Abstract Algebra & Number Theory
This term describes a function that is continuous everywhere but differentiable nowhere, with the most famous example named after Weierstrass.
What is a fractal/Weierstrass function?
This type of algebraic structure satisfies all field axioms except for commutativity of multiplication, with quaternions being a famous example.
What is a Division Ring (or Skew Field)
This inequality states that for any probability distribution with finite variance, the probability that a value differs from the mean by more than \(k\) standard deviations is at most \(1/k^2\).
What is Chebyshev's Inequality?
This millennium prize problem, currently unsolved, deals with the distribution of prime numbers and their relationship to the zeros of a specific function.
What is the Riemann Hypothesis?
This theorem relates a surface integral to a line integral, often used to compute circulation in vector fields.
What is Stokes' Theorem?
This theorem, proven by Wiles in 1995, states that no three positive integers \(a, b, c\) satisfy \(a^n + b^n = c^n\) for any integer value of \(n\) greater than 2.
What is Fermat’s Last Theorem?
This distribution is often used in survival analysis to model the time until a specific event occurs, possessing the "memoryless" property.
What is the Exponential Distribution?
This fundamental result in complex analysis states that the line integral of a holomorphic function around a closed loop is zero
What is Cauchy's Integral Theorem?
This theorem states that every finite group \(G\) is isomorphic to a subgroup of the symmetric group \(S_{n}\).
What is Cayley's Theorem?
This theorem proves that the distribution of the sum of a large number of independent, identically distributed variables approaches a normal distribution, regardless of the original distribution.
What is the Central Limit Theorem?
his sequence of functions, defined by \(f_n(x) = nx(1-x)^n\), provides a classic counterexample to the exchange of limit and integral.
What is the "pointwise but not uniformly convergent" sequence
This is the highest level of solvable group, defined as a sequence of subgroups where each is a normal subgroup of the next, ending in the trivial group
What is a Composition Series? [1]
what is 24 x 50000000
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