Algebra and geometry, 1st term. Problems with solutions

<jats:p>This manual contains problems with detailed solutions for the topics covered in the course “Algebra and Geometry” taught at the Faculty of Computational Mathematics and Cybernetics at Lomonosov Moscow State University during the first semester. It is assumed that the reader has a basic understanding of the following concepts: algebra of geometric vectors, equations of lines and surfaces of first and second order, determinant and rank of a matrix, linear spaces, complex numbers, algebraic polynomials, groups, rings, and fields.</jats:p>