So what is a computer?

Let me explain, from the name itself we can derive what it is i.e. "COMPUT+ER", now compute means to calculate and a Computer is just a computing or calculating device and nothing more.

    Now what kind of calculation? only the very basic ones that we learn in at our primary school i.e.

1. Arithmetic:- Addition, Subtraction, Multiplication etc
2. Logical:- Greater than, less than or equals to

    and these are done by the ALU(Arithmetic and Logical Unit) present in the Microprocessor.
         
                                            

                                         A general Symbol Of ALU(Image Source:- Wikimedia)

A MATHEMATICAL APPROACH TO DEFINING COMPUTERS:-
   
           A computer or a computing System can be defined as an information processing system whose function is to map a set A of input information items(i.e. a PROGRAM and its DATA) into an output set B(the result computed by the program acting on the data). Example:-                               

                                   f(a,b)  =   c

                                                       where a, b:-  are discrete data

                                                                 f:-      program or the instruction

                                                                 c:-      output

 
 Hope it makes sense. Do write in comments

SOURCE:

1. COA by JP Hayes
2. CO by V. Carl Hamacher.