Nevşehir Hacı Bektaş Veli University Course Catalogue
|
|||||
| Year/Semester of Study | 1 / Fall 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 couse is to show that order theory is playing a major role on the mathematical stage and that knowledges acquired in linear algebra and group theory are well understood when their diagrams are drawn and this is the theory of lattices which provides such facilities. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Be able to understand and interpret different algebraic concepts and structures. |
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 | Learn the concepts of source and sink. Perceive the product and coproduct of objects in categories. |
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 | Know the concepts of equaliser and limit. Can build pullback and pushout diagrams |
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 |
|||
| Course Contents | ||
| Ordered sets, diagrams, down-sets, up-sets; Equivalent definitions of lattices as ordered sets and as algebraically; Products of lattices, lattice-homomorphisms, chain conditions, complete lattices; Modular lattices, distributive lattices; Representation of finite lattices; Congruences; Galois connections. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Ordered sets | |
| 2 | Diagrams, down-sets, up-sets | Oral presentation |
| 3 | Equivalent definitions of lattices as ordered sets and as algebraically | Oral presentation |
| 4 | Equivalent definitions of lattices as ordered sets and as algebraically | Oral presentation |
| 5 | Products of lattices, lattice-homomorphisms | Oral presentation |
| 6 | Products of lattices, lattice-homomorphisms | Oral presentation |
| 7 | Chain conditions and complete lattices | Oral presentation |
| 8 | mid-term exam | |
| 9 | Modular lattices, distributive lattices | Oral presentation |
| 10 | Modular lattices, distributive lattices | Oral presentation |
| 11 | Representation of finite lattices | Oral presentation |
| 12 | Representation of finite lattices | Oral presentation |
| 13 | Congruences | Oral presentation |
| 14 | Congruences | Oral presentation |
| 15 | Galois connections | 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). | |
| 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 | ||