Bienvenido a 004x KyotoUx Fun with Prime Numbers: The Mysterious World of Mathematics
Fun with Prime Numbers: The Mysterious World of Mathematics
Instructor: Tetsushi Ito
Instructor
Tetsushi Ito
Associate Professor at the Department of Mathematics, Faculty of Science, Kyoto University. He received his Ph.D. in Mathematical Sciences from the University of Tokyo in 2003.
KyotoUx Staff
Toru Iiyoshi - Executive Director
Course Production Team
Hiroyuki Sakai - Managing Director
Masako Okamoto - Chief Course Production Manager
Motoko Okumoto - Instructional Design Manager
Wataru Kono - Course Production Specialist
Technology Development
Isanka Wijerathne - Technical Operations Manager
Media Production Team
Kazuya Fujioka - Primary Media Producer
Taiga Nagashima - Media Producer
Research Team
Mana Taguchi - Research Director
Takayuki Goto - Chief Researcher
Course Description
Prime numbers are one of the most important subjects in mathematics.
Many mathematicians from ancient times to the 21st century have studied
prime numbers.
In this math course, you will learn the definition and basic
properties of prime numbers, and how they obey mysterious laws. Some
prime numbers were discovered several hundred years ago whereas others
have only been proven recently. Even today, many mathematicians are
trying to discover new laws of prime numbers.
Calculating by a pen and paper, you will explore the mysterious world
of prime numbers. Join us as we tackle math problems, and work together
to discover new laws on prime numbers. Let's study and have fun!
Lectures
Each course will be provided with short lecture videos by the
instructor, Tetsushi Ito along with a set of short Problems related to
the contents of the lecture videos. By watching the videos and answering
the Problems, we hope that all participants will gain some basic
knowledge on prime numbers. We also hope that the participants will
recognize how prime numbers is, and how little we actually know about
it. We welcome questions and comments and hope this will lead to
fruitful exchanges and discussion.
Course Schedule
Week
Topic
Homework
1
Introduction to Prime Numbers
- Infinity of prime numbers
- Sieve of Eratosthenes
- Open problems on prime numbers - The twin prime conjecture and the Goldbach conjecture
Yes
2
Laws of Prime Numbers
- Dirichlet’s theorem on arithmetic progression
- Fermat’s theorems on sums of two squares (1)
- Fermat’s theorems on sums of two squares (2)
Yes
3
Reciprocity Laws and Mystery of Triangles
- What are reciprocity laws?
- Mystery of Triangles (1)
- Mystery of Triangles (2)
Yes
4
ABC Conjecture and Beyond
- Prime factorization and the ABC conjecture
- Examples of ABC triples
- Polynomial analogues of the ABC conjecture
Yes
Instructor
Tetsushi Ito
Associate Professor at the Department of Mathematics, Faculty of Science, Kyoto University. He received his Ph.D. in Mathematical Sciences from the University of Tokyo in 2003.
KyotoUx Staff
Toru Iiyoshi - Executive Director
Course Production Team
Hiroyuki Sakai - Managing Director
Masako Okamoto - Chief Course Production Manager
Motoko Okumoto - Instructional Design Manager
Wataru Kono - Course Production Specialist
Technology Development
Isanka Wijerathne - Technical Operations Manager
Media Production Team
Kazuya Fujioka - Primary Media Producer
Taiga Nagashima - Media Producer
Research Team
Mana Taguchi - Research Director
Takayuki Goto - Chief Researcher
Course Description
Prime numbers are one of the most important subjects in mathematics. Many mathematicians from ancient times to the 21st century have studied prime numbers.
In this math course, you will learn the definition and basic properties of prime numbers, and how they obey mysterious laws. Some prime numbers were discovered several hundred years ago whereas others have only been proven recently. Even today, many mathematicians are trying to discover new laws of prime numbers.
Calculating by a pen and paper, you will explore the mysterious world of prime numbers. Join us as we tackle math problems, and work together to discover new laws on prime numbers. Let's study and have fun!
Lectures
Each course will be provided with short lecture videos by the instructor, Tetsushi Ito along with a set of short Problems related to the contents of the lecture videos. By watching the videos and answering the Problems, we hope that all participants will gain some basic knowledge on prime numbers. We also hope that the participants will recognize how prime numbers is, and how little we actually know about it. We welcome questions and comments and hope this will lead to fruitful exchanges and discussion.
Course Schedule
Course Production Team
Hiroyuki Sakai - Managing Director
Masako Okamoto - Chief Course Production Manager
Motoko Okumoto - Instructional Design Manager
Wataru Kono - Course Production Specialist
Technology Development
Isanka Wijerathne - Technical Operations Manager
Media Production Team
Kazuya Fujioka - Primary Media Producer
Taiga Nagashima - Media Producer
Research Team
Mana Taguchi - Research Director
Takayuki Goto - Chief Researcher
Course Description
Prime numbers are one of the most important subjects in mathematics. Many mathematicians from ancient times to the 21st century have studied prime numbers.
In this math course, you will learn the definition and basic properties of prime numbers, and how they obey mysterious laws. Some prime numbers were discovered several hundred years ago whereas others have only been proven recently. Even today, many mathematicians are trying to discover new laws of prime numbers.
Calculating by a pen and paper, you will explore the mysterious world of prime numbers. Join us as we tackle math problems, and work together to discover new laws on prime numbers. Let's study and have fun!
Lectures
Each course will be provided with short lecture videos by the instructor, Tetsushi Ito along with a set of short Problems related to the contents of the lecture videos. By watching the videos and answering the Problems, we hope that all participants will gain some basic knowledge on prime numbers. We also hope that the participants will recognize how prime numbers is, and how little we actually know about it. We welcome questions and comments and hope this will lead to fruitful exchanges and discussion.
Course Schedule
| Week | Topic | Homework |
| 1 | Introduction to Prime Numbers
|
Yes |
| 2 | Laws of Prime Numbers
|
Yes |
| 3 | Reciprocity Laws and Mystery of Triangles
|
Yes |
| 4 | ABC Conjecture and Beyond
|
Yes |
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