Foundations of Mathematics and Foundations of Analysis [Under Revision and Expansion]
These notes, written for MAT 3013 and MAT 3213, two junior-level courses, are very introductory in nature. This is a joint undertaking with Professor Eduardo Dueñez. We begin by describing at a very elementary level the beginnings of a way to construct the ZF universe. (These notes are not meant for a course in logic.) Then, we move on to the reals, sequences, series and continuity. The second half of the notes is still heavily under construction.

Foundations Notes
Note 0: Background
Note 1: The Propositional Calculus
Note 2: The Predicate Calculus
Note 3: Sets
Note 4: The Natural Numbers
Note 5: Functions and Relations
Note 6: Numbers and Arithmetic
Note 7: The Axiom of Choice
Note 8: The Real Numbers

The following are under revision/completion.
Note 9: Important Subsets of the Reals
Note 10: Sequences and Series
Note 11: Continuity

The middle of this page is closed for remodeling.

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AMI-5 is an adaptive multidimensional five-point integrator written in FORTRAN. I simulated recursive descent in a nonrecursive FORTRAN environment. It is one of the oldest programs still in use pretty much as originally written. See Roy Milton's "Computer evaluation of the multivariate normal integral" (Technometrics, Vol. 14, No. 4, 1972, pp. 881-889) for a significant application of this little subroutine. See Robert Bohrer's and Mark J. Schervish's "An error-bounded algorithm for normal probabilities of rectangular regions" (Technometrics, Vol. 23, No. 3, 1981, pp. 297-300) for a follow-up. Incidentally, the original was called MDQUAD ("MD" for multidimensional and "QUAD" for quadrature). I did not use the word cubature to emphasize that recursive quadrature was used.

For more, check the Differential Automata and the Numerical Examples pages. Recheck all of these pages, and the present page, from time to time.