| School/Faculty/Institute | Faculty of Education | |||||
| Course Code | MATH 139 | |||||
| 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 | Introductory | |||||
| Semester | Fall | |||||
| Contact Hours per Week |
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| Estimated Student Workload | 112 hours per semester | |||||
| Number of Credits | 4 ECTS | |||||
| Grading Mode | Standard Letter Grade | |||||
| Pre-requisites | None | |||||
| Expected Prior Knowledge | None | |||||
| Co-requisites | 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 Description in Turkish | Mantık, bilgisayar algoritması temelleri, ispat metodları, sayılar teorisindeki matematiksel ifadeleri ispatlama, sayma problemleri |
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) Thorough knowledge of the major concepts, theoretical perspectives, empirical findings, and historical trends in psychology. | ||||||
| 2) Understanding of and ability to apply essential research methods in psychology, including research design, data analysis, and data interpretation. | ||||||
| 3) Competence to use critical and creative thinking, skeptical inquiry and a scientific approach to solving problems related to behavior and mental processes. | ||||||
| 4) Understanding and ability to apply psychological principles, skills and values in personal, social, and organizational contexts. | ||||||
| 5) Ability to weigh evidence, to tolerate ambiguity, and to reflect other values that underpin psychology as a discipline. | ||||||
| 6) Internalization and dissemination of professional ethical standards. | ||||||
| 7) Demonstration of competence in information technologies, and the ability to use computer and other technologies for purposes related to the pursuit of knowledge in psychology and the broader social sciences. | ||||||
| 8) Skills to communicate the knowledge of psychological science effectively, in a variety of formats, in both Turkish and in English (in English, at least CEFR B2 level). | ||||||
| 9) Recognition, understanding, and respect for the complexity of sociocultural and international diversity. | ||||||
| 10) Recognition for the need for, and the skills to pursue, lifelong learning, inquiry, and self-improvement. | ||||||
| 11) Ability to formulate critical hypotheses based on psychological theory and literature, and design studies to test those hypotheses. | ||||||
| 12) Ability to acquire knowledge independently, and to plan one’s own learning. | ||||||
| 13) Demonstration of advanced competence in the clarity and composition of written work and presentations. |
| N None | S Supportive | H Highly Related |
| Program Outcomes and Competences | Level | Assessed by | |
| 1) | Thorough knowledge of the major concepts, theoretical perspectives, empirical findings, and historical trends in psychology. | N | |
| 2) | Understanding of and ability to apply essential research methods in psychology, including research design, data analysis, and data interpretation. | N | |
| 3) | Competence to use critical and creative thinking, skeptical inquiry and a scientific approach to solving problems related to behavior and mental processes. | H | Exam,HW,Participation |
| 4) | Understanding and ability to apply psychological principles, skills and values in personal, social, and organizational contexts. | N | |
| 5) | Ability to weigh evidence, to tolerate ambiguity, and to reflect other values that underpin psychology as a discipline. | N | |
| 6) | Internalization and dissemination of professional ethical standards. | N | |
| 7) | Demonstration of competence in information technologies, and the ability to use computer and other technologies for purposes related to the pursuit of knowledge in psychology and the broader social sciences. | N | |
| 8) | Skills to communicate the knowledge of psychological science effectively, in a variety of formats, in both Turkish and in English (in English, at least CEFR B2 level). | N | |
| 9) | Recognition, understanding, and respect for the complexity of sociocultural and international diversity. | S | Participation |
| 10) | Recognition for the need for, and the skills to pursue, lifelong learning, inquiry, and self-improvement. | S | HW,Participation |
| 11) | Ability to formulate critical hypotheses based on psychological theory and literature, and design studies to test those hypotheses. | N | |
| 12) | Ability to acquire knowledge independently, and to plan one’s own learning. | S | Exam,HW |
| 13) | Demonstration of advanced competence in the clarity and composition of written work and presentations. | H | Exam,HW |
| Prepared by and Date | İLKER ARSLAN , May 2018 |
| Course Coordinator | BENGİ BİRGİLİ |
| Semester | Fall |
| Name of Instructor | Asst. Prof. Dr. İLKER ARSLAN |
| Week | Subject |
| 1) | Statements, variables • Universal, and conditional statements • The Set-Roster and Set-Builder 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 • "if-else" 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 problem-solving 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 face-to-face 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 face-to-face. • 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 |
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| Course Administration |
arslanil@mef.edu.tr +90 212 395 36 16 5th Floor |
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| 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 | 4 | ||||||