Anthony's Reviews > Algebraic Topology

Great introduction to algebraic topology. For those who have never taken a course or read a book on topology, I think Hatcher's book is a decent starting point. However, ( IMO) you should have a working familiarity with Euclidean Geometry, College Algebra, Logic or Discrete Math, and Set Theory before attempting this book. While some people might complain about the book's lack of rigor, I think this is irrelevant. What is important is that the book manages to convey the essentials of topology. If you are an intuitive learner with a rudimentary background in topology , you'll find this book to be more accessible than a book which focuses on rigor. However, if you are an academic, then you might find this book unsatisying.

Why study topology? Topology is like geometry on steroids. It has practical applications in the physical sciences, computer graphics, and statistics. Furthermore, there is an inherent beauty in topology which cannot be easily described in words. Topology expands our means of working with geometric figures. Unlike Euclidean Geometry, the geometry which you encounter in a high school math class, Topology is primarily concerned with transformations of connected geometric objects through bending, stretching, and twisting. Algebraic topology translates topological figures into algebraic images.