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 | HATİCE TOPCU (hatice.kamit@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| The aim of this course is that after the acqusition of basic concepts in Introduction to Lattice Theory I, lattices are investigated, as it is the case recent years, in point of topology and modal logic. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Be able to make up ways of forming and determine mathematical theorems |
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. |
Examination |
| LO-2 | Be able to exemplify the theorems and the 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. |
Examination |
| LO-3 | Be able to apply the ability of abstract thinking to solving problem. |
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 | Be able to remember which approaches can be used for problem solving. |
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 | ||
| Complete Partially Ordered sets, fix point theorems and calculating fix points; Maximallity principles; Zorn’Lemma and Axiom of Choice; Prime and maximal ideals, prime filters and ultrafilters; Representation of general lattices; Stone’s Representation Theorem for Boolean algebras; Lindenbaum algebra; Modal logic and, logic and topology of S4. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Complete Partially Ordered sets, fix point theorems and calculating fix points | Oral presentation |
| 2 | Complete Partially Ordered sets, fix point theorems and calculating fix points | Oral presentation |
| 3 | Maximallity principles | Oral presentation |
| 4 | Zorn’Lemma and Axiom of Choice | Oral presentation |
| 5 | Zorn’Lemma and Axiom of Choice | Oral presentation |
| 6 | Prime and maximal ideals | Oral presentation |
| 7 | Prime and maximal ideals | Oral presentation |
| 8 | mid-term exam | |
| 9 | Representation of general lattices | Oral presentation |
| 10 | Stone’s Representation Theorem for Boolean algebras | Oral presentation |
| 11 | Stone’s Representation Theorem for Boolean algebras | Oral presentation |
| 12 | Lindenbaum algebra | Oral presentation |
| 13 | Modal logic | Oral presentation |
| 14 | Modal logic | Oral presentation |
| 15 | Logic and topology of S4 | Oral presentation |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Burris, S. and Sankappanavar, H. P., “A Course in Universal Algebra”; Springer-Verlag New York, (1981). | |
| 2 | Davey, B. A. and Priestley, H. A.; “Introduction to Lattices and Order”; Cambridge University Press; (2002). | |
| 3 | Haim, M.; “Duality for Lattices with Operators: A Modal Logic Approach”; MOL-2000-02; Universiteit van Amsterdam, (2000). | |
| 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 | 5 | 14 | 70 |
| b) Search in internet/Library | 2 | 14 | 28 |
| 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 |
| 0 | |||
| 0 | |||
| Total work load; | 180 | ||