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Image:15-344_Note_1.jpg|Summary |
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Image:15-344_Note_1.jpg|Summary |
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== Handwritten Lecture Notes in PDF == |
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[[Media:15-344(lecture1).PDF|MAT344 - Lecture1 (Sep 15)]] |
Latest revision as of 11:33, 7 November 2015
Welcome to Math 344!
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Edits to the Math 344 web sites no longer count for the purpose of good deed points.
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#
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Week of...
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Notes and Links
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1
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Sep 14
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About This Class, Day One Handout, Tuesday, Hour 3 Handout, Thursday, Tutorial 1 Handout
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2
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Sep 21
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Tuesday, Tutorial 2 Page 1, Tutorial 2 Page 2, Thursday, HW1
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3
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Sep 28
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Tuesday, Class Photo, Tutorial 3 Page 1, Tutorial 3 Page 2, Thursday, HW2
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4
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Oct 5
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Tuesday, Drawing -cubes, Thursday, HW3
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5
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Oct 12
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Tuesday, Tutorial Handout, Thursday, HW4
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6
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Oct 19
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Tuesday, Tutorial Handout, Thursday
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7
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Oct 26
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Term Test on Tuesday, Dijkstra Handout,Thursday,HW5
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8
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Nov 2
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Tuesday, Tutorial Handout, Thursday, HW6, Sunday November 8 is the last day to drop this class
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9
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Nov 9
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Monday-Tuesday is UofT Fall Break, Thursday, HW7
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10
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Nov 16
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Tuesday, Thursday, HW8
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11
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Nov 23
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Tuesday, Thursday, HW9
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12
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Nov 30
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Tuesday, Thursday, HW10
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13
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Dec 7
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Tuesday, FibonacciFormula.pdf, semester ends on Wednesday - no class Thursday
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F
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Dec 11-22
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The Final Exam
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Register of Good Deeds
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Add your name / see who's in!
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We mostly went over Day One Handout today.
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Dror's notes above / Students' notes below
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Lecture Note for September 15
DEFINITION 1 Graph A graph is a set (usually finite, "vertices")
along with a set ("edges") of unordered pairs of distinct elements of
.
DEFINITION 2 Incident If an edge , we say that is incident to
and .
DEFINITION 3 N-valent In a graph , a vertex is called
bivalent if it is incident to precisely two edges and n-valent if incident to precisely n edges, where .
DEFINITION 4 Edge Cover An edge cover for graph is a subset such that every edge of incident to at least one vertex in .
DEFINITION 5 Independent Let be a graph. A subset is called independent if whenever , then .
THEOREM 1 Edge covers are complementary to independent sets. In other words, is an edge cover if and only if
the complementary subset is an independent set.
Proof
Assume is an edge cover. I assert that is independent.
Indeed, if , then since is an edge cover, either or
, which implies does not connect any two elements of .
Assume is independent. Pick any edge . As is independent,
does not connect any two members of . Hence, either or , which implies is incident to an element of . QED
DEFINITION 6 Matching is a subset of edges of a graph where no two edges share a common vertex. A matching is said to be perfect if
all edges in a graph are matched.
Scanned Lecture Notes for September 15
Handwritten Lecture Notes in PDF
MAT344 - Lecture1 (Sep 15)