Campus:  Ohio University, Athens Campus 

Department:  Mathematics 
Academic Year:  2017  2018 
Term:  Spring Semester 
Course:  Math 3050 
Title:  Discrete Mathematics 
Section:  101 (Class Number 8439) 
Instructor:  Mark Barsamian 
Contact Information:  My contact information is posted on my web page. 
Office Hours:  My office hours are posted on my web page. 
Course Description: Course in discrete mathematical structures and their applications with an introduction to methods of proofs. The main topics are introductions to logic and elementary set theory, basic number theory, induction and recursion, counting techniques, graph theory and algorithms. Applications may include discrete and network optimization, discrete probability and algorithmic efficiency.
Prerequisites: MATH 113 or MATH 1200 or Placement level 2 or higher.
Note: Students cannot earn credit for both MATH 3050 and either of CS 3000. (If a student takes both courses, the first course taken is deducted.)
Class meetings: Section 101 (Class Number 8439) Meets Mon, Wed, Fri 10:45am  11:40am in Morton Hall Room 218.
Syllabus: For Section 101 (Class Number 3763), this web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), print this web page.
Calculators will not be allowed on exams.
Websites with Useful Math Software: In lectures, I often use a computer for calculating. The software that I use is free and is easily accessible at the following list of links. I use the same software in my office, instead of a calculator. You are encouraged to use this same free software instead of a calculator. (Link)
Special Needs: If you have physical, psychiatric, or learning disabilities that require accommodations, please let me know as soon as possible so that your needs may be appropriately met.
Attendance Policy: Attendance is required for all lectures and exams, and will be recorded.
Missing Class: If you miss a class for any reason, it is your responsibility to copy someone’s notes or download my notes from the course web page, and study them. I will not use office hours to teach topics discussed in class to students who were absent.
Missing an Exam Because of Illness: If you are too sick to take an exam, then you must
Missing Exams Because of University Activity: If you have a University Activity that conflicts with one of our exams, you must contact me before the exam to discuss arrangements for a makeup. I will need to see documentation of your activity. If you miss an exam because of a University Activity without notifying me in advance, you will not be given a makeup.
Missing Exams Because of Personal Travel Plans: All of our InClass Exams are on Fridays. Please don't bother asking me if you can make up an exam, or take it early, because your ride home is leaving earlier in the day, or because you already bought a plane ticket with an early departure time. The answer is, No you may not have a makeup exam, or take the exam early. You will just have to change your travel plans or forfeit that exam.
Cheating on Exams: If cheat on an exam, you will receive a zero on that exam and I will submit a report to the Office of Community Standards and Student Responsibility (OCSSR). If you cheat on another exam, you will receive a grade of F in the course and I will again submit a report to the OCSSR.
Grading for Section 101: During the semester, you will accumulate points as described in the table below. (Note that no scores are dropped.)
Class Presentations (10 presentations, 10 points each)  100 points possible 
Homework (10 assignments, 20 points each):  200 points possible 
InClass Exams (best 3 of 4 exams, 150 points each):  450 points possible 
Cumulative Final Exam:  250 points possible 
Total:  1000 points possible 
At the end of the semester, your Total will be converted to your Course Grade as described in the table below. (Note that there is no curve.)
Total Score  Percentage  Grade  Interpretation 

900  1000  90%  100%  A, A  You mastered all concepts, with no significant gaps 
800  899  80%  89.9%  B, B, B+  You mastered all essential concepts and many advanced concepts, but have some significant gaps. 
700  799  70%  79.9%  C, C, C+  You mastered most essential concepts and some advanced concepts, but have many significant gaps. 
600  699  60%  69.9%  D, D, D+  You mastered some essential concepts. 
0  599  0%  59.9%  F  You did not master essential concepts. 
Blackboard Gradebook: Throughout the semester, your current scores and current course grade will be available in an online gradebook on the Blackboard system.
Class Presentations: Each of you will be called upon to make class presentations ten times during the semester. Sometimes these presentations will be about introducing a new concept to the class. Other times, the presentations will involve presenting an example that illustrates a new concept. They will always involve new concepts, which means that to prepare for them, you will need to learn material that has not yet been presented in class. You will always receive your presentation assignment at least a week before you have to make the presentation, and you are welcome to come and discuss your assignment with me in the week before your presentation. Please note that the Class Presentations cannot be madeup in the case of absence, because they involve material that is part of a class lesson plan.
The daily Class Presentation Assignments can be found at the links in the course calendar below. They can also be found at this link: (Class Presentation Assignments)
Homework: One learns math primarily by trying to solve problems. For that reason, homework plays a central role in Math 3050 Section 101. There are two kinds of homework: suggested homework problems and assigned homework sets.
The suggested homework problems, shown in the table below, are selected from the textbook. These problems are not to be turned in and are not part of your grade. But in order to learn the material covered in the course, you should do as many of the suggested problems as possible and keep your solutions in a notebook for study.
Section  Suggested Homework Problems (do not turn in) 

