ““. In the second formula (for the transformed distribution), “” should be ““.

p.997: In equation (7), “” should read ““. (This is what is given in equation (1.3) of the reference Andrews (1998), and the following equation in the present book defines only for even subscripts.)

]]>*Given any closed path of length [in the smooth compact manifold ] there is a disk of minimal area that is bounded by that path.*

This is false as stated – you need to assume that the path is null-homotopic.

Also, I have a couple of additional minor criticisms of the hypotheses on . First, it seems appropriate to mention that should be equipped with a Riemannian metric for the notion of the area of a disc to make sense.

Secondly, the assumption of compactness for is unnecessary, and also confusing as the examples of the Euclidean and hyperbolic planes are discussed in the following paragraph. Presumably one needs to assume some milder condition like completeness to guarantee the existence of a minimal-area disc.

Therefore, it seems to me that rather than describing as a smooth, compact manifold, one should describe it as a complete Riemannian manifold.

]]>Unfortunately I need to exchange my copy since it has 2 production flaws:

1) pages 843 to 890 appear twice

2) pages 891 to 938 are missing

Hopefully PUP can use this information to help minimize such instances.

Marc

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