This page covers pure mathematics. This includes analysis and group theory.
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MSMQP2 Sequences & Series |
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| Introduction to the ideas behind analysis; introduces the definition of a limit and proves the Algebra of Limits for sequences. Infinite seris are also covered and some convergence theorems are proven. | ||
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141 (183) |
MSMXP1 Differentiable Functions |
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| Continues from MSMQP2 to define limits for real valued functions of a real variable, and develops the ideas of continuity and differentiability proving various theorems along the way. | ||
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72 (77) |
MSM2P2 Symmetry And Groups |
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| Introduction to group theory, covering group actions, Lagrange's Theorem and the Orbit-Stabiliser Theorem, cosets, normal subgroups, and factor groups. A proof of the First Isomorphism Theorem is also given. | ||
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50 (134) |
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342 (481) |
MSMXP5 Rings & Polynomials |
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| Introduction to ring theory, defining division rings, integral domains, and field. A polynomial over a field is defined, the division algorithm is stated and proved and irreducibility is discussed including proof of Eisenstein's Criterion. | ||
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27 (70) |
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120 (228) |
MSMYP2 General Topology |
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| Begins with a discussion of metric spaces then generalises to topological spaces, generalising also the definition of a limit and of continuity. Product and subspace topologies are defined as is topological union. Connectedness is covered and it is shown that the real line is connected. Path connectendess is also introduces. Also covered is compactness and various theorems are proved. | ||
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242 (619) |
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125 (242) |