Famous Theorems
a2 + b2 = c2
"_ days a week" by The Beatles + "Mambo No. _" by Lou Bega
What is 13?
The bunkbed conjecture was unexpectedly proven false, using one of these with 7222 vertices.
What is a graph?
"Focuses on learning to write logically sound mathematical arguments"
What is Introduction to Mathematical Reasoning?
This type of shape has infinite self-similarity. The Mandelbrot set is an example of one.
What is a fractal?
For any f, a continuous function on [a,b], all values between f(a) and f(b) are in the image of f
What is the Intermediate Value Theorem?
"_ Guns" by Green Day / "_ Nation Army" by The White Stripes
What is 3?
Last year, the distributed computing program GIMPS found the new largest of this kind of number, with value 2136279841-1.
Two words
What is a Mersenne prime?
"Covers further techniques and applications of integration, infinite series, and introduction to vectors."
What is Calculus 2 (for Science and Engineering)?
This 4D analog of of a cube has 16 vertices.
What is a hypercube or tesseract?
Any non-constant complex polynomials has a complex root
What is the Fundamental Theorem of Algebra?
"_ Luftballons" by Nena / "_ in the Afternoon" by Panic! at the Disco
What is 11?
In 2024, amateur mathematicians found that the fifth busy beaver number, the length of the longest five state programs on one of these.
What is a Turing Machine?
"Prerequisites: MATH 3150 and MATH 3175"
What is Research Capstone?
Despite having three corners, this shape has constant width, so you can roll smoothly on top of it.
What is a Reuleaux triangle?
If there exist injections from A to B and from B to A, there exists a bijection between them
What is the (Cantor–)Schröder–Bernstein Theorem?
"_" by Taylor Swift + "_" an album by Taylor Swift
What is 2011?
The prime factorization of 2024.
What is 22 * 11 * 23?
"with an emphasis on SU(2) and SO(3) as fundamental examples, and introduces the notion of a Lie algebra."
What is Advanced Group Theory?
Discovered in 2022, this type of shape can tile the plane aperiodically. Its name is a pun in German, meaning "one stone".
What is an einstein tile?
No consistent system of axioms can prove all true statements
What is Gödel's (first) incompleteness theorem?
sin("American _" by Don McLean / "_ Little Birds" by Bob Marley)
In May, it was announced that this conjecture was proven with over 1000 pages, giving a correspondence between algebraic geometry and representation theory.
What is the Geometric Langlands Conjecture
"universal coefficients theorems, Bockstein homomorphism, Knnneth formula, cup and cap products, Hopf invariant, Borsuk-Ulam theorem"
What is Topology 2?
This space can be realized as a hemisphere with antipodal equatorial points identified.
What is the real projective plane?