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Algebra gives us tools to solve equations. The integers, the rationals, and the real numbers have special properties which make algebra work according to the circumstances. In this course, we generalize algebraic processes and the sets upon which they operate in order to better understand, theoretically, when equations can and cannot be solved. We define and study abstract algebraic structures such as groups, rings, and fields, as well as the concepts of factor group, quotient ring, homomorphism, isomorphism, and various types of field extensions. This course introduces students to abstract rigorous mathematics.
Format: lecture; Remote lectures. TA sessions will be held in person. If taken pass/fail, this course does not count towards the Mathematics major.
Grading: yes pass/fail option,
yes fifth course option
MATH 250 or permission of instructor
300-level math course