New variable stars from TESS sector 86

In this research, we conducted a search for new variable stars among recent TESS space telescope observations.We have chosen data from the 86th sector.As the main result, we discovered 56 variable stars with sufficient signal-to-noise (SNR) ratio, which were not known as variables before.Then we tried to figure out the correct classification and calculate the period of each star, where possible.We implemented a series of cross-checks to avoid false classification and incorrectly calculated periods.Those methods proved to be highly efficient, although for classification of pulsating variables, they do not guarantee 100% accurate results.For the final list of newly identified variable stars, we performed two additional and essential calculations: the determination of the initial epoch T0 and the amplitude of variability.By using accurate approximations of the extrema, we determined precise timings for either the minimum or maximum light (one extremum per object), and then shifted all T0 values to be as close as possible to JD = 2457000.To determine the amplitude, we applied sigma clipping followed by N -point linear smoothing to each light curve and then calculated the amplitude as the difference between the maximum and minimum magnitudes.This project was conducted for educational purposes: to attract new students to astronomy and to teach them the basics of variable stars research.