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.

Textbook Information
Title:Discrete Mathematics with Applications, 4th Edition click on the book to see a larger image
click to enlarge
Authors:Suzanna Epp
Publisher:Brooks/Cole (Cengage Learning), 2010
ISBN-10:0495391328
ISBN-13:978-0495391326

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

  1. send me an e-mail before the exam, telling me that you are going to miss it because of illness, then
  2. then go to the Hudson Student Health Center.
  3. Later, you will need to bring me documentation from Hudson showing that you were treated there.
Without those three things, you will not be given a make-up.

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 make-up. 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 make-up.

Missing Exams Because of Personal Travel Plans: All of our In-Class 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 make-up 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
In-Class 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 ScorePercentageGradeInterpretation
900 - 100090% - 100%A-, AYou mastered all concepts, with no significant gaps
800 - 89980% - 89.9%B-, B, B+You mastered all essential concepts and many advanced concepts, but have some significant gaps.
700 - 79970% - 79.9%C-, C, C+You mastered most essential concepts and some advanced concepts, but have many significant gaps.
600 - 69960% - 69.9%D-, D, D+You mastered some essential concepts.
0 - 5990% - 59.9%FYou 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 made-up 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.

SectionSuggested Homework Problems (do not turn in)
2.19,14,16,18,25,27,36,41,48,50
2.22,4,7,15,19,20,21,22,23,24,26,30,33,35,41,43
2.34,5,6,7,8,14,18,24,27,29,37,38,40,41
3.11,4,5,7,12,16,17,19,25,28,30,31,33
3.22,3,4,5,12,14,15,19,22,29,32,37,40,42,44,47
3.32,3,4,10,11,12,17,19,23,30,41,42,43,44,56,57,58
3.44,6,11,12,13,14,19,20,24
4.12,5,6,9,13,14,17,20,25,33,35,39,41,43,51,53,54,55,56,57,58,59,60
4.22,6,9,11,14,15,16,18,19,20,21,23
4.31,2,3,9,11,15,20,26,27,29,36,37,38,47
4.42,6,9,10,19,21,22,28,29,30,37,39,40,44,46
4.6 Section 4.6 on Indirect Proofs is a bit of a mess. The book (and many mathematicians) over-uses 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:
  1. Suppose that q = a / b is a rational number. What does that tell you about a and b?
  2. Suppose that q = a / b is a rational number and q is known to be zero. What does that tell you about a and b?
  3. Suppose that q = a / b is a rational number and q is known to be non-zero. What does that tell you about a and b?
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
4.71,2,4,8,11,12,14,15,17,21,22,31
5.12,4,10,11,13,16,20,21,22,26,27,30,31,33,35,36,44,45,46,63,64,65,72,74,76,81
5.21,3,4,6,8,10,13,20,25,28
5.36,7,8,9,10,11,12,13,16,17,19,20,23,29,39
6.19,12,13,15,17,18,21,22,23,24,27,30,31,32,35
6.21,4,7,13,15,23bcd,28,29,31,32
6.37,9,10,11,12,13,16,17,18,19,20,21,28,30,31,32,34,35,39,41,43
7.12,3,4,6,5,6,7,8,11,13,14,15,17,18,19,20,22,30,31,32,33,38,39,41,42,43,46,47
7.24,5,8,9,11,12,13,17,18,23,46,47,48,49,54,55
7.31,4,11,12,14,16,17,18,19,25,26
8.11,3,4,12,13,15,16,21
8.24,5,7,8,9,10,11,13,14,15,16,30,32,33
8.33,5,7,15,16a,20,25,28,29,32,42,45
9.13,5,7,9,11,12,16,18,20
9.21,3,6,7,9,11,12,13,14,16,19,21,22,32,33,34,35,37,38,39,40,41,42,43
9.31,3,11,13,16,18,23,25,31,32,35,37
9.53,5,6,11,16,17,18,19,22,25,27
9.61,3,10,11,16,18,19
AllComplete 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_Relations
WeekDatesMeeting
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 In-Class 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 In-Class 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)
(H6 due) (Solutions)
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 In-Class 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 One-to-One 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 In-Class 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 r-Combinations 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