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I am also very much interested in manual calculation, math behind astrology such as calculation ASC manually. If you have any recommendation please let me know where I can start.

Are you interested in exact calculation to use for chart calculation or only in general to get a feel for the astronomy behind it, say within a degree? If it is the latter, you can use a rising times table and divide the times by 30 (like the one here does
https://horoscopes.astroseek.com/traditionalastrology), or more accurately use a table of right ascension for each degree, and add an ascensional degree to the Ascendant for each four minutes of a time. If the rising time of a sign is 30 ascensional degrees, then that sign rises in 2 hours, if 20 in 1 hour and 20 minutes, if 15, in 1 hour etc. The early Hellenistic astrologers used this method, although it is approximate since the rising time of the sign is not uniform from the beginning to the end, nor is the sidereal day exactly 24 hours (it is 23 hours 56 minutes and 4 seconds  that is the time for the Ascendant to make one revolution, or rather for the zodiac to make one revolution around the earth). But this calculation is very easy and involves only simple arithmetic.