MAT 149A - Discrete Mathematics Homework Assignment

MAT 149A - DISCRETE MATHEMATICS Homework Assignment

Winter Quarter 2004

Instruction:

Every week 10 homework problems are assigned. They are due in class every Friday.

Print clearly (1) your full name; (2) student ID number; (3) the course number (MAT 149A) and the instructor name (Mulase); and (4) the due date; at the top right corner of the front page of your homework paper.
Please staple your homework if you use more than one sheet of paper.
Every solution to a problem has to be presented with a proof. The final answer alone without any proof will not receive any credit.
Only a perfect solution with proof receives a credit. Partial credits are not given.

Weekly Homework Assignment

Homework #5 - #8 carry double weights, credited as midterm make-up points.

Optional Project: Due Monday March 15.

Consider a graph drawn on a torus (i.e., the surface of a donut) that gives a triangulation. Find its Euler characteristic. Show that the Euler characteristic does not depend on the choice of the triangulation of the torus.

The project carries extra 2% of the course grade. Your course grade will not be affected if you do not submit the optional project.

HW#8: Due Friday March 12. p.360: #25.1.1, 25.1.2; p.366: #25.3.1, 25.3.2, 25.3.3, 25.3.4.

Please read section 25.1 and 25.3.

HW#7: Due Friday March 5.

1. Make a paper model of a dodecahedron. Search the Internet for construction instructions. Please bring your model to class for sharing.
2. Compute the number of different colored dodecahedrons when you use r colors to paint the 12 faces. Write the full steps of your investigation.

HW#6: Due Friday February 27. p.295: #21.7.19, 21.7.20, 21.7.21.
You have already done these problems, but this time provide a perfect paper with completely detailed solutions.

Please read sections 27.1, 27.3.

HW#5: Due Friday February 20. p.290: #21.4.1, 21.4.2, 21.4.3; p.295: #21.7.1, 21.7.2, 21.7.3, 21.7.4.

Please read section 21.4.

HW#4: Due Friday February 6. p.283: #21.1.2, 21.1.3; p.284: #21.2.1; p.287: #21.3.1, 21.3.2, 21.3.3; p.295: #21.7.19, 21.7.20, 21.7.21.

Please read sections 21.1 - 21.3.

HW#3: Due Friday January 30. p.266: #20.4.1; p.270: #20.6.2; p.272: #20.7.4, p.276: #20.8.3; p.279: #20.10.7, 20.10.8, 20.10.10, 20.10.11, 20.10.12, 20.10.13.

Please read sections 20.1 - 20.8.

HW#2: Due Friday January 23. p.127: #12.1.2, 12.1.3; p.128: #12.2.2; p.132: #12.3.4, p.133: #12.4.2; p.136: #12.5.1; p.140: #12.6.3; p.140: #12.7.2, 12.7.4, 12.7.19.

To prepare for dealing with symmetric groups, we cover chapter 12 this week. Please read sections 12.1 - 12.6. The first two sections will be covered in the Tuesday Discussion Section.

HW#1: Due Friday January 16. p.103: #10.6.1, 10.6.2; p.104: #10.7.8; p.179: #15.1.2, 15.1.3; p.181: #15.2.3; p.182: #15.3.2; p.185: #15.4.3; p.187: #15.5.2; p.191: #15.8.1.

Please read sections 10.6 and 15.1 - 15.5.