List of posts:
- Taking Homotopy to the next level
- Homotopy & Paths
- The Fundamental Group
- The Fundamental Group – part 2
- Homotopy Equivalence To Isomorphism
- Simply connected spaces
- The Fundamental Group Of a Circle
- What can we learn from the fundamental group of a circle?
- The fundamental theorem of algrebra – a topological proof
- Universal Problems
- Free product
- Free product with amalgamation
- The free group
Properties of exponantiation of ordinals
In the last post, we worked pretty hard to define ordinals exponentiation, however, This hard work revealed some great properties: If is a successor then: If is a limit ordinal then; Those properties are great – the first two are pretty intuitive, and the third is also a pretty comfortable definition of . We can…
The Cyclotomic polynomial
After we’ve met the terms of roots of unity, primitive roots, and deduced a great identity, we are now finally ready to define the Cyclotomic polynomial of order . It is the polynomial where it’s roots are the primitive roots of unity of order : Let’s find out what’s so special about it: First, note…
Roots of unity
After we’ve finally proved The Fundametal theorem of Galois Theory, we can officially say that we understand the correspondence, and we know exactly when it behaves as we want it to behave. So, it’s time to see some results! The first topic I want to discuss is related to the roots of unity. We’ve met…
Can’t find what you’re looking for? Use the search form to search the site.
Get new content delivered directly to your inbox.