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2 Fields

3 Solutions of Cubics

4 The Euclidean Algorithm for Polynomials

5 Simple Field Extensions

6 Galois's Method

7 The Galois Group of a Cubic

8 Permutation Groups

9 Normal Subgroups

10 Quotient Groups

11 Solutions of Equations of Degree Four

12 The Group of the Dodecahedron

13 Unsolvability of the Quintic

14 Review

. The syllabus for Analysis is This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.