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 | SURE KÖME (sure.kome@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 for the student to have detailed knowledge of quantum analysis theory. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can recognize the concept of q-hypergeometric functions. |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. 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. |
Examination |
| LO-2 | Can analyze Heine Binomial Formula. |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. 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. |
Examination |
| LO-3 | Can recognize the concept of q-integral. |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. 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. |
Examination |
| LO-4 | Can learn q-Gamma and q-Beta functions. |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. 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. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| q-Hypergeometric functions, Heine Binom Formula, q-Integral, q-Gamma and q-Beta Functions. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | q-Hypergeometric functions and Heine’s binomial formula | Oral expression, discussion, question-answer |
| 2 | More information on Heine’s binomial formula | Oral expression, discussion, question-answer |
| 3 | Ramanujan product formula | Oral expression, discussion, question-answer |
| 4 | Explicit formulas for Sums of two and four squares | Oral expression, discussion, question-answer |
| 5 | Explicit formulas for Sums of two and four triangular numbers | Oral expression, discussion, question-answer |
| 6 | Introduction to q-integral | Oral expression, discussion, question-answer |
| 7 | More information on q-integral | Oral expression, discussion, question-answer |
| 8 | mid-term exam | |
| 9 | Jackson integral | Oral expression, discussion, question-answer |
| 10 | Fundamental theorem of q-calculus | Oral expression, discussion, question-answer |
| 11 | q-Gamma functions | Oral expression, discussion, question-answer |
| 12 | q-Beta functions | Oral expression, discussion, question-answer |
| 13 | Article review including applications of q-analysis topic-1 | Oral expression, discussion, question-answer |
| 14 | Article review including applications of q-analysis topic-2 | Oral expression, discussion, question-answer |
| 15 | Article review including applications of q-analysis topic-3 | Oral expression, discussion, question-answer |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Kac, Victor, and Pokman Cheung. Quantum calculus. Springer Science & Business Media, 2001. | |
| Required Course instruments and materials | ||
| 1) Textbooks - Victor Kac, Pokman Cheung, Quantum Calculus, Springer, 2001. 2) 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) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 0 | ||
| b) Search in internet/Library | 0 | ||
| 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 | 4 | 16 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 5 | 4 | 20 |
| final exam | 2 | 1 | 2 |
| Individual study before class | 2 | 14 | 28 |
| Individual study after class | 5 | 14 | 70 |
| Total work load; | 180 | ||