Algebra and Number Theory

Algebra explores the structures of solution sets for algebraic equations, as well as the properties of permutations, combinations, and transformations. Algebraic Geometry focuses on the solution sets of polynomial equations involving one or more variables, utilizing abstract mathematical frameworks such as varieties, schemes, and stacks to aid in this analysis. Additionally, power-series equations naturally emerge within this area of study. Number Theory primarily examines integers, with a particular emphasis on prime numbers. A significant aspect of this field investigates integer or rational solutions to systems of polynomial equations with multiple variables. Algebraic structures and its representations as transformation groups serve as essential tools in understanding the symmetries of complex geometric shapes and objects.