MA275 Discrete and Combinatorial Algebra

MTRF 9 G221
John Rickert, Associate Professor of Mathematics
Office: G-215A, Crapo Hall
Phone: (812) 877-8473

Office hours week: MTRF 7, or make an appointment, or drop in. Here’s my schedule

The final exam takes Thursday, February 25 1:00PM-5:00PM in G317.
http://www.rose-hulman.edu/~rickert/Classes/ma275
Moodle
To Homework …Questions
Homework for our next class …Today’s questions

For Tuesday, December 1: Section 1.2 #1,7,11,14,15,17,26,31,39. Turn in these exercises on Thursday.
For Thursday, December 3: Turn in the Section 1.2 exercises. Section 1.3 #1,6,9,14,16,17,23,27,32.
For Friday, December 4: Section 1.4 #1,7,10,16,22,25,27. Turn these exercises in on Monday.
For Monday, December 7: Turn in the Section 1.4 exercises. Review the homework exercises. We will have a quiz Monday covering the material through Section 1.4.
For Tuesday, December 8: Work exercises Section 1.5 #1,4,7,9,11.
For Thursday, December 10: Work exercises Section 2.1 #3,5,6,8,17. Turn in these exercises on Friday.
For Friday, December 11: Turn in the Section 2.1 exercises. Work exercises Section 2.2 #1,6,9,14,15. turn in these exercises on Thursday.

For Monday, December 14: There will be a quiz covering laws of logic or the rules of inference. Section 2.3 #5,7,11,12.
For Tuesday, December 15: Section 2.3 #13; Section 2.4 #1,9.
For Thursday, December 17: Turn in the Section 2.2 exercises. Section 2.4 #8,14,16,21,22.
Friday, December 18: Exam #1 average was 869. Equivalent grades are A 900-1000, B 800-899, C 700-799, D 600-699, F <600.

For Monday, January 4: Work exercises Section 2.5 #5,9.
For Tuesday, January 5: Work exercises Section 2.5 #14,15,17,19,21,23.
For Thursday, January 7: Work exercises Section 3.1 #1,5,8,9,10,23,27. Turn in these exercises on Friday.
For Friday, January 8: Turn in the Section 3.1 exercises. Work exercises Section 3.2 #1,3,6,16,19.

For Monday, January 11: Work exercises Section 3.3 #1,4,5,6,9.
For Tuesday, January 12: Work exercises Section 3.4 #1,5,6,9,11,14.
For Thursday, January 14: We will have a probability quiz. Work exercises Section 3.5 #1,4,7,9,14.
For Friday, January 15: Work exercises Section 4.1 #1.

For Monday, January 18: Work exercises Section 4.1 #2,6,8,12,16. Turn in these exercises on Thursday.
For Tuesday, January 19: Work exercises Section 4.2 #1,7,11,12,14,18.
For Thursday, January 21: Turn in the Section 4.1 exercises #2,6,8,12,16. Review through Section 4.2 for the exam.
Friday, January 22: Exam #2 average was 805. Equivalent grades are A 900-1030 B 790-899 C 650-789 D 500-649 F <500.

For Tuesday, January 26: Work exercises Section 4.3 #1,4,9,10,13.
For Thursday, January 28: Work exercises Section 4.3 #17,21,29.
For Friday, January 29: Work exercises Section 4.4 # 1,4,6,12,14,17.

For Monday, February 1: Work exercises Section 4.4 # 1,4,6,12,14,17.
For Tuesday, February 2: Work exercises Section 4.5 #8,15.
For Thursday, February 4: Work exercises Section 4.5 #5,11,18,22,27.
For Friday, February 5: Work exercises Section 5.1 #1,3,6,8,13.

For Monday, February 8: Work exercises Section 5.2 #1,5,8,14,22,27.
For Tuesday, February 9: Work exercises Section 5.3 #1,3.
For Thursday, February 11: Work exercises Section 5.3 #10,15,18.
Friday, February 12: The average score on Exam #3 was 603. Equivalent grades are A 750-940, B 600-749, C 500-599, D 400-499, F <400.
For Tuesday, February 16: Work exercises Section 5.5 #2,9,11,14,16,20.
For Thursday, February 18: Work exercises Section 5.6 #1,3,9,12,14,22.
Bring your computers to class Thursday.

For Monday, September 8:
Turn in the Section 1.2 exercises.
Section 1.3 #1,6,9,14,16,17,23,27,32.
Extra Credit:
Generalize Exercise 1.2.31(iii)(a) to D-digit integers base B, where B is even.

For Tuesday, Setpember 9:
Section 1.4 #1,7,10,16,22,25,27
For Thursday, September 11:
We will have a Quiz covering material through Section 1.4.
Turn in the Section 1.4 homework.
Section 1.5 #1,4,7,9,11.
For Friday, September 12:
Section 2.1 #3,5,6,8,17.

For Monday, September 15:
Section 2.2 #1,6,9,14,15.
Turn in these exercises on Tuesday.
For Tuesday, September 16:
Turn in the Section 2.2 exercises.
Section 2.3 #5,7,11,12.
For Thursday, September 18:
We will have a Quiz covering through Section 2.3.
Section 2.4 #1,4,9,21.
For Friday, September 19:
Section 2.5 #5,9,14,15,19,21. Turn in these exercises on Monday.

