# Fundamental Theorem of Curves and Non-Unit Speed Curves - Essay - Mathematics - Prof. Adrian Down

1.1 Basis orientation Recall that the triple product of three vectors is defined as, [A,B,C] = hA × B,Ci Definition (Handedness). If { A,B,C } is a basis of R3, { A,B,C } is called right handed (left-handed) if [A,B,C] > 0 ( < 0).

# Ordinary Differential Equations - Essay - Mathematics - Prof. Adrian Down

Recall that the general solution of a system of n first-order differential equations contains n constants. These constants must be determined from the given conditions on the system.

# Analysis Reviews - Essay - Integral Calculus

Definition. A metric space is a set X with a distance function d : X ×X ! [0,1) satisfying d(x, x) = 0, 8x d(x, y) = 0 , x = y d(x, y) = d(y, x), 8x, y 2 X d(x1, x3)  d(x1, x2) d(x2, x3), 8x1, x2, x3 2 X

# Random Variables - Essay - Mathematics

In many situations we are not concerned directly with the outcome of an experiment, but instead with some function of the outcome.

# Decision Theory - Essay - Mathematics

Enough probability; we have what we need now to start doing statistics. “Decision theory” is about how to behave optimally under uncertainty, and as such provides a nice backbone for the various statistical procedures we’ll be looking at.

# Markov Chains Renewal Process and Renewal Equation - Essay - Mathematics

Syed's computer has three critical parts, each of which is needed for the computer to work. The computer runs continuously as long as the three required parts are working. The three parts have mutually independent exponential lifetimes before they...

# Central Limit Theorem - Essay - Mathematics

Paninski, Intro. Math. Stats., October 5, 2005 35 probability, ZN !P Z, if P(|ZN − Z| > !) ! 0 as N ! #. (The weak LLN is called “weak” because it asserts convergence in probability, which turns out to be a somewhat “weak” sense of stochastic conv...

# Fundamental Theorem of Curves and Non-Unit Speed Curves - Essay - Mathematics - Prof. Adrian Down

1.1 Basis orientation Recall that the triple product of three vectors is defined as, [A,B,C] = hA × B,Ci Definition (Handedness). If { A,B,C } is a basis of R3, { A,B,C } is called right handed (left-handed) if [A,B,C] > 0 ( < 0).

# Function of finite Order - Essay - Mathematics

This chapter is another review of standard material in complex analysis. See for instance Chapter 11 of [Davenport 1967], keeping in mind that Davenport uses \integral function" for what we call an \entire function

# Field and Galois Theory - Essay - Mathematics

Let f .X/ 2 F X be a monic polynomial of degree m, and let .f / be the ideal generated by f . Consider the quotient ring F X=.f .X//, and write x for the image of X in F X=.f .X//, i.e., x is the coset X C.f .X//

# Euler Project - Essay - Mathematics

Euler [Eul] achieved the rst major advance beyond Euclid's proof by combining his method of generating functions with another highlight of ancient Greek number theory, unique factorization into primes

# Evaluation of Definite Integral - Essay - Mathematics

We evaluate the following de¯nite integral by using the theory of residues and a branch of a holomorphic function.

# Algebraic Number Theory - Essay - Mathematics

An algebraic number field is a finite extension of Q; an algebraic number is an element of an algebraic number field. Algebraic number theory studies the arithmetic of algebraic number fields — the ring of integers in the number field, the ideals...