Difference between revisions of "MAT5423"

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(Created page with "Introduction to basic discrete structures. Sample textbooks: [1] Gordon Pace, ''Mathematics of Discrete Structures foe Computer Science'', Springer, 2012 [2] Vladlen Koltu...")
 
 
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Introduction to basic discrete structures.
 
  
Sample textbooks:
 
  
[1] Gordon Pace, ''Mathematics of Discrete Structures foe Computer Science'', Springer, 2012
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'''Catalog entry'''
[2] Vladlen Koltun, ''Discrete Structures Lecture Notes, Stanford University'', 2008.[https://web.stanford.edu/class/cs103x/cs103x-notes.pdf link]
 
  
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''Prerequisite'': Combinatorics and Probability [[MAT2313]], or Applied Graph Theory [[MAT4323]], or instructor consent.
  
==Topics List==
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''Contents'':
{| class="wikitable sortable"
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Partially ordered sets, maximum/maximal and minimum/minimal elements. Well-ordered sets. Maximality principlies (Zorn's lemma, Well-ordering principle, Hausdorff maximality lemma). Boolean algebras and the Stone representation theorem. Generalizations of the Stone representation theorem.
! Week !! Topic !! Sections from Pace's book !! Prerequisites
 
|-
 
|  1-2 
 
|| [[Propositional logic]]
 
|| 2.1-2.4
 
|| Undergraduate real analysis.
 
|-
 
|  3-4 
 
|| [[Completeness and soundness]]
 
|| 2.5-2.7.
 
||
 
|-
 
|  4-5 
 
|| [[Lebesgue measurable sets]]
 
|| 2.1-2.7
 
||
 
|-
 
|  7-9 
 
|| [[Lebesgue measurable sets]]
 
|| 2.1-2.7
 
||
 
|-
 
|  10-12 
 
|| [[Lebesgue integration]]
 
|| 4.1-4.6
 
||
 
|}
 

Latest revision as of 13:44, 29 January 2025


Catalog entry

Prerequisite: Combinatorics and Probability MAT2313, or Applied Graph Theory MAT4323, or instructor consent.

Contents: Partially ordered sets, maximum/maximal and minimum/minimal elements. Well-ordered sets. Maximality principlies (Zorn's lemma, Well-ordering principle, Hausdorff maximality lemma). Boolean algebras and the Stone representation theorem. Generalizations of the Stone representation theorem.