A core course unit for second year Arts students in Mathematical Studies . The mathematical structures known as groups and fields play a central role in modern mathematical thinking. They have evolved from more intuitive ideas which most students accept and use without wondering about their formal justification. The course shows how the axioms for groups and fields are developed, referring back to elementary number theory and matrix theory for motivation. Certain key theorems are proved, which often rely on the results proved in the prerequisite first year course.
Examples show how abstract ideas are studied in practice.
Syllabus Equivalance relations. Equivalence classes and their representatives. Examples of equivalence classes. Field axioms, elementary consequences of the field axioms. Fields of rational and real numbers.