Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Spring Semester | ||||
| Level of Course | 2nd 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 | |||||
| The purpose of this course is to gain information and skills related with the generating functions and binomial formulas. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can explain the advanced concepts of generating functions, partition polynomials and operators. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. PO-5 Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. PO-17 Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Generating functions, partition polynomials, Forward and backward operators. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Generating Functions | Questioning-Answering, Problem solving |
| 2 | Products of generating functions | Questioning-Answering, Problem solving |
| 3 | Multisection of series | Questioning-Answering, Problem solving |
| 4 | Cycles of binomial coefficients | Questioning-Answering, Problem solving |
| 5 | Lagrange series | Questioning-Answering, Problem solving |
| 6 | Partition polynomials | Questioning-Answering, Problem solving |
| 7 | Bell polinomları | Questioning-Answering, Problem solving |
| 8 | mid-term exam | |
| 9 | Bell polynomial inverses | Questioning-Answering, Problem solving |
| 10 | Polynomials for derivatives of inverse functions | Questioning-Answering, Problem solving |
| 11 | partition polynomials in number theory | Questioning-Answering, Problem solving |
| 12 | Operators | Questioning-Answering, Problem solving |
| 13 | Delta difference operator | Questioning-Answering, Problem solving |
| 14 | Forward and backward difference operators | Questioning-Answering, Problem solving |
| 15 | Central difference operator | Questioning-Answering, Problem solving |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Riordan, J. (1968). Combinatorial identities (Vol. 6). New York: Wiley. | |
| Required Course instruments and materials | ||
| 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) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 3 | 14 | 42 |
| b) Search in internet/Library | 2 | 7 | 14 |
| c) Performance Project | 2 | 8 | 16 |
| 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 | 3 | 8 | 24 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 3 | 13 | 39 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 181 | ||