by FEREGO Research
Applied mathematics is one of FEREGO's interests. It is not our only interest of course. This web page collects some of our results from applied mathematics research and also contains various sets of references to other mathematics sources.
Our interests span many areas of mathematics but are mainly focused on classical subjects such as engineering classical analysis. Our interests will probably expand over time. At some future time we more state our interests more specifically. There is quite a large lists of things that we would like to learn, and we are working slowly on improving our pure and applied mathematical abilities.
Mathematical interests and computer interest are closely related. Our interest in mathematics is also reflected in our interest in computers. This page may also contain results pertaining to computer aspects of applied mathematics.
This page collects items that are of a less popular nature and that are more academically flavored. This page is specifically limited to results and research that has been performed by FEREGO. Compilations of references to outside work is extensive and are given elsewhere.
Abstracts. Results are collected here in more of a mathematical abstract form. This is the most mathematical in form and contains equations and very technical discussion. A number of results in mathematical form are collected here.
Number theory. Some results from Ramanujan theory. These results are incredibly interesting. A site with original work is also referenced.
Economics and finance. Math for business. Some of our applied mathematical interests are in the area of money, business, and financial analysis. We will be stating more about this in the future at this location.
Differential equations of finance. Around the time frame of 1996-1997 we performed some calculus analysis of continuous interest compounding systems. We posed some basic equations of finance and mortgage theory as differential equations (i.e., a calculus problem) and solved them in closed form. We obtained some nice closed form results. Then we showed the relationship to the corresponding discrete equations. The results here are interesting in two respects: (1). The results themselves are useful. There can be advantages to obtaining closed form results. (2). The method of derivation gives insights, and can be applied to other similar problems.
This formulation also contains derivations of closed form expressions for the total tax paid on a continuous mortgage and for this amount continuously discounted at a given rate.
We are also capable of finding closed form solutions for the discrete case (in addition to the continuous case above). Thus there are a number of nice results that we have found in closed form.
These results are useful if you have never seen the continuous differential equations describing mortgages and investment. In many respects the continuous equations are more useful than the discrete analogues.
As time permits we will try to get this result out on our web pages. It is also possible that we may continue our work to find more results.
Fibonacci numbers. We have done some work regarding the Fibonacci and related integer number sequences. We have prepared a separate web page regarding Fibonacci numbers and related items.
We are working on more items, and we are also working on adding more items to this list. More work than listed here has been performed, so we are trying to bring out more results.
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