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In this course we'll derive the formula for the roots of general cubic and 4th degree polynomials using complex numbers and some basic group theory and try to see why NO such formula exists for higher degree polynomials! This will require us to learn the theory of symmetry groups and explore it's connection to polynomials via permutations of roots, in the process we'll catch a glimpse of a much deeper algebraic theory in mathematics called Galois theory. Recommended Course Background: Students should be comfortable with Complex Numbers and Proof by Induction [This course will be taught in the mode of Inquiry Based Learning which means that problem sheets will be handed out in the class instead of a regular lecture and students will learn the subject by actively solving problems instead of passively listening to a lecture.]