Intro to mathematics

These class notes explore the fundamental principles of geometry, including the properties and relationships of points, lines, angles, and shapes in both two and three dimensions. Topics covered include Euclidean geometry, geometric proofs, congruence, similarity, transformations, and applications of geometry in various real-world scenarios. These notes provide a solid foundation for understanding the geometry of the physical world and its relevance in mathematics and practical applications.

These class notes delve into the fascinating intersection of algebraic geometry and number theory. Topics covered include algebraic varieties over number fields, Diophantine equations, the arithmetic of elliptic curves, and the deep connections between algebraic structures and number theory. These notes offer insight into how mathematical objects, equations, and geometric shapes are studied in the context of whole numbers and their extensions.