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Week - 1
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Basics; Properties of the integers and rational numbers, |
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Week - 2
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Euclidean algorithm, fundamental theorem of arithmetic, Euler phi-function, Fermat theorem, Linear Congruence, modular arithmethic. |
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Week - 3
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Definitions and examples of groups. |
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Week - 4
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Direct Products. |
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Week - 5
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Subgroups, cyclic groups and subgroups of cyclic groups . |
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Week - 6
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Lagrange Theorem. |
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Week - 7
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Normal subgroups. |
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Week - 8
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The homomorphism and isomorphism theorems. |
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Week - 9
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Symmetric groups. |
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Week - 10
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Factor groups. |
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Week - 11
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Finite abelian groups. |
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Week - 12
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Classification of finite abelian groups. |
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Week - 13
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p-Sylow subgroups. |
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Week - 14
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Applications of the Sylow Theorems. |