CATEGORY THEORY IN COMPUTATION

Course Code:

MATH 424

Course Type:

Area Elective

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

7

Prerequisite Courses:

INTRODUCTION TO SET THEORY AND LOGIC

INTRODUCTION TO GROUP THEORY

Course Language:

English

Course Objectives:

This course aims to equip students with knowledge of fundamentals of category theory and applications in computing sciences.

Course Content:

Some preliminaries for categories, Sets, functions. Definitions of categories, functors, natural transformations. Functional programming languages as categories. Category of sets. Categories of sets with extra structure. Yoneda Lemma. Universal properties. Initial and Terminal objects. Adjoint functors. Monads/Lawvere theories. Finitary algebraic theories. Universal Algebra and Programming Languages.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) Learn categories, functors and natural transformations.	1,2,4	1	A,B
2) Learn Yoneda lemma and its consequences.	1,2,4,7	1	A,B
3) Learn universal algebra through monads and Lawvere theories	1,2,4,7	1	A,B
4) Understand the link between universal algebra and programming	1,2,3,4,7,9	1	A,B
5) Master categorical constructions.	1,2,3,4,7,9	1	A,B

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1	Preliminaries
2	Categories, functors and natural transformations
3	Mathematical structures and functional programming languages as categories
4	Categories of sets
5	Categories of sets with extra structures
6	Representable functors and Yoneda lemma.
7	Universal properties: Initial and terminal objects
8	Categorical products, coproducts
9	Categorical limits and colimits
10	Adjoint functors
11	Lawvere theories/Monads: Definitions and Examples
12	Universal algebra via Lawvere theories/Monads
13	Lawvere theories/Monads in Computer Science
14	Universal algebra and programming

Recommended Sources

RECOMMENDED SOURCES

Textbook

Barr, Michael, and Charles Wells. Category theory for computing science. Vol. 49. New York: Prentice Hall, 1990.

http://www.tac.mta.ca/tac/reprints/articles/22/tr22.pdf

Additional Resources

Mac Lane, Saunders. Categories for the working mathematician. Vol. 5. Springer Science & Business Media, 2013.

Leinster, Tom. Basic category theory. Vol. 143. Cambridge University Press, 2014.

Milewski, Bartosz. Category theory for programmers. Blurb, 2018.

Material Sharing

-

Assessment

ASSESSMENT
IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	60
Quizzes		-
Assignments	3	40
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM
No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamental research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)				x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability form and interpret the relations between research topics in mathematics					x
4	Ability to define, formulate and solve mathematical problems					x
5	Consciousness of professional ethics and responsibility			x
6	Ability to communicate actively			x
7	Ability of self-development in fields of interest				x
8	Ability to learn, choose and use necessary information technologies			x
9	Lifelong education			x

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	5	70
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms (Including self-study)	2	10	20
Quizzes	-	-	0
Assignments	3	8	24
Final examination (Including self-study)	1	19	19
Total Work Load			175
Total Work Load / 25 (h)			7
ECTS Credit of the Course			7

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