Tayo Tai to Ha Nani Ka Kukan to Jigen Kara Manabu Gendai Kagaku No Kiso Gainen (Blue Backs)

[Machine Translation] An introduction to the basic concepts necessary to study this natural world we live in! This book provides an overview of manifolds, a type of figure, which is the basis of modern mathematics, modern physics, and everything else. The course reviews the basics of planes, spaces, and coordinates, and then moves on to 0-dimensional manifolds, 1-dimensional manifolds, 2-dimensional manifolds, 3-dimensional manifolds, and higher dimensional manifolds, increasing the number of dimensions as the course progresses. As applications, the Poincare Conjecture, the Standard Model of quantum field theory, and superstring theory will be touched upon, and unsolved problems in this field will be introduced.

我々の住む、この自然界を研究するために必要な基礎概念を学ぶ入門書!現代数学や現代物理、すべての基本である、図形の一種である多様体を俯瞰します。平面や空間、座標といった基本事項を復習し、0次元多様体、1次元多様体、2次元多様体、3次元多様体、高次元多様体と、次元を増やしながら多様体を理解していきます。さらに応用として、ポアンカレ予想、場の量子論の標準模型、超弦理論などにも触れ、この分野の未解決問題も紹介します。