HW1: Exercise 1-1~1-5

1-1 & 1-2:  5.  11.  13.  23.  29.  32. 35.  37.

1-3:  8.  20.  23.  31. 34.

1-4:  8.  14.  19.  23.  24.

1-5:  1.  7.  10.  11.

• Additional Exercise 1:

Loops vs.  Catalan Numbers.

• Additional Exercise 2:

Formalize the proofs to Catalan Number: 

            (1) Cn = (2n, n)-(2n, n+1), and (2)  Cn = (2n, n)/(n+1).

HW2: Exercise 2-1~2-5 & 3-1~3-3

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)

HW3: Exercise 4-1~4-3

4-1:  2,  28
          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 and in general using p colors.

4-3:  13
          Prove:
          (1) If n ∈ Z+ and n is composite, then there is a prime p such that p|n.

          (2) There are infinitely many primes.

          (3) If n∈Z+ and n is composite, then there is a prime p such that p|n and p ≤ √n .

HW4: Exercise 5-1~5-6 & 9-1

5-1 :  4, 6 

5-2 :  17, 20, 21

5-3 :  4, 6, 8, 17

5-4 :  5, 8

5-5 :  4, 24, Example 5.43

5-6 :  10

9-1 :  5