General Help for Combinatorics and Graph Theory

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Discussion Overview

The discussion revolves around challenges faced by participants in understanding concepts related to combinatorics and graph theory, particularly in the context of a finite mathematical structures course. Topics include isomorphisms, edge coverings, and definitions such as "incident" and "adjacent."

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses difficulty in grasping graph theory problems early in the semester, particularly with concepts like isomorphisms and edge coverings.
  • Another participant suggests the Bondy and Murty text as a resource, indicating a preference for it over calculus.
  • A participant questions the meaning of the term "incident," prompting a clarification that it refers to the relationship between nodes and edges.
  • Further explanation is provided regarding adjacency and incidence, with an example involving a graph defined by vertices and edges, along with an incidence matrix.
  • One participant reflects on their experience with graph theory, noting the abundance of definitions as a challenge.

Areas of Agreement / Disagreement

Participants express varying levels of difficulty with specific terms and concepts, indicating that there is no consensus on the ease of understanding these topics. Some participants find certain textbooks helpful, while others have different experiences.

Contextual Notes

There are mentions of specific terms and concepts that may require further clarification, such as "incident" and "adjacent," which are not universally understood among participants. The discussion also reflects a transition from calculus to more abstract mathematical concepts.

Who May Find This Useful

Students taking courses in discrete mathematics, combinatorics, or graph theory, particularly those transitioning from calculus to more abstract mathematical topics.

JasonJo
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hey guys I am taking a class right now called Finite Mathematical Structures, and I am having a pretty tough time. although it's only about 1 - 2 weeks into the semester, i am having a hard time actually understanding graph theory problems.

so far we are doing isomorphisms, edge coverings, corner coverings, the even-odd edge theorem, etc.

i am using Applied Combinatorics by Tucker (coincidentally, he is also my Professor for the course) and I think the text is kinda weak for theory, but for applications and problems its great.

can anyone offer me any links or general seeds of advice for a discrete math course like this? i am so used to calculus and things of that nature, i am not used to such an abstract level of mathematics.
 
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bondy and murty text.

Lol calculus over combinatoris/number/graph...hehe. NEVER.

Which terms are you having problems with?
 
his textbook does not explain what incident means, what does it mean?
 
sure it does...he's got examples...well the vs i have its bondy & MURTY

adjacent is node 2 node right? if that's correct
then incident is node to edge...

that is if you have G=[V,E] V = { v0,v1,v2 } E= {e0,e1,e2}
s.t e0 = [v0,v1], e1 = [v1,v2], e2=[v0,v0] i ignore the psi(i think it is) notation.
then e0 is incident to v0 once and e2 is incident 2x.

and the incidence matrix is
xxe0e1e2
v0 1 0 2
v1 1 1 0
v2 0 1 0
as for its uses its been a while so i don't really know.
 
oh. it's god damn hard
 
I took Graph Theory last term. I enjoyed it very much.

No textbook though. Mostly his lecture notes and browsing books and internet for assignments.

My main issue was all the definitions. So many of them.
 

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