Not all software projects are the same, no more than all construction projects are the same. You can quickly nail a dog house together with only vague planning and minimal craftsmanship. But if you want to build a house for people, you have to plan more, pay more attention to what you're doing, and make sure the result meets the local codes. If you want to build a skyscraper, you have to put even more work into planning, robust engineering, and code-meeting than you do with a house.
I've worked on software for iPhones and on software for jumbo jets. The two activities almost aren't even the same thing. Drawing on other life experiences, I might liken it to jazz improvisation vs. classical performance, or to mobile phone snapshots vs. professional portraiture. Overlapping, yet different enough that methods which work for one do not necessarily make sense for the other.
Also, you might consider looking at Don Knuth's book Concrete Mathematics, which is a somewhat more casual coverage of the math chapter in the first volume of TAOCP.
You mention in a comment that you want to learn software architecture. I really like this book:
If you're into web applications at all, perhaps the best book to understand the basics of design is:
Either way, don't give up on TAOCP. Whether if you're ready for it now, or if you want to wait a few years, it's great that you're interested in reading it, and I would encourage you to study it as much as you can, if you discover that you are indeed intrigued by the topics it covers.
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