Yet there is at least one famous person in CS and EE (and physics?), who says, that mathematical notation is not all that great, compared to how precise computer languages are or can be. Yet I remember often struggling to decide the order of things expressed with mathematical notation, when merely the minimal number of parentheses was employed by a lecturer or teacher.
Mathematical notation is very concise, but I would not call it a great notation in terms of intuitively being clear, which operations to apply in which order or which symbol groups its argument(s) in what way and found myself rather tending to write an extra pair of parentheses, to make things clearer for myself.
There is also the mix of operators and functions. Some computer languages do not mix that, but employ only functions, which makes things clearer as well.
IDK, for instance, I'm familiar with Structure and Interpretation of Classical Mechanics, and even though I have had my share of fun from it, the (functional) presentation there still looks terrible, to the point of becoming completely opaque in places, compared to the traditional mathematical notation of the Lagrangian etc. I have also seen books on calculus that focus on function composition (resembling the style of category theory) rather than on sets, and I felt that this was completely unnecessary as it only served to complicate both the exposition and the understanding of the subject that is already difficult enough.
Comments
Much of the progress in mathematics over the past 500 years can be attributed to the development of a good, concise notation.
Yet there is at least one famous person in CS and EE (and physics?), who says, that mathematical notation is not all that great, compared to how precise computer languages are or can be. Yet I remember often struggling to decide the order of things expressed with mathematical notation, when merely the minimal number of parentheses was employed by a lecturer or teacher.
Mathematical notation is very concise, but I would not call it a great notation in terms of intuitively being clear, which operations to apply in which order or which symbol groups its argument(s) in what way and found myself rather tending to write an extra pair of parentheses, to make things clearer for myself.
There is also the mix of operators and functions. Some computer languages do not mix that, but employ only functions, which makes things clearer as well.
IDK, for instance, I'm familiar with Structure and Interpretation of Classical Mechanics, and even though I have had my share of fun from it, the (functional) presentation there still looks terrible, to the point of becoming completely opaque in places, compared to the traditional mathematical notation of the Lagrangian etc. I have also seen books on calculus that focus on function composition (resembling the style of category theory) rather than on sets, and I felt that this was completely unnecessary as it only served to complicate both the exposition and the understanding of the subject that is already difficult enough.