Looking for resources on asymptotic notation/analysis

[LoA]

Hello all,

I've come across big and little o notation a few times now in my mathematics studies, but only ever on a single homework assignment ("use taylor series to find the limit," that kind of thing) or a brief mention in a textbook. However, one of my instructors suggested in office hours recently that it was an extremely important tool. I'm looking for resources, especially practice problems, on using and manipulating asymptotic notation in a general context. I am also currently taking a first course in analysis and would be interested in any materials applying asymptotic notation to that subject. If there was a calculus-textbook style book over nothing but this subject that would be awesome, but I honestly don't even know what search terms to use to look for this. Thanks for any and all advice you good people might have.

 

[jvicens]

Hello there,

As a fellow scientist, I can definitely attest to the importance of asymptotic notation in various fields of study, including mathematics and analysis. It is a powerful tool that allows us to analyze the behavior of functions and their growth rates, without having to deal with complicated and often tedious calculations. In essence, it helps us simplify and understand complex mathematical concepts.

For resources on using and manipulating asymptotic notation, I would recommend checking out textbooks on algorithms and data structures, as well as those on analysis and calculus. These often have dedicated chapters or sections on the topic, with plenty of practice problems for you to work on. You can also find many online resources, such as lecture notes, videos, and practice exercises, by searching for "asymptotic notation" or "big O notation."

As for applying asymptotic notation to analysis, I would suggest looking into topics such as limits, derivatives, and integrals, as these are fundamental concepts that can be described using asymptotic notation. In particular, you may want to explore the concept of "asymptotic behavior" in analysis, which deals with the behavior of functions as their inputs approach certain values.

Lastly, if you're interested in a book solely dedicated to asymptotic notation, I would recommend "Asymptotic Analysis" by F.G. Tricomi. It covers the topic in great detail and includes many examples and exercises to help you practice and apply what you've learned.

I hope this helps and good luck with your studies! Asymptotic notation may seem daunting at first, but with practice and persistence, you'll soon see its importance and usefulness in your research and studies. Keep at it!