English I and II are almost certainly required by any accredited school. Most accredited schools also have a humanities requirement, so Government and Anthropology are not unreasonable.
I would consider Algebra I a remedial course, so I agreed, replace it.
I also agree the programming tools class can be covered in other classes, including Project Management (Software).
Move Intro to Unix to the first semester. Or maybe second, if Intro to Computers is needed. This will give them a foundation for the suggested web server admin class.
And I agree with others that a fifth course per semester should be added. Include a third programming language.