CS 3511  Exam 1 Review Exercises                   Fall Semester, 2006

Here are some exercises similar to ones that might be on the first exam.
The items in parentheses are the corresponding items in the 6th edition 
of the text (since I think everyone is using the 5th edition).

Note that * exercises were in the assignments, but are computationally
too hard as stated (not enough time) to put on an exam - however, a
simpler/easier version may be used.

Ex. 4 of Appendix A-1 and Ex. 3 of Appendix A-2
 (= 4 of Appendix A-2 and Ex. 3 of Appendix A-3)

Ex. 23-32, 35 (77 is low priority) of Section 1.5 pages 75-77
 (= 1.6.1, 1.6.6, 1.6.9-14, 1.6.23, 1.6.24, 1.7.5 (1.5.35 low priority) )

Supplementary Ex. 26, 27 page 116 of Chapter 1
 (= 32, 33 page 108 of Chapter 1 )

Ex. 16-18, 37, 51-56 of Section 2.1 pages 130-131
 (= 16-18, 37, 51-56 of Section 3.1)

Ex. 1-4, 18-24, 44, 62 of Section 2.2 pages 142-144
 (= 1-4, 18-24, 44, 62 of Section 3.2)

Ex. 1, 4, 7, 8, 13 of Section 2.3 pages 151-152
 (= 1, 4, 7, 8, 13 of Section 3.3)

Ex. 3-7,     23, 24,    50,     54-57 of Section 2.4 pages 166-168
 (= 3.4.3-7, 3.5.15-16, 3.4.28, 3.4.32-35)

Ex. 13-17, of Section 2.5 page 180
 (= 13-17, of Section 3.6)

Ex. 3-6, 9, 11, 12, 15, 17*, 18, 23, 27-29, 48-50* of Section 2.6
 pages 194-196
 (= 3-6, 9, 11, 12, 15, 17*, 18, 23, 27-29, 48-50* of Section 3.7)

Ex. 1, 13-16, of Chapter 2 Supplement pages 209-211
 (= 1, 13-16, of Chapter 3 Supplement)


Also, be able to name/describe 4 applications of modular arithmetic and/or
number theory in computer science.  Answer:
cryptography
error detection/correction
hash functions
pseudo-random numbers

You should know how the Chinese Remainder Theorem works - that is the
formula for solving the congruences at the top of page 187