Elementary Mathematics Education  
Bachelor  Length of the Programme: 4  Number of Credits: 240  TRNQFHE: Level 6  QFEHEA: First Cycle  EQF: Level 6 
School/Faculty/Institute  Faculty of Education  
Course Code  MATH 137  
Course Title in English  Introduction to Discrete Mathematics  
Course Title in Turkish  Introduction to Discrete Mathematics  
Language of Instruction  EN  
Type of Course  Lecture  
Level of Course  Seçiniz  
Semester  Fall  
Contact Hours per Week 


Estimated Student Workload  112 hours per semester  
Number of Credits  5 ECTS  
Grading Mode  Standard Letter Grade  
Prerequisites  None  
Corequisites  None  
Expected Prior Knowledge  None  
Registration Restrictions  Only Undergraduate Students  
Overall Educational Objective  To understand the basic algorithms on discrete mathematics structure.  
Course Description  Logic, basics of computer algorithms, methods of proof, proving mathematical statements in elementary number theory, problems on counting. 
Course Learning Outcomes and CompetencesUpon successful completion of the course, the learner is expected to be able to:1) exhibit reading, writing, and questioning skills in mathematics, more specifically discrete mathematics 2) understand logical arguments and how a simple computer algorithm is designed 3) use inductive and deductive reasoning skills necessary for their educational profession 4) come up with ideas to develop approaches to prove mathematical statements. 5) demonstrate relational understanding of logic and discrete structures by knowing the purpose of Discrete Mathematics 6) appreciate Discrete Mathematics as a coherent body of knowledge and as a human accomplishment. 
Program Learning Outcomes/Course Learning Outcomes  1  2  3  4  5  6 

1) Apply effective and studentcentered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills.  
2) Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics.  
3) Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics.  
4) Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs.  
5) Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning.  
6) Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness.  
7) Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multidisciplinary as well as take individual responsibility when they work alone.  
8) Have awareness of need for lifelong learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways.  
9) Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources.  
10) Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio.  
11) Have awareness of and sensitivity to different cultures, values and students’ democratic rights.  
12) Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws.  
13) Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities.  
14) Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. 
N None  S Supportive  H Highly Related 
Program Outcomes and Competences  Level  Assessed by  
1)  Apply effective and studentcentered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills.  S  Exam 
2)  Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics.  N  
3)  Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics.  H  Exam,Derse Katılım,Proje 
4)  Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs.  S  Derse Katılım 
5)  Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning.  N  
6)  Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness.  N  
7)  Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multidisciplinary as well as take individual responsibility when they work alone.  H  Derse Katılım,Proje 
8)  Have awareness of need for lifelong learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways.  S  Exam,Derse Katılım,Proje 
9)  Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources.  S  Proje 
10)  Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio.  S  Select,Derse Katılım 
11)  Have awareness of and sensitivity to different cultures, values and students’ democratic rights.  N  
12)  Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws.  N  
13)  Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities.  N  
14)  Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology.  N 
Prepared by and Date  İLKER ARSLAN , 
Course Coordinator  BENGİ BİRGİLİ 
Semester  Fall 
Name of Instructor  Asst. Prof. Dr. İLKER ARSLAN 
Week  Subject 
1)  Statements, variables • Universal, and conditional statements • The SetRoster and SetBuilder Notations; Cartesian Products • Relations, Functions 
2)  • Compound statements • Evaluating truth values • Logical equivalences, tautologies and contradictions 
3)  • Logical equivalences of conditional statements • The negation of a conditional statement • The contrapositive of a conditional statement • The converse and inverse of a conditional statement 
4)  • Modus Ponens and Modus Tollens • Rules of inference • Fallacies • Contradictions and valid arguments • Predicates and quantified statements • The universal and the existential quantifier • Formal versus informal 
5)  Negations of quantified and universal conditional statements • The relation among existential, universal quantifier, conjunction and adjunction 
6)  Vacuous (by default) truth of universal statements • Variant of universal conditional statements • Statements with multiple quantifier • Arguments with quantified statements 
7)  • Variables and structures in Python • "ifelse" codes • For and while loops • Designing simple algorithms 
8)  Midterm 
9)  • Proof methods (direct proof, counter example, proof by taking contrapositive) 
10)  • Proving properties of numbers and elementary number theoretical statements (divisibility, factorisation,…) 
11)  Induction and strong induction (proving about sequences, sums, products by this method) 
12)  Rules for counting (addition and multiplication rules) • Permutation, Combination 
13)  • Inclusion and exclusion principle • Pigeonhole principle 
14)  • Applying counting rules to various types of problems 
15)  Final Examination Period 
16)  Final Examination Period 
Required/Recommended Readings  Required Textbooks: 1. Discrete Mathematics and its Applications,7th Edition, Kenneth H. Rosen. Recommended Textbooks: 1. Discrete Mathematics with Applications, Fourth Edition. Susanna S. Epp. 2. Discrete and Combinatorial Mathematics. Fifth Edition. Ralph Grimaldi.  
Teaching Methods  • Flipped Classroom model will be used while teaching Discrete Mathematics. Students will gain first exposure to new course material outside of class, usually via reading or watching lecture videos/audios, and then class time will be used to assimilate that prior mathematical knowledge through problemsolving or classroom discourse. • Students will access key Discrete Mathematics content individually or in small groups prior to class time, generate their questions, underline the points that they find most difficult or hardly understand, and then meet facetoface in the larger group with similar misunderstandings to explore content through active learning and engagement strategies. • Students will take the responsibility of their own learning, and study core content either individually or in groups before class and then apply mathematical knowledge and skills to a range of activities using higher order thinking. • Lecturing is still important but there will be a greater focus on gaining significant learning opportunities through facilitating active learning of mathematics, engaging students in the use of mathematical language, guiding learning, correcting misunderstandings and providing timely feedback, etc. • In the Flipped Classroom setting, there will be a greater focus on concept exploration, meaning making, and demonstration or application of mathematical knowledge facetoface. • Students are expected to watch the relevant week’s video/audio before attending to the class, and track their progress toward fulfilling the requirements of the course.  
Homework and Projects  The course is of an abstract nature compared to most other courses; comprehension of the mathematical arguments and a careful reading of the lecture notes or the textbook are important. It should be noted that an important part of the homework assigned is reading the required textbook. This is a study habit that many students are not accustomed to, but is essential to thoroughly understanding the course. Students should attempt to solve all of the questions at the end of each chapter, and regularly keep in touch with the instructor about questions that they cannot solve. Homework will not be graded or corrected. Students are strongly recommended to have the suggested textbook in order to fully understand the course and successfully solve the problems in the worksheets.  
Laboratory Work  None  
Computer Use  There are applications of logic to designing algorithms on computer.  
Other Activities  None  
Assessment Methods 


Course Administration 
arslanil@mef.edu.tr +90 212 395 36 16 5th floor 
Activity  No/Weeks  Hours  Calculation  
No/Weeks per Semester  Preparing for the Activity  Spent in the Activity Itself  Completing the Activity Requirements  
Course Hours  14  1  2  1  56  
Laboratory  7  1  1  14  
Presentations / Seminar  1  10  10  
Midterm(s)  1  12  2  14  
Final Examination  1  16  2  18  
Total Workload  112  
Total Workload/25  4.5  
ECTS  5 