Math 2513 - 002     Discrete Mathematical Structures         Spring 2016

Course Handouts and Information

• The class meets in PHSC 416 on MWF 11:30am-12:20pm.
• Dr Brady's Office Hours.   Mon 10:20a-11:20a,   Tue 10:30a-11:30a,   Thu 11:30a-12:30p.
• Information Sheet Up to date.
• Solutions to in class proof activities.
• Solutions to in class proof activities.
• Handout on properties of the real numbers.
• Examples using the definition of continuity.
• Examples of doubly quantified statements in class.
• Here is a handout which summarizes the material covered in class on Friday and Monday on congruences.
• Here is a review sheet/list of topics for midterm 1.
• Here is a set of solutions to Mid I, and a blank exam.
• Here are some comments about Q3 of Mid I and some other comments.
• Here is a handout on the Division Algorithm.
• Here is the Least Principle handout.
  It has been updated to keep with the gcd notation used in lectures.
• The following handout is meant to help you read the section on the equivalence of the Least Principle and Induction in the previous handout.
  It has been updated to include a proof by Least Principle of a statement that is often used in textbooks as the prototypical example for proofs by Induction.
• Here are solutions to the "Die Hard" class activity problems.
• Solutions to the Division Algorithm applications homework
• The class handout on topics in elementary number theory.
• The class handout on the idea behind public key cryptography.
• Solutions to Midterm II and a blank exam.
• Here is the class handout on permutations.
• Here is a handout on group theory.
• Here are solutions to Midterm III and a blank exam.
• Here is a handout on symmetries of the cube.

Messages

• Midterm I is held in class on Friday, Feb 12.
  It covers chapters 1, 2 and 3 (through section 3.3) of the book and whatever class notes we used to supplement this reading material.
  Look at the handouts above for good review material.
• Midterm II is held in class on Friday, Mar 11. This handout contains information about topics covered etc.
• Midterm III is held in class on Friday, Apr 22. This handout contains information about topics covered etc.
• Here is an old midterm III exam. There are solutions posted online on the 2014 class page.
  Here are other old exam questions.
• Some old final exams here and here.
• Recall that the final exam takes place in PHSC 416 from 1:30-3:30pm on Tuesday, May 10, 2016.
• Here is a sheet that will be provided with the final examination.

Homework

• [01]. Due Wed 01/27.   P 27:   4(a,b), 5(a).
• [02]. Due Mon 02/01.   Pp 40+:   1, 2, 5.   Pp 48+: 1, 7, 10.
• [03]. Due Fri 02/05.   Pp 62+:   4, 5.   Pp 74+: 1, 2(a,b,c), 11, 12(a,d).
  Also look at (but don't turn in) 12(b,c), 14,15.
• [04]. Due Mon 02/08.   Pp 96+:   1c, 5, 7a,b.   Pp 112+:   4a,b.   Pp 126+:   6a,b,c,d, 7c.
• [04]* Due Mon 02/15.   Read the handout (posted above) on the Division Algorithm before class on Monday.
  We will have class activities based on this on Monday.
• [05]. Due Fri 02/19. Do this homework set. They are the problems we started on in class.
• [06]. Due Fri 02/26. Do questions 2, 4, 6, 8, 11, 17, 18, 19, and 21 from the induction handout.
• [07] Due Mon 02/29.   Do all 5 Strong Induction problems on page three of the updated induction handout.
  refresh your browser to ensure that you have the updated version.
  Start reading chapter 8 of the text (greatest common divisors) for Monday's class.
• [08]. Due Fri 03/04.   Pp 424+:   1(a,c,f), 5(a,b,d).   Pp 436+:   5(a,b), 7(a,b,c), and these two additional problems.
  Let m be an integer which is not the 10th power of another integer. Prove that the 10th root of m is irrational.
  Prove that the logarithm of 15 to the base 12 is an irrational number.
• [09]. Due Mon 03/07.   Do the problems in items 14 and 19 of the elementary number theory handout.
  An extra hint for "mod pq" portion of 19 is provided as item 20 of the online version of the handout.
• [10]. Due Fri 03/25.   Do questions 1(b), 1(d), 2(b), 2(d) from here and questions 4(a), 4(b) and 7 from here.
• [11]. Due Wed 03/30.   Pg 227.   Q11 (4 separate diagrams).   Pp 239+.   Q4, Q7(a,b), Q13.
• [12]. Due Mon 04/04.   Do the questions on this handout on images and pre-images.
• [13]. Due Wed 04/13.   Do questions 9, 10, 11 from this handout on bijections. Also do the questions on this sheet about permutations.

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