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1. Field Theory - Nicholson - Algebraic Extensions - Section 6.2 - pages 281-282

I am reading Nicholson: Introduction to Abstract Algebra Section 6.2 Algebraic Extensions. On page 282 the Corollary to Theorem 5 states the following: (see attachment for Theorem 5 and the Corollary)...
2. Polynomial Rings and UFDs - Dummit and Foote pages 303-304

I am reading Dummit and Foote Section 9.3 Polynomial Rings That are Unique Factorization Domains (see attachment Section 9.3 pages 303 -304) I am working through (beginning, anyway) the proof of Theorem 7 which states the following: "R is a Unique Factorization Domain if and only if R[x] is a...
3. How many pages?

The pages of a book are numbered, beginning with page 1. If all of the pages in the book are considered, there are a total of 2,989 individual digits needed to print the page numbers. How many pages does the book contain?
4. How many pages?

The pages of a book are numbered, beginning with page 1. If all of the pages in the book are considered, there are a total of 2,989 individual digits needed to print the page numbers. How many pages does the book contain?
5. Algebra Problem Concerning Pages in a Book

A 120-page book has p lines to a page. If the number of lines were reduced by three on each page the number of pages would need to be increased by 20 to give the same amount of writing space. How many lines were there on the page originally?
6. Pages in a book - need to verify my solution

Hi All, I have solved this problem below. But the required answer and my answer don't match. Please help me find the mistake in my solution. The pages of a book are numbered as 1, 2, 3, .... It is found that 195 digits are used. (a) How many pages are numbered with a single-digit...
7. Split 'tabular' over two pages?

Hi, I'd like to have the tabular environment make my table continue over the page rather than force it all together on a new page when it gets too big for the current one, as it leaves ugly blank space. Any suggestions?
8. Theorom from Serge Lang's Complex Analysis - pages 89-90

I am a math hobbyist/amateur studying complex analysis from Serge Lang's book Complex Analysis. I need some help regarding Theorem 1.1 on Page 89 The theorem and is proof as given by Lang are as follows: "Theorem 1.1 Let U be a connected open set, and let f be a holomorphic function on U...