James S. Freeman WebPage

Tangential Imagination (PDF) A dramatization of a past class discussion and an imaginative approach to the arc-tangent function using complex logarithms.

Probable Probability (PDF) A dramatization of a past class discussion on Bertrand's Paradox involving the extra-mathematical nature of probabilities. An unambiguous probability space must be associated to a well-defined random process.

Dimensional Transcendentalism (PDF) A dramatization of a past class discussion of physical units, the six fundamental dimensions and transcendental functions. They central point is that units cannot be destroyed and, hence, the input to a transcental function must be "unitless".

Tensions over Tension (PDF) A dramatization of a past class discussion of a physics homework problem: Is tension a vector or a scalar? It is neither. Technically, tension is a tensor, a special type of function with vectors as the input and output.

David Darlington Novels

"Whether 'tis Nobler ..." (kindle) and "... the Cruelest Month" (kindle)

Writings and Handouts from or related to the Courses

Inductive and Deductive Reasoning - Intuitive, Inductive and Deductive Logic are the basis of how we obtain information about the world, which, as Wittgenstein said, "Is all that is the case".

Theory, Fact and Law in Science - Are scientific theories unproven, and once proven become laws or facts? No. Theories, Laws and Facts are three very different sorts of scientific (or mathematical) statements. Theories are generally the most complex and well-confirmed of all scientific statements.

What is a Number, Really?(PDF) - A Logical Pseudo-History of Numbers. "Numbers are what we count with." Everything else follows from that.

Axioms, Geometry and Algebra (PDF) Mathematics is based upon Axioms or Postulates. These are not indubitable truths, but merely assumptions upon which we base deductions.

Fundamental Dimensions and Units (PDF) A summary of the fundamental units and dimensions by which physical science measures the world.

Radially Symmetric Manifolds (PDF) Some original results in the theory of curved surfaces and Riemannian manifolds.

History of Unix and the Internet (PDF) A brief history of computers and the Internet with an Overview of the Unix operation system.

SQL Relational Databases (PDF) A brief introduction to the concept and mathematical foundations of relational databases and SQL - Structured Query Language.

Probabilities of Poker (PDF) The probabilities of the nine basic 5-card poker hands are calculated using a "branching tree" approach.

The Logistic Growth Model The basic Malthusian exponential growth model is enhanced to incorporate the effect of crowding. A recursive function and mathematical chaos are the result.

Game Theory and Recursive Programs An introduction to game theory is presented by analyzing weighted voting systems using recursive algorithms.

Pyhagorean Theorem (PDF) An new proof of the Pythagorean Theorem using a simple geometric construction composed of three similar trianlges and one rectangle.

Bell's Theorem (PDF) One of my favorite theorems: The area of a lattice polygon may be calculated by counting lattice points.

Brief History of the Calendar The Gregorian calendar used through the western world, and its confusing leap year convention, is the result of successive corrections to older calendars.

Pythagorean Musical Scale (PDF) The Do-Re-Mi music scale made famous in The Sound of Music dates back to the mathematician Pythagoras, circa 550BC.

Education

BA in Mathematics - Rice University - 1972

MA & ABD in Mathematics - SUNY at Stony Brook - 1975

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