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Math 118

Syllabus

Course grades

Thursday, 12-20

The final exams are graded. By and large, work on the final exam was good. The scores and the final course grades are posted here: finalgrades.html.

Happy holidays and have a good break.

The final exam

Wednesday, 12-19

Here are my solutions to the final exam. I haven't finished grading your exams yet. When they are graded and the course grades are determined, I will post the grades on a sheet provided by the registrar outside my office door (4th floor, math tower, room 106). It probably won't be before Thursday.

A correction to a practice problem

Saturday, 12-15

There is an error in problem two of the practice problems. The question should read

If I draw a three-regular graph of size twenty without crossings, how many faces will it have?

The answer is 11 since a graph with 20 vertices that is three regular has 30 edges and if I draw it on the plane without crossings, we must have v-e+f=1. So, from 20-30+f=1, we conclude that f=11.

Office hours

Tuesday, 12-11

I want to remind you about office hours between now and the final exam:

• Tuesday, 12-11: I have office hours in the math learning center in Physics 127-a from 2:30-3:30.
• Thursday, 12-13: I have office hours in my office in room 106 on the fourth floor of the Math Tower from 2:30-3:30.
• Friday, 12-14: Rodrigo has office hours in the math learning center in Physics 127-a from 11:00am-1:00pm.
• Monday, 12-17: I have office hours in my office in room 106 on the fourth floor of the Math Tower from 10:30-12:00.

Practice exam

Thursday, 12-6

Here is a practice exam. It is longer than your final exam will be, but it is comprehensive and what I consider the most important topics appear on this exam.

This web page can serve as a chronology of the course: the midterms with solutions are available here, and all of the assigned homework is recorded here.

The lecture on Thursday, December 13th, will be a review of the course. I expect that questions about the practice exam will direct the review, so it would be a good idea to work hard on this practice exam before Thursday.

Exam reminder

Thursday, 12-6

The final exam for this course will be on Tuesday, December 18th from 11:00am-1:30pm in the usual classroom. The exam will be comprehensive.

Homework 10

Thursday, 12-6

Here is some homework for the weekend:

• In the text on page 479, the authors find that gcd(600,1400)=20. Use the division algortithm to verify this result and then reuse the equations produced by the Euclidean algorithm to find integers x and y satisfying

  20=660x+1400y.

• Use the Euclidean algorithm to find gcd(218,49) and then find integers x and y so that

  gcd(49,218)=49x+218y.

• (Harder) Use the Euclidean algorithm to find gcd(228,49) and then find integers x and y so that

  gcd(49,228)=49x+228y.

• Read section 8.2 and do exercises 1, 3, 5, 9, 21, 23 on page 486.

Homework 9

Thursday, 11-29

Here are some problems to work on over the weekend.

• Read section 8.1 and do exercises 1-10, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 27, 33, 34, 39, 40, 41, 42, 43, 44, 45, 49, 50, 51, 52, 53, 54, 55, 56, 61, 62
• Read section 8.2

Turn these problems during recitation the week of December 3.

Exam scores

Monday, 11-19

I apologize for the delay, but the exam scores will not be available until Tuesday, November 27th.

Answers to the exam

Tuesday, 11-13

Here are my solutions to the second exam.

Some review problems

Saturday, 11-10

Here are some good review problems to work on this weekend:

From the book:

• Section 3.4: 2, 4, 6, 8;
• Section 3.5: 2, 4, 6
• Section 6.1: 2, 3, 10, 11, 12, 15, 16, 21, 22
• Section 6.2: 15, 16, 17, 18, 19, 20, 21

Other problems/questions you should think about:

• Create your own travelling salesman problem by drawing K_5 and assigning randomly some weights to the edges. Use both the nearest neighbor and the greedy algorithm to approximate a solution. List all twelve essentially distinct Hamiltonian circuits and find the best solution to the traveling salesman problem. Did either algorithm produce this solution?
• Construct a 3-regular, diameter 3 graph of size 12. Can you construct your graph to be planar?
• Construct a map on the plane whose territories can be colored with three colors. Can you construct a map on the plane that cannot be colored with four colors?
• Are there any graphs that you can draw on the sphere without crossings that you cannot draw on the plane without crossings? Are there any graphs that you can draw on the plane without crossings that you cannot draw on the sphere without crossings?
• Can you embedd K_5 on the sphere? on the torus?
• What is the Euler number of a sphere? a torus? a surface of genus 2? a surface of genus g?
• It is possible to draw K_(8,2) on a sphere without any crossing. How many faces will it have?
• Construct a map of territories on the tous that requires five colors. See if you can construct one that requires six colors.

