Comments concerning the disposition of the Items of A.I. memo 239 in the
HAKMEM to be published in book form. Suggestions are welcome.
ES - We need people willing to assume responsibility for topics: Doing literature
searches, writing programs, and trying to solve the problems posed in the
old HAKMEM, and typing in the text of the new HAKMEM.
ES - If possible, solutions should be given to problems. If too lengthy, then
cite references. Unsolved problems should be included only if they are
particularly elegant.
ES - Back issues of American Mathematical Monthly should be perused for ideas.
1. ES - Flush it.
2. ES - Flush it.
3. ES - Interesting. Needs proof, more elaboration, and extention to higher degree.
Include it under discussion of flows.
4. ES - Incorporate into Item 10.
5. ES - Incorporate into Item 10.
6. ES - Flush it.
7. ES - Flush it.
8. ES - Incorporate into Item 10.
9. ES - Incorporate into Item 10.
10. ES - We need a discussion of the theory of roots of polynomials. Topics to
be included are the calculation of the Galois group, obtaining the
roots from the structure of the Galois group, what to do if the group
is unsolvable, and expressing roots in the form F(h(G(x))) where F and
G are inverses of each other and h is some fairly simple function. As
discussed in Item 10, for the cubic F is a trig function, for the
quintic F is an elliptic modular function. In general, is F an
automorphic function?
11. ES - Proof given in Coxeter, "Introduction to Geometry". This is interesting
and should be kept.
12. ES - Incorporate into Item 13.
13. ES - Should mention application to computing (or even defining) functions
of matrices. As it is now, it is really about algebraic field extensions
and relates to Item 10.
14. ES - Incorporate into Item 13.
15. ES - As it appears in HAKMAM, it is merely a handbook type formula and should
be flushed. Chebychev polynomials play an important role in "flows",
Items 126, et. seq.
16. ES - Same comment as for Item 15.
17. ES - Flush it or provide some references (surely there must be some).
Questions: Why no OR gates? Why are NOT gates free? Why not allow
any available IC, and minimize package count or total propagation delay?
18. ES - Contains two topics, both interesting and deserve greater elaboration.
19. ES - A really great problem, especially its extension to the N2 case.
20. ES - Flush it.
21. ES - Flush it or solve it or provide references.
22. ES - Flush it or solve it or provide references.
23. ES - Flush it.
24. ES - Flush it.
25. ES - I don't think PDP-10 code should be included in the book. However,
a discussion of random number generators is appropriate.
26. ES - Not worth more than brief mention.
27. ES - Not worth more than brief mention.
28. ES - Perhaps we could include Schroeppel's factoring algotithm.
29. ES - This ought to be backed up by more data or theorems.
30. ES - I would recommend flushing it, but this sort of thing could appeal to
M. G., and a good review from him will sell more books.
31. ES - How was search done? Reference to proof needed.
32. ES - Needs more detail. Belongs in Flow section.
33. ES - Even without a proof, this has good M. G. appeal. Maybe give a list
of the maximal primes in various radices.
34. ES - Flush it.
35. ES - Look up Dirichlet's theorem on primes in arithmetical progression.
36. ES - Solve it or flush it.
37. ES - Include proof.
38.
39.
40. ES - Flush it.
41. ES - Flush it.
42.
43.
44. ES - Flush it.
45.
46. ES - Flush it.
47.
48. ES - I like it. Let's see what the reference has to say.
49.
50. ES - This is good stuff. Andrews: "Magic Squares and Cubes", Dover
and various papers by John Hendricks mostly in J. Recr. Math.
should provide for interesting Items on magic objects.
51. ES - Incorporate into Item 50.
52.
53. ES - Incorporate into Item 52.
54. ES - Incorporate into Item 52.
55.
56.
57. ES - Schroeppel's answer should be generalizable.
58. ES - This and other such identities are nice and take up little room.
59. ES - What is the significance of this Item? Is it largest such example
known?
60. ES - This Item introduces a generalization of "perfect number". It would
nicer if we had more to say about it. Also, S = k N.
61. ES - This looks interesting.
62. ES - There must be alot of literature on amicable pairs. If we do an Item
about them, we will have to say much more.
63.
64. ES - Say more, or flush it. M.I.T. A.I. memo 257, out of print.
65. ES - Say more, or flush it.
66. ES - No content in this Item.
67-76. ES - Games could easily take up a whole volume. Let's include only
our own contributions and exceptionally clever results of others.
Alleged solutions should be backed up.