For Monday, September 22:
Turn in The homework exercises from Friday, Section 2.5 #5,9,14,15,19,21.
We will have a Quiz covering through Section 2.3 asking you to justify a conclusion.
Work exercises Section 2.5 #17,20,23; Section 3.1 #1,5,9.
For Tuesday, September 23:
Section 3.1 #8,10,23,27;
Section 3.2 #1,6.
Friday, September 26:
Exam 1 average was 729/1000.
Equivalent grades are A 850-925 B 725-849 C 600-724 D 475-599 F <475
.
For Monday, September 29:
Section 3.2 #4,16;
Section 3.3 #1,4,5,6,9.
For Tuesday, September 30:
Section 3.4 #1,5,6,9,11,14.
For Thursday, October 2:
Section 3.5 #1,4,7,9,14.
For Friday, October 3:
Pages 189-190 #2,5,16,20,40.
For Monday, October 6:
Section 4.1 #1,2,6,12,16.
For Tuesday, October 7:
We will have a quiz on probability.
Section 4.2 #1,7,11.
Turn in these exercises on Tuesday.

For Monday, October 13:
Section 4.2 #12,14,18.
Turn in these exercises on Tuesday.
For Tuesay, October 14:
Turn in the six Section 4.2 exercises.
Section 4.3 #1,4,9,10,13. Turn in these exercises on Friday
For Thursday, October 16:
Section 4.3 #17,21,29. Turn in these exercises on Friday
For Friday, October 17:
Turn in the Section 4.3 exercises.
Review the first three sections of Chapter 4. Practice writing induction proofs.

For Monday, October 20:
Section 4.4 #4,6,12.
For Tuesday, October 21:
Section 4.4 #1,8,14,17.
For Thursday, October 23:
Section 4.5 #5,8,11,15,18,27.
For Tuesday, October 28:
Section 5.1 #1,3,6,8,13.
For Thursday, October 30:
Section 5.2 #1,5,8,14,22,27.
For Friday, October 31:
Section 5.3 #1,3.
For Monday, November 3:
Section 5.3 #10,15,18.
For Thursday, November 6:
Section 5.5 #2,9,11,14,16,20.

Friday, November 7:
Section 5.6 #1,3,9,22.
For Monday, November 10:
Turn in the take-home exam.
Section 5.6 #5,12,14.
For Tuesday, November 11:
Chapter 5 supplementary exercsies pages 305-306: #2, 10, 11,12,22c.

Questions from class

To today’s questions
In the “Questions” section, I’ll color the active questions green so that they are easier (in theory) to find as you scan through the page. Please let me know if I’ve missed anything.
From Tuesday, January 12: A k-sided dies is rolled three times. Determine the probability that the second and third rolls are greater than the first. What is the limit as k increases without bound?
Determine the probability that the second roll is greater than the first and the third is greater than the second. What is the limit as k increases without bound?
Extra credit will be awarded for solutions turned in by the end of class Friday, January 22.

Monday, September 3:
The Maple command for the binomial coefficient n choose k
is binomial(n,k)
Tuesday, September 4:
A commentary about the ABC-conjecture and Mochizuki’s proposed proof is at
http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/
Tuesday, September 18:
For Extra Credit think about the Dice problem. The two conditions on the dice are

No ties are possible
Each die has an equal chance of displaying the highest number.

The problem disussed
in the article we looked at is to come up with four twelve sided dice so that the conditions are satisfied. The open question considered is How many solutions are there?
What is the answer for two dice? How small can the dice be? With k-sided dice, how many configurations for 1,2,…2k satisfy the conditions?
What is the answer for three dice? How small can the dice be?
With k-sided dice, how many configurations for 1,2,…3k satisfy the conditions?
Explore similar questions for four dice, five dice, etc.

Homework is due at the beginning of class on the day that it is due. You should turn in your homework in a pile on the desk at the front of the classroom. Homework may be turned in later but will be penalized based on just how late it is – typically
1 point off for turned in late during the class,
5% off for being turned in late the same day,
10% off per day. (weekends count for two days) i.e. 10 days later, it’s too late to get a makeup homework turned in.
When writing up homework, you should circle (or otherwise clearly indicate) your answers.
It’s good to work together, but you should write/type your own homework. Simply copying another person’s work or Maple file will result in a 0 and a letter to the Dean of Students.
You should come to class prepared. This means that I expect you to have done the homework, brought your book to class, and silenced your cell phone.
If you have a cell phone, please make sure that it does not ring audibly during class. Phone calls should, in general, not be answered during class. No texting during class.

If you don’t understand something, ASK,
If I’m going too fast, STOP ME. I enjoy mathematics. When I get on a roll, I tend to keep going. SHOW YOUR WORK. The correct answer will only be worth 1 point. I want to verify that you understand the process.If you are having problems understanding the material, see me or go to the learning center.

The final exam is 36% of the course grade. Homework, quizzes and exams constitute the other 64%.

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