Reminder: second midterm exam

Wednesday, 11-7

The second midterm exam will be in class on Tuesday, November 13. The exam will be over the material covered since the first midterm. This includes the topics in sections 3.4, 3.5, 6.1, 6.2 of the texbook, as well as the additional graph theoretic material discussed during the lectures.

Homework 8

Tuesday, 10-30

Here is a little project to do before class on Thursday

• Draw any five graphs, without crossings, and make a table listing the number of vertices, the number of edges, and the number of faces (connected territories surrounded by edges) in each.

Here are some more travelling salesman problems to work on for next week:

• Section 6.2: exercises 15b,c, 17c, 18c, and 21c, 24.
• Read the "Branching Out" on pages 394-395.
• Is the complete graph on 5 vertices planar?

Turn these problems during recitation the week of November 5.

Homework 7

Thursday, 10-25

Here are some problems to work on over the weekend.

• Section 6.2: exercises 15a, 17a,b,d, 18a,b, and 21a,b

Turn these problems during recitation the week of October 29.

Homework 6

Tuesday, 10-16

We will now be studying graph theory, which is the subject of chapter six in the textbook. To get started, read sections 6.1 and 6.2. Here are some good exercises:

• Section 6.1: exercises 3, 11, 15, 16, 22
• Section 6.2: exercises 1, 3, 5, 6
• Construct a 3-regular, diameter 3 graph of size 12.

These problems are due in recitation the week of October 22.

Homework 5

Thursday, 10-4

For Tuesday, October 9 carefully read section 3.4 and work on the problems from that section. The homework due in recitation the week of October 15 is below:

• Section 3.4: exercises 3, 5, 9, 13, 23
• Section 3.5: work through the examples and do exercises 1, 3, 5, 7, 9, 13, 23, 31, 37, 41, 47.

Exam scores

Thursday, 10-4

The exams are graded and the scores will be curved according to this formula:

curved score = (raw test score) x (3/4) +25.

The average before the curve is about 65 and after the curve is about 75.

Note about office hours

Thursday, 10-4

My 2:30-3:30 office hour on Thursday, October 11 is canceled.

Solutions to the exam

Tuesday, 10-2

Here are my solutions to the exam problems: test1a.pdf in pdf format.

Some more problems to study for the test

Friday, 9-28

The test will cover the material discussed in class thus far: all of chapter 1 and sections 3.1, 3.2, 3.3.

Here are some good exercises to work on as you study:

• Voting: review exercises 3, 4, 5, 6, 7, 8, 9 on pages 66, 67, and 68
• Compound interest: 35, 39, 43, 45, 47, 49, and 51 on pages 152, 153.

Reminder: test on Tuesday, October 2.

Thursday, 9-20

Just a reminder that there will be a test during the scheduled lecture on Tuesday, October 2.

Homework 4

Thursday, 9-20

This homework is due in recitation the week of September 24.

• Review section 3.1.
• Read section 3.3 and do exercises: 6, 10, 14, 18, 22, 41, 53
• Read section 3.4 and do exercise 22.

A note about homework 3

Friday, 9-14

You should complete homework 3, but you do not have to turn it in.

Homework 3

Tuesday, 9-11

This homework is due in recitation the week of September 17.

• Read Sections 3.1 and do exercises: 5, 25
• Read Sections 3.2 and do exercises: 3, 13, 20, 24, 26

Homework 2

Tuesday, 9-4

This homework is due in recitation the week of September 10.

• Read Sections 1.3 and do exercises: 11, 19, 22.
• Read Sections 1.4 and do exercises: 5, 14.
• Read Sections 1.5 and do exercises: 1, 2, 3 and writing exercise 2.

Two brief notes

Wednesday, 8-29

Exam dates

The dates on the syllabus for the midterm exams were wrong. The correct dates are

• midterm exam 1: Tuesday, October 1
• midterm exam 2: Tuesday, November 13

and they are now correct on the syllabus.

Labor day

There is no class on Monday, September 3. People who are scheduled to have a recitation on Monday should turn in homework 1 in lecture on Tuesday, September 4th and I will give it to Rodrigo Perez.

Homework 1

Monday, 8-27

This homework is due in recitation the week of September 3.

• Section 1.1: 2, 3, 12, 15, 21, 23, 24, 25, 26
• Section 1.2: 1, 9, 12

Contact information and syllabus

Sunday, 8-26

Contact Information:

• Instructor: John Terilla
• Office: 4-106 Math Tower
• Office hours:
  • Tuesday 2:20-3:20 in Physics A-127
  • Thursday 2:20-3:20 in Math Tower 4-106
  • or by appointment
• Phone: (631) 632-4893
• Email: jterilla@math.sunysb.edu

There is more information on the syllabus.