Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 3 / Fall Semester | ||||
| Level of Course | 1st Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | SEZER SORGUN (ssorgun@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| To teach the basic concepts of discrete mathematics. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can learn the basic principle of counting |
PO-5 Develop suitable material for a subject on a mathematical area, to use the knowledge and experience gains with different methods |
Examination |
| LO-2 | Can know the Burnside – Polya and Möbius Inversion counting and apply their. |
PO-4 Analytically use the interdisciplinary approach at learning process. |
Examination |
| LO-3 | Can learn the Fibonacci, Catalan sequence etc. and know the generator functions of this sequence. |
PO- |
Examination |
| LO-4 | Perceive the combinatorial circuits. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| The basic principles of counting, permutations and combinations, Binomial coefficients and combinatorial identities, the pigeonhole principle, principle of inclusion and exclusion, partitions, Burnside – Polya counting formula, Möbius inversion counting formula, special sequences (Fibonacci, Catalan vb.), the generator functions, recurrence relations, finite differences, Boolean algebra, combinatorial circuits | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | The basic principles of counting | Teaching |
| 2 | Permutations and combinations | Teaching |
| 3 | Binomial coefficients and combinatorial identities | Teaching |
| 4 | The pigeonhole principle | Teaching |
| 5 | Principle of inclusion and exclusion | Teaching |
| 6 | Partitions | Teaching |
| 7 | Burnside – Polya counting formula | Teaching |
| 8 | mid-term exam | |
| 9 | Möbius inversion counting formula | Teaching |
| 10 | Special sequences (Fibonacci, Catalan etc.) | Teaching |
| 11 | The generator functions | Teaching |
| 12 | Recurrence relations | Teaching |
| 13 | Finite differences | Teaching |
| 14 | Boolean algebra | TeachingTeaching |
| 15 | Combinatorial circuits | Teaching |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Kenneth H. Rosen, Discrete Mathematics and Its Applications, 7th Edition McGraw-Hill Companies, Inc., 2012 | |
| 2 | Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, 5th Edition, Pearson Addison Wesley, 2004. | |
| Required Course instruments and materials | ||
| Books and lecture notes | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 4 | 14 | 56 |
| Outside Class | |||
| a) Reading | 2 | 14 | 28 |
| b) Search in internet/Library | 3 | 14 | 42 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 4 | 7 | 28 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 4 | 7 | 28 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 186 | ||