User contributions for Arr0w

14:0514:05, 2 July 2022 diff hist −30 m P Adic Solenoid No edit summary current
14:0414:04, 2 July 2022 diff hist +605 N P Adic Solenoid Created page with "The canonical group homomorphisms <center><cmath>\varphi_n:\mathbb{R}/p^{n+1}\mathbb{Z}\to \mathbb{R}/p^n\mathbb{Z},~x\pmod{p^{n+1}\mathbb{Z}}\mapsto x\pmod{p^n\mathbb{Z}}</cm..."

16:1016:10, 1 July 2022 diff hist 0 m Newton's method No edit summary
16:0916:09, 1 July 2022 diff hist −2 m Newton's method No edit summary
16:0816:08, 1 July 2022 diff hist +5,477 Newton's method I added some applications into some more advanced mathematics, specifically how Newton's Method could be applied to concepts in analytic number theory.

13:5013:50, 23 June 2022 diff hist +6,578 Cyclotomic polynomial This page was absolutely abysmal in the state I found it. I added many well-known results and proofs of all of my conjectures. One could extend this to algebraic number theory and Galois theory, which currently I haven't the time to write about. current

16:5916:59, 12 June 2022 diff hist +1,915 N Cauchy's Criterion Created page with "'''Cauchy's Criterion''' is a result in analysis that states that a sequence of real numbers <math>(a_n)</math> converges if and only if it is a Cauchy sequence. A sequen..." current
16:1816:18, 12 June 2022 diff hist −2,355 Bolzano-Weierstrass Theorem No edit summary current

21:4121:41, 28 May 2022 diff hist +4,695 N Rank Nullity Theorem I added the statement of the theorem, as well as a complete proof. Indeed, there are some definitions that could probably be added, but I hope that someone else would add the definitions to these terms, such as linear transformations and bases. current

21:2621:26, 12 May 2022 diff hist +1,240 N The Class Equation Created page with "The '''Class Equation''' is a result in group theory. It states that <center><math>|G|=|Z(G)|+\sum_{i=1}^r|G : C_{G}(g_i)|</math></center> where <math>g_i</math> are rep..." current
21:2021:20, 12 May 2022 diff hist +12 Well Ordering Principle No edit summary current
21:1921:19, 12 May 2022 diff hist +1,848 Well Ordering Principle This article had a horrendous proof that was really informal. I added significant rigor and formalism to this topic.

21:0621:06, 12 April 2022 diff hist +1 Complex analysis forgot to add \oint current
21:0621:06, 12 April 2022 diff hist 0 Complex analysis It is supposed to be "Cauchy's Integral Formula" instead of "Theorem". These two are very different things, and is not what is written here.
21:0221:02, 12 April 2022 diff hist +26 Laurent Series No edit summary current
21:0221:02, 12 April 2022 diff hist +18 Laurent Series No edit summary
21:0021:00, 12 April 2022 diff hist +7,977 N Laurent Series Created page with "The '''Laurent series''' of a complex function <math>f(z)</math> is a representation of that function as a power series which includes terms of negative degree. It may be used..."

13:0113:01, 7 April 2022 diff hist +804 N Wolstenholme's Theorem Created page with "'''Wolstenholme's Theorem''' is a result in Number Theory from English Mathematician Joseph Wolstenholme. It states that for primes <math>p>3</math> that if the equation..." current

17:5417:54, 15 March 2022 diff hist +1,743 Mobius inversion formula Made major edits to this. current

10:3210:32, 3 March 2022 diff hist +211 Fundamental Theorem of Arithmetic No edit summary
10:2610:26, 3 March 2022 diff hist +1,510 N Matrix Tree Theorem Created page with "The '''Matrix Tree Theorem''' is a theorem in Graph Theory that counts for the number of spanning trees of a connected graph. It was discovered by Gustav Kirchhoff, which..." current

01:5801:58, 1 March 2022 diff hist +2,936 Mobius function I made major edits to this page. The proofs were not comprehensive and the details were nonexistent/uninformative. I have tried to prove as many of the results that I could, but I would appreciate it if others could fill some of the gaps. current

23:5423:54, 30 December 2021 diff hist +739 Field I revamped this entire page due to the lack of rigor and explanations behind any of the examples presented.
19:5719:57, 30 December 2021 diff hist +5 m Fermat's Little Theorem No edit summary
19:5519:55, 30 December 2021 diff hist +2,210 Fermat's Little Theorem I added another proof of Fermat's Little Theorem using field theory.
19:2419:24, 30 December 2021 diff hist +545 Euler's Totient Theorem Added a proof of the theorem using Group Theory.

16:0816:08, 8 December 2021 diff hist +906 Fermat's Little Theorem Added another proof using Lagrange's Theorem.

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