morphism said:There was a thread about this not too long ago:
https://www.physicsforums.com/showthread.php?t=195378
Nothing seems to have changed since then though.
I really don't understand why the TA&DG is so-named. Surely topology warrants more attention than "tensor analysis" - whatever this means?
sorry, rob, but that's rubbish, I don't recall learning topology in high school, and I'm no expert in topology or geometry but an undergraduate student who learns this stuff, and I don't see how high schooler can choose to post at a forum where he sees all posts in subjects unfamiliar to him.robphy said:I guess part of the current title is meant to get people who are interested in mathematical aspects of General Relativity...particularly Tensors [which is probably why it is distinguished there]. While an expert would appreciate the title "geometry & topology"... the novice probably won't. With that title, one might get lots of questions about high-school geometry. Maybe "Advanced Geometry & Topology"... but one might need to throw in "Tensors".
There could be several reasons for this. The study may not be directly related to topology, so it was not included in the discussion. Alternatively, topology may not be relevant to the specific research question being addressed. Additionally, the study may be limited in scope and did not have the resources to include a discussion on topology.
Topology is the study of the properties of a geometric figure that are preserved under continuous deformations, such as stretching or bending. In many scientific fields, topology can provide valuable insights into the structure and behavior of complex systems. For example, in biology, topology can help understand the shape and function of proteins, while in physics, it can explain the behavior of quantum particles.
It depends on the specific field of study. In some areas, such as mathematics, topology is a fundamental concept and is used extensively. In other fields, its relevance may vary. However, with the growing complexity of scientific research, topology is becoming increasingly important in understanding and analyzing complex systems.
Topology is a rapidly evolving field, and new developments are continuously being made. It is possible that there may be recent studies or theories in topology that could shed light on the topic at hand. It is always recommended to stay updated on current research and advancements in related fields.
Topology has numerous applications in various fields, including physics, biology, computer science, and engineering. It can be used to model and analyze complex systems, understand network structures, and make predictions about the behavior of these systems. Additionally, topology can also be applied in data analysis, optimization, and machine learning.