Algorithms are the most important, durable, and original part of computer science because they can be studied in a language- and machine-independent way. This means that we need techniques that enable us to compare algorithms without implementing them. Our two most important tools are (1) the RAM model of computation and (2) asymptotic analysis of worst-case complexity.
This method of keeping score will be the most mathematically demanding part of this book. However, it is important to understand why we need both of these tools to analyze the performance of algorithms. Once you understand the intuition behind these ideas, the formalism becomes a lot easier to deal with.