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I'm studying algorithms complexities by myself (my university didn't it to me) and I'd love if someone could help me in finding good resources to learn fundamental algorithms complexities proofing. There are lots of non-mathematical resources about big-Oh notation but I'd like something more mathematical and rigorous (although understandable) on the topic

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Last chapter (on asymptotics) in $\mathit{Concrete Mathematics}$ by Graham, Knuth and Patashnik – Alex Mar 25 '13 at 22:02

As a double major in maths and CS I liked Introduction to Algorithms by cormen et al., when I was taught about algorithms for the first time.

This book tries to be complete, therefore it was sometimes too mathematical for the general CS audience so parts were skipped in my algorithm course(proof of the Master Theorem e.g.).

Besides the rigor rarely seen in CS textbooks, there is a vast amount of algorithms which are explained. Because of this, it is the CS book I own I pick up the most, mostly for some algorithm I want to review.

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