Chester Starr's A History of the Ancient World has been the standard college level text on the topic for a number of decades. Don't let it's brick-like appearance and lack of illustrations throw you off. Starr's writing style is clear and concise and he is unswervingly true to his subject without being drawn off into odd side digressions dictated by various stands of trendy modern scholarship.
Students will be covering about 400 pages in the first year and about 300 in the second year, so even those with a low tolerance for text book reading should find it quite manageable.
When reading Starr, try to keep moving at a decent speed and don't get too bogged down in names and dates. Remembering these is certainly important, but there are a lot. If you choose to dig deeper into some of the periods Starr covers, you will realize that even the rapid play of pleople, places and dates is actually a pretty quick overview.
If you find that note taking helps you retain information, you may find it helpful to write up a brief schematic for each period covered by Starr listing off major cultures or trends covered in the chapter and important people, events and dates that relate to them.
Most of the chapters are under twenty pages long. We'd generally advise that you read a whole chapter at a sitting (or at least on a single day) in order to get the whole thrust of the topic in mind.
NB: Some Christian parents may find Starr's account of the origins of Christianity a little sketchy. Some have accused him of making it sound like St. Paul invented Christianity more or less on his own. Certainly, feel free to supplement with an appropriate book on the history of Christianity, but I would encourage you not to shun Starr for religious reasons. I've generally found him to be quite fair and unbiased in his treatment of all religions he deals with.
Buy Starr's A History of the Ancient World from Amazon
They also have used editions of Starr for rather less.
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