Mathematical Structures and Formalization(MAT440)
Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
---|---|---|---|---|---|---|---|
MAT440 | Mathematical Structures and Formalization | 7 | 3 | 0 | 0 | 3 | 5 |
Prerequisites | |
Admission Requirements |
Language of Instruction | |
Course Type | Elective |
Course Level | Bachelor Degree |
Course Instructor(s) | Ayberk ZEYTİN azeytin@gsu.edu.tr (Email) |
Assistant | |
Objective | - |
Content |
Overview of functional programming, Types, Terms, Equality, di?erent kinds of types, structures, classes Setting up well-known mathematical structures in Lean, proving well-known theorems via Lean |
Course Learning Outcomes |
1. Understand the need for a formalism in mathematics. 2. To learn functional programming basics 3. To be able to use proof assistants |
Teaching and Learning Methods | Face to face or online |
References |
How To Prove It (with Lean), Daniel J. Velleman Theorem Proving in Lean 4, Jeremy Avigad, Leonardo de Moura, Soonho Kong, and Sebastian Ullrich, |
Theory Topics
Week | Weekly Contents |
---|---|
1 | Overview and Installation |
2 | Lean Syntax and Proof Interface |
3 | Logic Review in Lean |
4 | Proof Tactics and Style |
5 | Structures and Type Classes |
6 | Inductive Types and Recursion |
7 | Proofs by Induction |
8 | Sets and Relations |
9 | Algebraic Hierarchy |
10 | Number Theory in Lean I |
11 | Number Theory in Lean II |
12 | Finite Structures and Combinatorics I |
13 | Finite Structures and Combinatorics II |
14 | Analysis in R |
Practice Topics
Week | Weekly Contents |
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Contribution to Overall Grade
Number | Contribution | |
---|---|---|
Contribution of in-term studies to overall grade | 6 | 60 |
Contribution of final exam to overall grade | 1 | 40 |
Toplam | 7 | 100 |
In-Term Studies
Number | Contribution | |
---|---|---|
Assignments | 0 | 0 |
Presentation | 6 | 60 |
Midterm Examinations (including preparation) | 0 | 0 |
Project | 0 | 0 |
Laboratory | 0 | 0 |
Other Applications | 0 | 0 |
Quiz | 0 | 0 |
Term Paper/ Project | 0 | 0 |
Portfolio Study | 0 | 0 |
Reports | 0 | 0 |
Learning Diary | 0 | 0 |
Thesis/ Project | 0 | 0 |
Seminar | 0 | 0 |
Other | 0 | 0 |
Make-up | 0 | 0 |
Toplam | 6 | 60 |
No | Program Learning Outcomes | Contribution | ||||
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 |
Activities | Number | Period | Total Workload |
---|---|---|---|
Class Hours | 14 | 3 | 42 |
Working Hours out of Class | 14 | 3 | 42 |
Assignments | 0 | 0 | 0 |
Presentation | 3 | 5 | 15 |
Midterm Examinations (including preparation) | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Laboratory | 0 | 0 | 0 |
Other Applications | 0 | 0 | 0 |
Final Examinations (including preparation) | 1 | 36 | 36 |
Quiz | 0 | 0 | 0 |
Term Paper/ Project | 0 | 0 | 0 |
Portfolio Study | 0 | 0 | 0 |
Reports | 0 | 0 | 0 |
Learning Diary | 0 | 0 | 0 |
Thesis/ Project | 0 | 0 | 0 |
Seminar | 0 | 0 | 0 |
Other | 0 | 0 | 0 |
Make-up | 0 | 0 | 0 |
Yıl Sonu | 0 | 0 | 0 |
Hazırlık Yıl Sonu | 0 | 0 | 0 |
Hazırlık Bütünleme | 0 | 0 | 0 |
Total Workload | 135 | ||
Total Workload / 25 | 5.40 | ||
Credits ECTS | 5 |