61 lines
1.2 KiB
TeX
61 lines
1.2 KiB
TeX
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% use [nosolutions] flag to hide solutions.
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% use [solutions] flag to show solutions.
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\documentclass[
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solutions,
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singlenumbering,
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shortwarning,
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unfinished
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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\usepackage{units}
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\uptitlel{Advanced 2}
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\uptitler{Fall 2023}
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\title{Quotient Groups}
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\subtitle{Prepared by \githref{Mark} on \today{}}
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\def\znz#1{\nicefrac{\mathbb{Z}}{#1\mathbb{Z}}}
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\begin{document}
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\maketitle
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\input{parts/0 mod}
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\input{parts/1 groups}
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\input{parts/2 subgroups}
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% Rough outline:
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%
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% Part 1: (DONE)
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% mod, eqrel, eqclass.
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%
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% Part 2: (IN PROGRESS)
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% groups, Z/nZx, graphs, isomorphism.
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% generators, generating sets.
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%
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% Part 3: (IN PROGRESS)
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% subgroups, isomorphic subgroups,
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% TODO:
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%
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% cosets
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% normal subgroups
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% quotient groups
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% Understand Z/nZ
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% Functions as objects (groups of functions)
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% Q/Z problems (mod generalization)
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% isomorphism groups (which are iso to symmetric group)
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% Another handout:
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%
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% symmetric group, number of permutations,
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% cycle notation, type and sign,
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% proofs about generators, alternating group
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% alternating group generators, fun problems.
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\end{document}
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