iOS Some newbie syntax questions

Why is it that IBAction functions have a semicolon in them right before the curly brackets, while all other functions I am aware of do not?

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It is an oddity of Objective-C syntax that placement of a semicolon before the curly brace is optional. There's nothing special regarding IBActions in this regard; it's the case for all methods.

Why does the asterisk, which I assume is for declaring a the new variable "application", come inside of the parenthesize? (UIApplication *)

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The star indicates that this is a pointer. You read pointer expressions like this from right to left. Pointer to UIApplication object. You need to read more about this in a book about C and then one about Objective-C. In the line of code that you show the pointer expression is the type of the parameter named application.