Where Can I Learn This Notation?

[Physics_wiz]

I'm trying to read a mathematical systems theory book (by Heij, Ran, and van Schagen) and he uses notation that I don't understand. He's not the only one...other books use the same notation too, but I never learned it. For example:

"Definition 1.2.2. An input-output system consists of a set of input trajectories $$\{u : T \rightarrow U\}$$ and output trajectories $$\{y : T \rightarrow Y \}$$ related by a mapping F. The system behaviour is given by $$\beta = \{(u, y) : T \rightarrow U \times Y ; y = F(u)\}$$."

The parts of the quote in latex is what I don't understand. I can have a general idea what he means, but where do students learn this notation? Is it real analysis? If so, I can just buy a book and read since I've seen notation like this practically everywhere without explanation which leads me to think that it's rather elementary.

 

[JasonRox]

I'm trying to read a mathematical systems theory book (by Heij, Ran, and van Schagen) and he uses notation that I don't understand. He's not the only one...other books use the same notation too, but I never learned it. For example:

"Definition 1.2.2. An input-output system consists of a set of input trajectories $$\{u : T \rightarrow U\}$$ and output trajectories $$\{y : T \rightarrow Y \}$$ related by a mapping F. The system behaviour is given by $$\beta = \{(u, y) : T \rightarrow U \times Y ; y = F(u)\}$$."

The parts of the quote in latex is what I don't understand. I can have a general idea what he means, but where do students learn this notation? Is it real analysis? If so, I can just buy a book and read since I've seen notation like this practically everywhere without explanation which leads me to think that it's rather elementary.

It's rather an elementary thing, which is a good thing!

I would say just read any decent Analysis, Topology or Set Theory introduction and you'll get it. Only like chapter 1 pretty much.

It might look weird now, but once you get it, you won't want to write any other way. It's the easiest way to write math ideas down.

 

[tacman]

The notation used in mathematics can vary depending on the specific field and author. It can be overwhelming to encounter unfamiliar notation, but it is important to remember that it is a language used to communicate complex ideas and concepts.

To learn this notation, it is helpful to have a strong foundation in mathematics, including courses in calculus, linear algebra, and possibly real analysis. However, even with a strong background, it may still take some time and practice to become comfortable with new notation.

One of the best ways to learn new notation is to consult a textbook or online resources that specifically focus on the topic you are trying to understand. In this case, a book on systems theory or mathematical modeling may have a section devoted to explaining the notation used in the field.

Additionally, it can be helpful to reach out to a professor or fellow students who have experience in the subject and can provide guidance and clarification. Asking questions and seeking out resources is key to understanding new notation and concepts in mathematics.

Remember, learning new notation is a process and it takes time and practice. Don't be discouraged if it doesn't come easily at first, keep working at it and eventually it will become more familiar.