Enumerative or Non-enumerative Combinatorics?

  • Thread starter Thread starter altcmdesc
  • Start date Start date
  • Tags Tags
    Combinatorics
AI Thread Summary
Enumerative combinatorics focuses on counting and arranging objects, while non-enumerative combinatorics deals with properties and structures without counting. Many students find enumerative techniques foundational, suggesting a solid understanding of this area may enhance comprehension of non-enumerative topics. Personal experiences indicate that both areas have their merits and can be engaging. Ultimately, the choice may depend on individual interests and future applications in mathematics. A strong foundation in enumerative combinatorics is often recommended before tackling non-enumerative concepts.
altcmdesc
Messages
64
Reaction score
0
Which one do you find more interesting and why?

My school offers separate classes in these two subjects and I'm wondering about which one I should take. I have very little experience with combinatorics (not much more than my high school algebra II course), so I have no idea.
 
Mathematics news on Phys.org
Jolly hard question for me to answer! The first combinatorics class I took, I studied enumerative techniques for the first half and then non-enumerative for the second half. I liked both of them honestly.

I think it's probably important to have a good basis for enumerative combinatorics before studying non-enumerative. Just my opinion though I guess.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

Similar threads

Replies
2
Views
2K
Replies
1
Views
1K
Replies
7
Views
3K
Replies
4
Views
2K
Replies
52
Views
6K
Replies
25
Views
7K
Replies
13
Views
2K
Back
Top