I am trying to initialize a global NSMutableArray that I can add integers to later. I just need to know how and where I should initialize my array so that it can be accessed
You can initialise your array in app delegate's application:didFinishLaunchingWithOptions: method, as this is called pretty much immediately after your app is launched:
// In a global header somewhere
static NSMutableArray *GlobalArray = nil;
// In MyAppDelegate.m
- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions
{
    GlobalArray = [NSMutableArray arrayWithCapacity:180];
    ...
}
Alternatively, you could use lazy instantiation:
// In a global header somewhere
NSMutableArray * MyGlobalArray (void);
// In an implementation file somewhere
NSMutableArray * MyGlobalArray (void)
{
    static NSMutableArray *array = nil;
    static dispatch_once_t onceToken;
    dispatch_once(&onceToken, ^{
        array = [NSMutableArray arrayWithCapacity:180];
    });
    return array;
 }
You can then access the global instance of the array using MyGlobalArray().
However, this is not considered good design practice in object-oriented programming. Think about what your array is for, and possibly store it in a singleton object that manages related functionality, rather than storing it globally.