User:Onthenet/AppliedMathematics

Applied Mathematics
Matematics was born out of practical needs in the history of human development, and since evolved along it's own intrinsic modes of study, though however, far it is ventured, it continues to bear fruit in the endeavors it whence came. In this discussion, some of the areas of, what is referred to here as, Industrial Mathematics, are presented.

Student T-Test
The ability to descern when two sample populations are being drawn from two different parent population is of natural value. The t-test is does precisely this, under the condition that the udnderlying populations are normal. The test is formulated in terms of the null hypothesis that the sample populations have the same mean. This null hypothesis can be evaluated by considering the distribution of the t-statistic. The t-statistic being a measure of the difference between the means of two distributions. In the case of normality the distribution of the t-statistic can be found according to the common form of this test. The method was introduced in 1908 by Gosset, while working at the Guinnes Brewing Company.

Least Squares
There are a number of approaces to the least squares problem.

Minimization

Pseudo Inverse

Singular Value Decomposition

Kernel Methods
For some data set $$ X $$ with possibly infinite members, $$ x_i $$, a convenient representation is required in order to utilize a corresponding mathematical frame work to derive the desired results. A vector space representation is often used. However, certain data sets do not readily lend themselves to this. Kernel methods are characterized by a representation of the data and algorithms in terms of an innerproduct in a feature space, and so provides data sets for which vector representation are not readily had, a means for desired results to be derived.

 Representations