1-1 & 1-2: 5. 11. 13. 23. 29. 35. 37.
1-3: 8. 20. 23. 33.
1-4: 8. 14. 19.
1-5: 7. 11. Loops vs. Catalan Numbers (as below). Formalize the proofs to Catalan Number: (1) Cn = (2n, n)-(2n, n+1), and (2) Cn = (2n, n)/(n+1).
2-1: 3. 4. 10. 13.
2-2: 4. 12. 17. 18(a). 20(a).
2-3 : 7. 10.
2-4 : 3. 5. 21.
2-5 : 9.
3-1: 4, 7, 11, 19, 23, 27 (to understand the basic properties of sets)
3-2: 15, 16, 17 (to understand the operations and laws of sets)
3-3: 7, 9 (to understand the couting kills via Venn diagrams)
4-1: Please formalize the proofs of
(1) WOP => PMI
(2) PMI => WOP
4-2: 18 (Originality of Eulerian numbers); Design a recursive formula for coloring the sectors of a circle using 4 colors.
5-1 : 4. 6.
5-2 : 17. 20. 21.
5-3 : 4. 8.
5-4 : 5. 8.
5-5 : 4. 24.
5-6 : 10.
9-1 : 5.