{"id":711,"date":"2016-09-07T15:11:38","date_gmt":"2016-09-07T15:11:38","guid":{"rendered":"http:\/\/wordpress.rose-hulman.edu\/rickert\/?page_id=711"},"modified":"2017-03-27T17:39:25","modified_gmt":"2017-03-27T17:39:25","slug":"ma275-discrete-and-combinatorial-algebra","status":"publish","type":"page","link":"https:\/\/wordpress.rose-hulman.edu\/rickert\/ma275-discrete-and-combinatorial-algebra\/","title":{"rendered":"MA275 Discrete and Combinatorial Algebra"},"content":{"rendered":"

MTRF 9 G221
\n<\/span> John Rickert, Associate Professor of Mathematics
\nOffice:<\/b> G-215A, Crapo Hall
\nPhone:<\/b> (812) 877-8473<\/p>\n

e-mail:<\/b> rickert@rose-hulman.edu<\/span><\/u><\/a><\/p>\n

Office hours week: MTRF 7, or make an appointment, or drop in. Here’s my schedule<\/span><\/u><\/a><\/p>\n

The final exam takes Thursday, February 25 1:00PM-5:00PM in G317.
\n http:\/\/www.rose-hulman.edu\/~rickert\/Classes\/ma275
\nMoodle<\/span><\/u><\/a>
\nTo Homework<\/span><\/u> …Questions<\/span><\/u>
\nHomework for our next class<\/span><\/u> …Today’s questions<\/span><\/u><\/p>\n

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

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

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

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

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

For Tuesday, January 26<\/i>: Work exercises Section 4.3 #1,4,9,10,13.
\nFor Thursday, January 28<\/i>: Work exercises Section 4.3 #17,21,29.
\nFor Friday, January 29<\/i>: Work exercises Section 4.4 # 1,4,6,12,14,17.<\/p>\n

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

For Monday, February 8<\/i>: Work exercises Section 5.2 #1,5,8,14,22,27.
\nFor Tuesday, February 9<\/i>: Work exercises Section 5.3 #1,3.
\nFor Thursday, February 11<\/i>: Work exercises Section 5.3 #10,15,18.
\nFriday, February 12<\/i>: 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. <\/span>
\nFor Tuesday, February 16<\/i>: Work exercises Section 5.5 #2,9,11,14,16,20.
\nFor Thursday, February 18<\/i>: Work exercises Section 5.6 #1,3,9,12,14,22.
\nBring your computers to class Thursday.<\/p>\n

For Monday, September 8<\/i>:
\nTurn in<\/span> the Section 1.2 exercises.
\nSection 1.3 #1,6,9,14,16,17,23,27,32.
\nExtra Credit:
\nGeneralize Exercise 1.2.31(iii)(a) to D<\/i>-digit integers base B<\/i>, where B<\/i> is even.
\n<\/span>
\nFor Tuesday, Setpember 9<\/i>:
\nSection 1.4 #1,7,10,16,22,25,27
\nFor Thursday, September 11<\/i>:
\nWe will have a Quiz<\/span> covering material through Section 1.4.
\nTurn in the Section 1.4 homework.
\nSection 1.5 #1,4,7,9,11.
\nFor Friday, September 12<\/i>:
\nSection 2.1 #3,5,6,8,17.<\/p>\n

For Monday, September 15<\/i>:
\nSection 2.2 #1,6,9,14,15.
\nTurn in<\/span> these exercises on Tuesday.
\nFor Tuesday, September 16<\/i>:
\nTurn in<\/span> the Section 2.2 exercises.
\nSection 2.3 #5,7,11,12.
\nFor Thursday, September 18<\/i>:
\nWe will have a Quiz<\/span> covering through Section 2.3.
\nSection 2.4 #1,4,9,21.
\nFor Friday, September 19<\/i>:
\nSection 2.5 #5,9,14,15,19,21. Turn in<\/span> these exercises on Monday.<\/p>\n

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

For Monday, October 13<\/i>:
\nSection 4.2 #12,14,18.
\nTurn in<\/span> these exercises on Tuesday.
\nFor Tuesay, October 14<\/i>:
\nTurn in<\/span> the six Section 4.2 exercises.
\nSection 4.3 #1,4,9,10,13. Turn in<\/span> these exercises on Friday
\nFor Thursday, October 16<\/i>:
\nSection 4.3 #17,21,29. Turn in<\/span> these exercises on Friday
\nFor Friday, October 17<\/i>:
\nTurn in<\/span> the Section 4.3 exercises.
\nReview the first three sections of Chapter 4. Practice writing induction proofs.<\/p>\n

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

Friday, November 7<\/i>:
\nSection 5.6 #1,3,9,22.
\nFor Monday, November 10<\/i>:
\nTurn in<\/span> the take-home exam.
\nSection 5.6 #5,12,14.
\nFor Tuesday, November 11<\/i>:
\nChapter 5 supplementary exercsies pages 305-306: #2, 10, 11,12,22c.<\/p>\n

\n

 <\/p>\n

Questions from class<\/p>\n

<\/a>To today’s questions<\/span><\/u>
\nIn the “Questions” section, I’ll color the active questions green<\/span> so that they are easier (in theory) to find as you scan through the page. Please let me know<\/span><\/u><\/a> if I’ve missed anything.
\n From Tuesday, January 12<\/i>: A k<\/i>-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<\/i> increases without bound?
\nDetermine 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<\/i> increases without bound?
\nExtra credit will be awarded for solutions turned in by the end of class Friday, January 22.<\/span><\/p>\n

Monday, September 3<\/i>:
\nThe Maple<\/i> command for the binomial coefficient n<\/i> choose k<\/i>
\nis binomial(n,k)<\/tt>
\nTuesday, September 4<\/i>:
\nA commentary about the ABC-conjecture and Mochizuki’s proposed proof is at
\nhttp:\/\/quomodocumque.wordpress.com\/2012\/09\/03\/mochizuki-on-abc\/<\/a>
\nTuesday, September 18<\/i>:
\nFor Extra Credit think about the Dice problem. The two conditions on the dice are<\/p>\n

    \n
  1. No ties are possible<\/li>\n
  2. Each die has an equal chance of displaying the highest number.<\/li>\n<\/ol>\n

    The problem disussed
    \n    in the article we looked at<\/a> 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?<\/i>
    \nWhat is the answer for two dice? How small can the dice be? With k<\/i>-sided dice, how many configurations for 1,2,…2k<\/i> satisfy the conditions?
    \nWhat is the answer for three dice? How small can the dice be?
    \nWith k<\/i>-sided dice, how many configurations for 1,2,…3k<\/i> satisfy the conditions?
    \nExplore similar questions for four dice, five dice, etc.<\/p>\n

    \n

    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
    \n 1 point <\/span>off for turned in late during the class,
    \n 5% <\/span>off for being turned in late the same day,
    \n 10% <\/span>off per day. (weekends count for two days) i.e. 10 days later, it’s too late to get a makeup homework turned in.
    \nWhen writing up homework, you should circle (or otherwise clearly indicate) your answers.
    \nIt’s good to work together, but you should write\/type your own homework. Simply copying another person’s work or Maple<\/i> file will result in a 0 and a letter to the Dean of Students.
    \nYou 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.
    \nIf 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.<\/p>\n