Logic turns up in the sylabus later, one usually starts with linear algebra and analysis where one assumes the underlying logic to be given.
I think the reason is because the study of logic already needs some intuitive application of logic, i.e. logic is applied to describe what actualy logic is.
Once you have defined what a language is and what a logic is you automaticaly also proved the meta-logic that you used to prove all the statements you made about language and logic in general.
A concrete example: Structural induction - You apply structural induction to prove something about the nature of statements, i.e. if you have proved that a property holds for all minimal structures (variables,True,False) and you know that if a property holds for all imediate substructures of a structure then it also hlds for the structure (If A,B have property then A&B). Then you can say the property holds for all structures (statements). You don't know why the principle of structural induction holds but you are still applying it. Later you will know more about the framework and the objects which it comprises.
My Question is it true that logic is applied to describe what actualy logic is ? or is there something I haven't taken into account?