Introduction to group theory, covering topics such as integers, permutations, the definition of groups, subgroups, quotient groups, and group homomorphisms.
This course introduces students to basic logic, proof methods, sets, mappings, relations, and mathematical induction, transitioning gradually from familiar systems to abstract structures. Topics include the division algorithm, unique factorization theorems for integers and polynomials, numbers, and algebraic systems such as groups, rings, and fields. Emphasis is placed on problem-solving and proof-writing, with regular written assignments required. Students are expected to gain a deep understanding of theoretical concepts and algebraic computation. Grades are based on problem sets, midterms, and a comprehensive final exam. The course is taught by faculty members and includes a discussion section led by a TA.