The subject of this course is mathematical. When new mathematics is created, the researcher starts with a more or less vague mental picture of the of the subject area and tries to clarify that picture by making precise definitions and asking questions about their consequences. Since mathematical results have to be proved beyond any doubt, the results of the investigation are traditionally presented in a very stylized form in which definitions are made completely precise and each result is justified using reasoning that clearly separates assumptions from conclusions and makes transparent the dependency of each new assertion on what has come before. However, one must not lose sight of the fact that the clear mental picture, not the stylized presentation, is the actual outcome of a mathematical investigation.
In studying mathematics that has already been created (which is what most students who take mathematics courses do), one attempts to "learn" the subject from the stylized presentation. It is easy to fall into the trap of thinking that memorizing definitions, theorems, and proofs is what this learning entails. However, this is inadequate. The actual objective should be to reconstruct the underlying clear mental picture, so that the truth or falsity of the various theorems becomes more or less obvious as a result.
In order to "decode" mathematical formalism and reconstruct the underlying mental picture, it is necessary to adopt an approach much like that used when the mathematics was created. As each definition is presented, one should try to understand why the definition is stated the way it is and what are and are not consequences of it. As each theorem is studied, one should try to understand how it and its proof serve to elucidate the properties of the mathematical objects under study. In achieving this understanding, it is often useful to consider possible alternatives to what is written in the text; for example, are there simpler (but possibly less general) versions of the theorem that are also true, are there counterexamples that show the necessity of technical hypotheses, is a complicated proof actually necessary or would a simpler argument suffice?
To facilitate this kind of active approach to assimilating mathematical material, mathematics books often include "exercises". Typically these explore the kinds of "what if" questions that are helpful in reconstructing the underlying mental picture. They are not really optional -- in most cases, if the answer to an exercise is not obvious, then some important feature of the material has been missed. Sometimes mathematics books also include "problems", which are more difficult and are used to introduce the reader to side topics that are not explored in depth in the main text, or to indicate directions for possible extensions or generalization of the existing material. Since the student cannot always easily distinguish an "exercise" from a "problem", it is helpful if textbooks separate the two, but this is not always done.
The point of all this is that doing exercises is an important and necessary part of learning mathematical material, and I expect that you will do as many basic exercises as you can manage. I typically don't include the most basic exercises as part of the formal homework assignments -- I assume you will do these automatically on your own. The kind of problems I usually do assign for homework are ones that (hopefully) teach you something interesting and that are somewhat more difficult than the most basic exercises, but that are easy enough that someone with a reasonable level of understanding and making a reasonable effort would be likely to solve them in the time available.