ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE

Syllabus ( MATH 621 )


   Basic information
Course title: Lattice Theory
Course code: MATH 621
Lecturer: Prof. Dr. Mustafa AKKURT
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 2016-2017, Fall and Spring
Level of course: Third Cycle (Doctoral)
Type of course: Area Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: none
Professional practice: No
Purpose of the course: The objective of this course is to introduce Partial order and lattice theory, and how useful this theory in other discipline of mathematics such as algebra, and number theory and group theory. This theory also plays an important role in many disciplines other than mathematics such as computer science and engineering.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Learning ordered sets; their diagrams; maps between ordered sets; maximal and minimal elements; and building new ordered sets.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics in a specialized way
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Work effectively in multi-disciplinary research teams
    4. Design and conduct research projects independently
    5. Develop mathematical, communicative, problem-solving, brainstorming skills.
    6. Effectively express his/her research ideas and findings both orally and in writing

    Method of assessment

    1. Written exam
  2. Learning lattices as ordered sets; complete lattices; chain conditions and completeness;

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics in a specialized way
    2. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
    3. Acquire scientific knowledge and work independently,
    4. Work effectively in multi-disciplinary research teams
    5. Develop mathematical, communicative, problem-solving, brainstorming skills.
    6. Support his/her ideas with various arguments and present them clearly to a range of audience, formally and informally through a variety of techniques

    Method of assessment

    1. Written exam
  3. To deal with lattices as algebraic structures; to form sublattices; homomorphisms

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics in a specialized way
    2. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
    3. Analyze critically and evaluate his/her findings and those of others,
    4. Question and find out innovative approaches.
    5. Acquire scientific knowledge and work independently,
    6. Work effectively in multi-disciplinary research teams
    7. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    8. Effectively express his/her research ideas and findings both orally and in writing

    Method of assessment

    1. Written exam
  4. Determine whether a given lattice is modular or distributive Learning Boolean algebras

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics in a specialized way
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
    4. Acquire scientific knowledge and work independently,
    5. Work effectively in multi-disciplinary research teams
    6. Develop mathematical, communicative, problem-solving, brainstorming skills.
    7. Effectively express his/her research ideas and findings both orally and in writing

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Ordered Sets
Week 2: Ordered Sets (HW 1)
Week 3: Lattices and Complete lattices
Week 4: Lattices and Complete lattices
Week 5: Lattices and Complete lattices (HW 2)
Week 6: Formal concept analysis
Week 7: Formal concept analysis (HW 3) (Midterm I )
Week 8: Modular and distributive lattices
Week 9: Modular and distributive lattices
Week 10: Boole lattices and algebras (HW 4)
Week 11: Representation
Week 12: Representation (HW 5)

Week 13: Congruences (Midterm II)
Week 14: Congruences (HW 6)
Week 15*: -
Week 16*: -
Textbooks and materials:
Recommended readings: B.A.Dallery and H.A.Pristley, “Introduction to lattices and order”, Second edition,
Cambridge University Press, 2002.
G. Gratzer, “General Lattice Theory”, Academic Press, New York
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 7,13 40
Other in-term studies: 0
Project: 0
Homework: 2,5,7,10,12 10
Quiz: 0
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 3 14
Practice, Recitation: 0 0
Homework: 6 10
Term project: 10 2
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 3 1
Personal studies for final exam: 10 1
Final exam: 3 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
-->