813 Recommended Exercises

Abbreviations and special notation used in denoting certain exercises:
!
especially important to do thoroughly and carefully
?
not clear if worth doing
NB
note well the result obtained; no comment on worth doing
+NB
note well the result obtained and worth doing
--
linked: regard as parts of one exercise (NOTE: 5--7 means 5 and 7 are linked, and says nothing about 6.)
[Chapter.section, pages #exercises.]
• XV.1, 500--1 #1, 3, 4, 5, 6.
• XV.2, 504 #1, 5, 6, 11; 10.
• XV.3, 506 #2.
• XV.4, 511 #1, 2, 3, 4, 5, 6, 7.
• XV.5, 516 #1, 2, 4, 6 state only, 7, 8, 10, NB11; 3, ?5.
• XV.6, 520 #1, 3, !4, 5.(b), 7--8, 10--11, !13.

• XI.1, 381 #?1, 2, 3, 4, 5.
• XI.2, 383 #1, 2, 3.
• XI.3, 388 #1, 3, 5, 6, 7, 8, 9.
• XI.5, 397 # 1, 3, 8, 9.
• XI.6, 400 # 1, 2, 3, 4.

• XII.1, 412 #1,2.
• XII.2, 416--7 #1, 2, 3, 4, 5.
• XII.3, 419 #1, 2, 4, 5, 6.
• XII.4, 422 #1, 3, 4.
• XII.5, 426 #1, 4, 5.
• XII.6, 428 #1, 2, NB3, 4, 5, NB6, 7.
• XII.7, 4291, 2, 3, 4, NB5.
• XII.8, 432--3 #1, ?2, 3, 7.
• XII.9, 435 #1, 3, !4.

• XIII.1, 439 #1, 2, NB3.
• XIII.2, 442 #1, 3, 4, 5, 6, NB7.
• XIII.3, 444--5 #?1, 2, 3, 4, ?5, ?6, 7, 8, !9, ?10.(a), 10.(b).
• XIII.4, 446 #1, 2.
• XIII.5, 450 #1, 2, 3, NB4: product of fields.
• XIII.6, 453 #?1, 2, 3--4--5, 6, NB 7 through 11.
• XIII.7, 456 #1, 2, 3, 4.
• XIII.8, 458 #1, 2, 3, 4, 5.
• XIII.9, 461 #1, ?2, ?3.
• XIII.10, 464--5 #!1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
• XIII.11, 469 #1, 2, +NB3, 4, "5:" converse of Thm. 17 !