Explore advanced asymptotic methods in this third lecture of the SISSA/IGAP/SUSTech series on "Standard and less standard asymptotic methods." Delve into techniques for evaluating infinite sums numerically and recognizing asymptotic patterns in number sequences. Learn about both standard approaches like the Euler-Maclaurin formula and less conventional methods through numerous examples. Tackle challenging problems such as evaluating a slowly convergent sum to 250 decimal places, analyzing the asymptotic behavior of complex coefficient expansions, and computing highly oscillatory infinite series. Cover topics including notations, binary and rational numbers, multiple forms, cost forms, irregular primes, and Fast Fourier Transform (FFT). Enhance your mathematical problem-solving skills with practical exercises and in-depth explanations of advanced asymptotic techniques.