'Read' or 'complete' a math text?

If you'd rather express some nuances besides what the neutral "work through" allows.

• plough through (I ploughed through Apostol's…)
• breeze through (I breezed through Apostol's…)
• plod one's way through (I plodded my way through Apostol's…)

Those three possibilities are not meant to be be used in a formal account of your achievements (for instance in a CV), as the people concerned are interested neither in the difficulties you might have had, nor in learning about the possible boredom those studies occasioned nor the ease with which you might have overcome the obstacles. Those verbs can be used for factual accounts in narratives and even in everyday speech. Anyway, before making them part of your vocabulary you should make sure you have a good idea of the nuances involved, as on account of their strong connotations those verbs and phrases are no exact synonyms of "work through".
(Take notice of this comment—due to user chasly; it is what prompted the present remarks.)

Having plowed through enough calculus in my time I can assure you that anyone familiar with an Author/Title reference of note, such as Apostol's Calculus, will not for one moment imagine that you read the book without working some or many of the exercises. In fact nearly no one works them all (except you know who) and there is no shame in that, or at least there shouldn't be.

The idea is described, the method explained, the process set forth and the exercises build the muscle. No reader could make head or tails, never mind maxima and minima, out of chapter eight without hand to hand combat in chapters two through seven. In (most) fiction one can understand the situations of characters with incomplete information, to be improved later; people are people. This is not the case with a math text one is new to.

To say you have read it is entirely well understood and adequate to the task. It is also quite correct to say you worked through it as Weather Vane suggests. I could stand to work through it again myself. Some good stuff in there.