2.1  9,14,16,18,25,27,36,41,48,50 
2.2  2,4,7,15,19,20,21,22,23,24,26,30,33,35,41,43 
2.3  4,5,6,7,8,14,18,24,27,29,37,38,40,41 
3.1  1,4,5,7,12,16,17,19,25,28,30,31,33 
3.2  2,3,4,5,12,14,15,19,22,29,32,37,40,42,44,47 
3.3  2,3,4,10,11,12,17,19,23,30,41,42,43,44,56,57,58 
3.4  4,6,11,12,13,14,19,20,24 
4.1  2,5,6,9,13,14,17,20,25,33,35,39,41,43,51,53,54,55,56,57,58,59,60 
4.2  2,6,9,11,14,15,16,18,19,20,21,23 
4.3  1,2,3,9,11,15,20,26,27,29,36,37,38,47 
4.4  2,6,9,10,19,21,22,28,29,30,37,39,40,44,46 
4.6  Section 4.6 on Indirect Proofs is a bit of a mess. The book (and many mathematicians) overuses the method of Proof by Contradiction. I feel that many indirect proofs that are commonly done using contradiction can be more easily done by using the indirect method of simply proving the Contrapositive. And some proofs that are commonly done as proofs by contradiction can actually be proven most clearly with a Direct Proof. So I have particular instructions for the exercises in this section, and many of my particular instructions are different from the book's instructions. 
Questions about rational and irrational numbers: 4.6 # 2 and these Three Extra Questions:


Exercises to be proven directly, not using contradiction or contraposition: 4.6 # 5,6,7  
More exercises to be proven directly, not using contradiction or contraposition: 4.6 # 4, 13 (The key to these two exercises is to use Theorem 4.4.1 The Quotient Remainder Theorem. Furthermore, on #13, you will need to use use two cases: m odd or m even. It is in the even case that you should use the Quotient Remainder Theorem.)  
Exercises to be proven indirectly, by proving the contrapositive: 4.6 # 10,20,22,24,25,26,27,28  
Exercises to be proven indirectly, by using the Method of Contradiction: 4.6 # 12,15  
4.7  1,2,4,8,11,12,14,15,17,21,22,31 
5.1  2,4,10,11,13,16,20,21,22,26,27,30,31,33,35,36,44,45,46,63,64,65,72,74,76,81 
5.2  1,3,4,6,8,10,13,20,25,28 
5.3  6,7,8,9,10,11,12,13,16,17,19,20,23,29,39 
6.1  9,12,13,15,17,18,21,22,23,24,27,30,31,32,35 
6.2  1,4,7,13,15,23bcd,28,29,31,32 
6.3  7,9,10,11,12,13,16,17,18,19,20,21,28,30,31,32,34,35,39,41,43 
7.1  2,3,4,6,5,6,7,8,11,13,14,15,17,18,19,20,22,30,31,32,33,38,39,41,42,43,46,47 
7.2  4,5,8,9,11,12,13,17,18,23,46,47,48,49,54,55 
7.3  1,4,11,12,14,16,17,18,19,25,26 
8.1  1,3,4,12,13,15,16,21 
8.2  4,5,7,8,9,10,11,13,14,15,16,30,32,33 
8.3  3,5,7,15,16a,20,25,28,29,32,42,45 
9.1  3,5,7,9,11,12,16,18,20 
9.2  1,3,6,7,9,11,12,13,14,16,19,21,22,32,33,34,35,37,38,39,40,41,42,43 
9.3  1,3,11,13,16,18,23,25,31,32,35,37 
9.5  3,5,6,11,16,17,18,19,22,25,27 
9.6  1,3,10,11,16,18,19 
All  Complete list of all Suggested Homework Problems 
The ten assigned homework sets are to be turned in and will be graded. The problems for each homework set are provided on the cover sheet found at the link provided in the list below. For each of the assigned homework sets, you should do the following:
Assigned Homework Sets (turn in)
Calendar for 2017  2018 Spring Semester MATH 3050 Section 101 (Class Number 8439)
Worksheets_on_Properties_of_RelationsWeek  Dates  Meeting Number  Class topics 

