Discrete Mathematics, Spring 2025
Day/Time: TuTh 12:30pm — 1:45pm
Syllabus: click here
Piazza: click here
Gradescope: click here
Homework:
Week 1: Section 1.1, Problems 1, 2, 5, 6, 10, 11, 12, 13 and Problems 16, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30 (but only parts a., c., e., and g. when they exist)
Week 2: Section 1.3, problems 1a.c.e., 3a., 4a., 5, 7a.c., 8a.c., 17a., 24, 25, 35, 36 (use truth tables for problems 24 and 25) and problems 11a.c.e., 12a.c., 15a., 16a., 20, 24, 25, 27 (for this latter collection, use the methods introduced Thursday for problems 15 and higher to deduce the equivalences from known ones)
Week 3: Section 1.4, problems 1, 2, 3, 5, 6, 11, 12, 13, 14, 15, 16, 17b., 18c., 19d., 23b., 24c., 25a.d., 32, 33; Section 1.5, problems 1a.c., 2a.c., 3b.e., 6b.e., 9b.d.f, 10d.f.g.h., 13c.d., 14c.d., 19a.d., 20a.d., 24b., 25b., 27a.d., 28a.d., 31a.d., 32a.d., 36d.e., 37a.d., 41, 42, 45, 46
Week 4: Section 1.6, problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13bd, 14bc, 15ad, 16ad, 17, 18, 19a, 20a, 23, 24
Week 5: Section 1.7, problems 1, 2, 4, 5, 6, 7, 9, 10, 13, 14, 17, 18, 19, 20, 25, 26 (hint: for these last two, it will help to read Example 10 in the book!)
Week 7: Section 1.8, problems 5, 9, 10, 11, 13; Section 2.1, problems 1, 2, 7, 8, 9, 10, 12, 19
Week 8: Section 2.1, problems 23, 27, 29, 32, 33, 34a, 37, 40; Section 2.2, problems 1, 2, 3, 4, 14, 16, 17, 20, 23, 26, 27, 31, 32, 33, 52, 53, 54, 56, 57
Week 9: Section 2.3, problems 1, 2, 4ab, 5d, 6ab, 7ab, 10, 11, 12, 13, 14, 15, 20, 21abd, 22, 23abd 30abd, 31a, 32, 33, 34, 36, 37, 42, 43a, 44, 45, 46, 47
Week 10+11: Section 4.1, problems 1, 2, 3, 5, 6, 7, 8, 12, 14abc, 21, 22, 24, 26ab, 27ab, 32, 33, 34, 35, 43, 44, 45, 46; Section 4.3, problems 1, 2, 12, 15, 24, 32cde, 33cef, 41, 42, 43, 44 (here, a “linear combination of a and b” means an expression of the form sa+tb for integers s and t), 55
Week 12+13: Section 5.1, problems 3, 5, 6, 10, 11, 38, 41, 49, 50, 51, 64; Section 5.2, problems 4, 5ac, 12, 25, 29, 30
Week 14: Section 9.1, problems 1, 2a, 3bdf, 4, 5, 6bdf, 7ad (but ignore “antisymmetric” for all of these, since we didn’t cover that concept); Section 9.5, problems 1bcd, 2, 3abc
Week 14+15 (as practice for the final): Section 9.5, problems 9, 15, 16, 27, 28, 35, 36, 41, 42, 44cde, 45abc (for these last four problems, you need the definition of a “partition” of a set A, which we introduced in lecture today, but didn’t refer to by this name. A partition of A consists of a collection of subsets A_i so that A is the union of the A_i, and so that if A_i isn’t equal to A_j, then their intersection is empty. See page 644 for more details.); Section 6.1, problems 1, 4, 7, 8, 22, 29, 40, 45, 55, 57ab; Section 6.3, problems 13, 15, 19, 29, 33ab, 35; Section 6.4, problems 3, 5, 7, 9, 16, 21, 25, 26a