Mathematics

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,
Print the course contents
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
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