File - Math at the Academy
... What is the minimum amount of parts that would need to be congruent to ensure two triangles are congruent? (work with a partner) • 1 side and 1 angle (SA)? True or False? ...
... What is the minimum amount of parts that would need to be congruent to ensure two triangles are congruent? (work with a partner) • 1 side and 1 angle (SA)? True or False? ...
Algebraic aspects of topological quantum field theories
... The main result in this context states that there is a bijection between (symmetric) monoidal functors 2Cob → Vectk and commutative Frobenius algebras. In other words given a 2d-TQFT there is a corresponding Frobenius algebra and vice versa. To prepare ourselves for the proof, this algebraic structu ...
... The main result in this context states that there is a bijection between (symmetric) monoidal functors 2Cob → Vectk and commutative Frobenius algebras. In other words given a 2d-TQFT there is a corresponding Frobenius algebra and vice versa. To prepare ourselves for the proof, this algebraic structu ...
Chapter 4 Notes 2010
... 2) If it’s a triangle use a small triangle in front of the vertices, for anything else, just use the word polygon Example: CAT JSD. List each of the following. 1. three pairs of congruent sides ...
... 2) If it’s a triangle use a small triangle in front of the vertices, for anything else, just use the word polygon Example: CAT JSD. List each of the following. 1. three pairs of congruent sides ...
The Computational Complexity of Linear Optics
... DA , then Theorem 1 shows that P#P ⊆ BPPNP —but only if the BPPNP machine gets to fix the random bits used by O. This condition is clearly met if O is a classical randomized algorithm, since we can always interpret a randomized algorithm as just a deterministic algorithm that takes a random string r ...
... DA , then Theorem 1 shows that P#P ⊆ BPPNP —but only if the BPPNP machine gets to fix the random bits used by O. This condition is clearly met if O is a classical randomized algorithm, since we can always interpret a randomized algorithm as just a deterministic algorithm that takes a random string r ...
Project Gutenberg`s The Foundations of Geometry, by David Hilbert
... The material contained in the following translation was given in substance by Professor Hilbert as a course of lectures on euclidean geometry at the University of Göttingen during the winter semester of 1898–1899. The results of his investigation were re-arranged and put into the form in which they ...
... The material contained in the following translation was given in substance by Professor Hilbert as a course of lectures on euclidean geometry at the University of Göttingen during the winter semester of 1898–1899. The results of his investigation were re-arranged and put into the form in which they ...
A Ch. 3 Angles
... proof above, ∠3 was not part of the original problem, so I just wrote it in there because I needed it. In the proof below, I used the Reflexive Property as a reason to use ∠3. Take note, the first proof was completed in 4 steps, the second proof for the same theorem was completed in 8 steps. Let’s l ...
... proof above, ∠3 was not part of the original problem, so I just wrote it in there because I needed it. In the proof below, I used the Reflexive Property as a reason to use ∠3. Take note, the first proof was completed in 4 steps, the second proof for the same theorem was completed in 8 steps. Let’s l ...
The noncommutative geometry of the quantum Hall effect
... Moreover, as proposed by Prange,“” Thouless,” and Halperin,51 the plateaux of the Hall conductance which appear while changing the magnetic field or the charge-carrier density, are due to localization. Neither the original Laughlin paper nor the TKN2 one however could give a description of both prop ...
... Moreover, as proposed by Prange,“” Thouless,” and Halperin,51 the plateaux of the Hall conductance which appear while changing the magnetic field or the charge-carrier density, are due to localization. Neither the original Laughlin paper nor the TKN2 one however could give a description of both prop ...
Exotic path integrals and dualities
... Supersymmetric localization is one of the fundamental reasons that supersymmetric field theory is quite elegant: supersymmetric path integrals simplify significantly as they can be evaluated by only considering certain fixed points of the supersymmetric theory. Topological field theories are theorie ...
... Supersymmetric localization is one of the fundamental reasons that supersymmetric field theory is quite elegant: supersymmetric path integrals simplify significantly as they can be evaluated by only considering certain fixed points of the supersymmetric theory. Topological field theories are theorie ...
Noether's theorem
Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.