1  Wed Jan 17  1  2.1 Logical form and Logical Equivalence 
Fri Jan 19  2  2.2 Conditional Statements (Class Presentation Assignments)  
2  Mon Jan 22  3  2.3 Valid and Invalid Arguments (CPA)(Argument Forms) (H1 due) 
Wed Jan 24  4  3.1 Predicates and Quantified Statements I (CPA)  
Fri Jan 26  5  3.2 Predicates and Quantified Statements II (CPA)  
3  Mon Jan 29  6  3.3 Statements with Multiple Quantifiers (CPA) (H2 due) 
Wed Jan 31  7  3.4 Arguments with Quantified Statements (CPA)(Universal Argument Forms)  
Fri Feb 2  8  InClass Exam 1 Covering Chapters 2 and 3  
4  Mon Feb 5  9  4.1 Direct Proof and Counterexample I: Introduction (CPA) 
Wed Feb 7  10  4.2 Direct Proof and Counterexample II: Rational Numbers (CPA)  
Fri Feb 9  11  4.3 Direct Proof and Counterexample III: Divisibility (CPA) (H3 due) 

5  Mon Feb 12  12  4.4 Direct Proof and Counterexample IV: Division into Cases (CPA) 
Wed Feb 14  13  4.6 Indirect Argument: Contradiction and Contraposition (CPA) (H4 due) 

Fri Feb 16  14  4.7 Indirect Argument: Two Classical Theorems (CPA)(Class Drill on Square Roots)(Handout on Fermat's Theorem)  
6  Mon Feb 19  15  InClass Exam 2 Covering Chapter 4 
Wed Feb 21  16  5.1 Sequences (Class Drill on Sequences, Summations, Products) (CPA)  
Fri Feb 23  17  5.1 Sequences (CPA) (Handout on Induction)  
7  Mon Feb 26  No Class  University Closed: No Class 
Wed Feb 28  18  5.2 Mathematical Induction I (Handout on Induction) (CPA)  
Fri Mar 2  19  5.2 Mathematical Induction I (CPA) (H5 due) 

8  Mon Mar 5  20  5.3 Mathematical Induction II (CPA) 
Wed Mar 7  21  6.1 Set Theory: Definitions and the Element Method of Proof (CPA)  
Fri Mar 9  22  6.2 Properties of Sets (CPA)  
9  Mon Mar 12  No Class  Spring Break 
Wed Mar 17  
Fri Mar 16  
10  Mon Mar 19  23  6.3 Disproofs, Algebraic Proofs (CPA)(Theorem 6.2.2 Set Identitites) 
Wed Mar 21  24  InClass Exam 3 Covering Chapters 5 and 6  
Fri Mar 23  25  7.1 Functions Defined on General Sets (Class Drills on Functions) (CPA)  
11  Mon Mar 26  26  7.2 OnetoOne Functions, Onto Functions (Line Tests) (CPA) 
Wed Mar 28  27  7.2 Inverse Functions (Graphing an Inverse Map) (Inverse Functions) (CPA)  
Fri Mar 30  28  7.3 Composition of Functions (CPA) (Inverse Functions And Composition) (H7 due) 

12  Mon Apr 2  29  Leftovers from Section 7.3 Composition of Functions (Inverse Functions And Composition) 
Wed Apr 4  30  8.1 Relations and Sets; 8.2 Reflexivity, Symmetry, and Transitivity (CPA)  
Fri Apr 6  31  8.2 Reflexivity, Symmetry, and Transitivity (CPA) (H8 due)  
13  Mon Apr 9  32  8.3 Equivalence Relations (Worksheet on Relations)(Solutions) 
Wed Apr 11  33  InClass Exam 4 Covering Chapters 7 and 8 (Exam Information)  
Fri Apr 13  34  9.1 Introduction to Counting (CPA)  
14  Mon Apr 16  35  9.2 Possibility Trees and the Multiplication Rule (CPA) 
Wed Apr 18  36  9.2 Possibility Trees and the Multiplication Rule (CPA) (H9 due) 

Fri Apr 20  37  9.3 Counting Elements of Disjoint Sets: The Addition Rule (CPA)  
15  Mon Apr 23  38  9.5 Counting Subsets of a Set: Combinations (CPA) 
Wed Apr 25  39  9.6 rCombinations with Repetition Allowed (CPA) (H10 due) 

Fri Apr Apr 27  40  Course Review (CPA)  
16  Mon April 30  41  Final Exam 10:10am  12:10pm in Morton 218 (Exam Information) 
(page maintained by Mark Barsamian, last updated Apr 23, 2018