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: 
20162017, 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 corequisites: 
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


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

Learning ordered sets; their diagrams; maps between ordered sets; maximal and minimal elements; and building new ordered sets.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics in a specialized way

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Work effectively in multidisciplinary research teams

Design and conduct research projects independently

Develop mathematical, communicative, problemsolving, brainstorming skills.

Effectively express his/her research ideas and findings both orally and in writing
Method of assessment

Written exam

Learning lattices as ordered sets; complete lattices; chain conditions and completeness;
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics in a specialized way

Understand relevant research methodologies and techniques and their appropriate application within his/her research field,

Acquire scientific knowledge and work independently,

Work effectively in multidisciplinary research teams

Develop mathematical, communicative, problemsolving, brainstorming skills.

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

Written exam

To deal with lattices as algebraic structures; to form sublattices; homomorphisms
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics in a specialized way

Understand relevant research methodologies and techniques and their appropriate application within his/her research field,

Analyze critically and evaluate his/her findings and those of others,

Question and find out innovative approaches.

Acquire scientific knowledge and work independently,

Work effectively in multidisciplinary research teams

Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment

Effectively express his/her research ideas and findings both orally and in writing
Method of assessment

Written exam

Determine whether a given lattice is modular or distributive
Learning Boolean algebras
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics in a specialized way

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Gain original, independent and critical thinking, and develop theoretical concepts and tools,

Acquire scientific knowledge and work independently,

Work effectively in multidisciplinary research teams

Develop mathematical, communicative, problemsolving, brainstorming skills.

Effectively express his/her research ideas and findings both orally and in writing
Method of assessment

Written exam


Contents


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



Method of assessment 
Week number 
Weight (%) 

Midterms: 
7,13 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 
2,5,7,10,12 
10 
Quiz: 

0 
Final exam: 
16 
50 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface 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 midterm exam: 
10 
1 

Midterm: 
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)



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