Holy Cross Mathematics and Computer Science
MATH 243, Mathematical Structures, Section 2, Fall 2017
Syllabus and Schedule
Examples, Class Notes, Solutions, etc.
Assignments
- Problem Set 1: Chapter 1 Exercises: 1.1, 1.2, 1.3, 1.5, 1.6, 1.8. -- due: Friday, September 8.
- Problem Set 2: Chapter 2 Exercises: 2.1, 2.2ab, 2.3ab, 2.4ab, 2.7, 2.8b, 2.9ac, 2.10ac (i.e. draw
the Venn diagrams corresponding to parts a and c of 2.9). -- due: Friday,
September 15.
- Problem Set 3: Chapter 3 Exercises: 3.2, 3.3, 3.4, 3.10 -- due: Friday, September 22.
- Problem Set 4 -- due: Friday, October 6.
- Problem Set 5: Chapter 4 Exercises: 4.12; Chapter 5 Exercises: 5.1, 5.4, 5.6, 5.7, 5.13, plus the following
added problem: Use the Euclidean Algorithm to determine d = gcd(20400,2754) and determine
integers m,n such that d = 20400 m + 2754 n -- due: Monday, October 23. Note extension.
- Problem Set 6: Added Problem: Solve the linear congruence 37 x ≡ 3 mod 54;
Chapter 6 Exercises: 6.1, 6.2, 6.8, 6.9a -- due: Friday, October 27.
- Problem Set 7: Exercises 6.10 (Note: There is a typo in the statement of the problem; the public information is (m,e) (e = encryption exponent), not (m,d). You
will need to determine the decryption exponent d using the other information in the
problem), 7.4 -- Important Note, added 11/10: part (b) of this statement is actually false as stated(!) Let's change the directions to: "Find a counterexample, then try to find an additional condition under which the given statement is true", 7.5, 7.6, 7.7, 7.9, 7.13 (Note for 7.13: ``well-defined mod R''
means that f takes the same value on each element of any one of the equivalence classes for R;
see Definition 7.48)-- due: Monday, November 13.
- Problem Set 8: Exercises 8.6, 9.3 (replace "complex" by "real" in the statement), 9.12,
9.13, 9.14, 9.18, 9.28, 10.3, 10.4 -- due: Monday, November 27.
Information and Announcements
- Exam 3 is coming up next week -- review sheet, including
practice questions (solutions for the practice questions.)
- Review session for Exam 3 -- Tuesday, December 5, Swords 302, 7pm - ?
- Exam 3 -- Thursday, December 7, 5 - 7pm in Swords 302.
- Class on Wednesday, December 6 is optional. We will either
do some additional review, or discuss the ``different sizes'' of infinities
I mentioned in passing in class on November 29, if there is interest.
- To help you get started reviewing for the final exam -- Information
on final exam (updated 12/6), and
Related Links
Downloading Information
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Last modified: December 14, 2017