General Help for Combinatorics and Graph Theory

In summary, the conversation is about a person struggling with a class called Finite Mathematical Structures and specifically with understanding graph theory problems. They are using a textbook by Tucker and are looking for additional resources to help with the course. The conversation also touches on terms like incident and adjacency in relation to graphs and their uses.
  • #1
JasonJo
429
2
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.
 
Mathematics news on Phys.org
  • #2
bondy and murty text.

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

Which terms are you having problems with?
 
  • #3
his textbook does not explain what incident means, what does it mean?
 
  • #4
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.
 
  • #5
oh. it's god damn hard
 
  • #6
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.
 

1. What is combinatorics and graph theory?

Combinatorics is a branch of mathematics that deals with counting and arrangements of discrete objects. Graph theory is a subfield of combinatorics that studies the properties and applications of graphs, which are mathematical structures used to model relationships between objects.

2. What are some real-world applications of combinatorics and graph theory?

Combinatorics and graph theory have numerous practical applications, such as in computer science, telecommunications, transportation networks, social networks, and genetics. They are also used in scheduling, optimization, and cryptography.

3. What are some basic concepts in combinatorics and graph theory?

Some fundamental concepts in combinatorics and graph theory include permutations, combinations, graph connectivity, Eulerian and Hamiltonian paths, and colorings. These concepts are used to solve various problems and analyze different types of graphs.

4. How can combinatorics and graph theory be helpful in problem-solving?

Combinatorics and graph theory provide a systematic approach to problem-solving, which involves breaking down a complex problem into smaller, more manageable parts. These fields also offer various techniques and tools, such as combinatorial formulas, graph algorithms, and graph visualization, to help solve problems efficiently.

5. What are some resources for learning more about combinatorics and graph theory?

There are many resources available for learning combinatorics and graph theory, including textbooks, online courses, and research papers. Some popular textbooks include "Concrete Mathematics" by Ronald Graham, Donald Knuth, and Oren Patashnik, and "Introduction to Graph Theory" by Douglas West. Online platforms like Coursera and edX also offer courses on these topics.

Similar threads

Replies
7
Views
2K
Replies
34
Views
3K
Replies
2
Views
600
  • Science and Math Textbooks
Replies
1
Views
1K
  • General Math
Replies
14
Views
2K
Replies
17
Views
1K
  • Programming and Computer Science
Replies
1
Views
1K
  • Science and Math Textbooks
Replies
1
Views
2K
  • Beyond the Standard Models
Replies
0
Views
410
Replies
1
Views
1K
Back
Top