Physical Sciences and Mathematics Commons^™

A Brief Introduction To Gödel’S Theorems, Michael Detlefsen

ACMS Conference Proceedings 1977

Gödel’s two famous incompleteness theorems are results that have come up a number of times in the discussions at the 1977 ACMS conference. This paper provides a brief and relatively non-technical statement on these results and of their significance for the foundations of mathematics.

Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley

ACMS Conference Proceedings 1977

Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of …

Existence In Mathematics, Willis Alberda

ACMS Conference Proceedings 1977

Contemplation of the existence of mathematical entities for very apparent reasons generates a mental cycling of arguments dealing with the nature of mathematical truth, meaning in mathematics, and the obviously related question of which of these two problems should be solved first. The problem of the existence of mathematical entities dates from the first thoughts and ideas of a mathematical nature. The problem of existence in mathematics is fundamental to the domain of speculation and research on the foundations of mathematics. When we try to put ourselves in the place of those philosophers who first explored this problem we must …

The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis

ACMS Conference Proceedings 1977

In teaching the foundations of mathematics within the framework of a Christian college, and particularly that of a Christian liberal arts college, there are two groups of students which must be served. The first consisted of the non-mathematics majors—those non-scientifically oriented “general anything” students who, as a catalog might put it, are to receive “an introduction to and an appreciation of the history, foundations, culture and applications of mathematics.” The second group consists of the mathematics majors, and the few science majors who have not been frightened away by the calculus. The gulf between these two groups is sufficiently large, …

Epistomology To Ontology, Charles R. Hampton

ACMS Conference Proceedings 1977

This paper offers commentary on the various philosophical approaches to the foundations of mathematics and then indicates how these ideas have implications in consideration of the existence question.

Introduction (1977), Robert Brabenec

ACMS Conference Proceedings 1977

No abstract provided.

Table Of Contents (1977), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1977

No abstract provided.

O(H^6) Discretization Error Finite Difference Approximation To Solutions Of The Poisson Equation In Three Variables, Robert E. Lynch

Department of Computer Science Technical Reports

No abstract provided.

Using A Prediction Model In Forecasting Appeals, Paul A. Rake

IUSTITIA

Following the 1972 reorganization of the Indiana Court of Appeals into three panels serving defined geographical districts, the Court soon found itself floundering with too many unevenly distributed cases. Lacking a sufficient base of statistical data from which to formulate a plan to cope with the problem, various proposals, including redistricting the court, adding more judges, and developing a more sophisticated staff research, could not be measured for effectiveness or advisability.

In response to these problems, the Court developed a project to deal with the future caseload by constructing a regression model to predict appeals. This model generated estimates of …

A Quantitative Connection Between Computer Programs And Technical Prose, M. H. Halstead

Department of Computer Science Technical Reports

No abstract provided.

Potential Contributions Of Software Science To Software Reliability, M. H. Halstead

Department of Computer Science Technical Reports

No abstract provided.

Stochastic Analysis Of The Effect Of Random Permeability Distributions On Confine Seepage, B. Dendrou, Elias N. Houstis

Department of Computer Science Technical Reports

No abstract provided.

The Effect Of Numerical Integration In The Finite Element Approximation Of Hyperbolic Problems, Elias N. Houstis

Department of Computer Science Technical Reports

No abstract provided.

Dual-Mode Sequential Logic For Function Independent Fault-Testing, Sumit Dasgupta, Carlos R.P. Hartmann, Luther D. Rudolph

Electrical Engineering and Computer Science - Technical Reports

This paper presents a method of using hardware redundancy to ease the problem of fault testing in sequential logic networks. Sequential logic networks are constructed using two kinds of dual-mode logic gates, one of which is specifically required to initialize a feedback loop to some logic value. Initially, it is shown that these networks can be tested for all single stuck-at-faults with six function-independent tests. Next, this method is generalized to detect large classes of multiple faults with six function-independent tests. In both cases, the network must have the proper number of extra inputs.

Operational Analysis Of Queueing Networks, Peter J. Denning, Jeffrey P. Buzen

Department of Computer Science Technical Reports

No abstract provided.

High Accuracy Finite Difference Approximation To Solutions Of Elliptic Partial Differential Equations, Robert E. Lynch, John R. Rice

Department of Computer Science Technical Reports

No abstract provided.

O(H^6) Accurate Finite Difference Approximation To Solutions Of The Poisson Equation In Three Variables, Robert E. Lynch

Department of Computer Science Technical Reports

No abstract provided.

A Time- And Space-Efficient Garbage Compaction Algorithm, F. Lockwood Morris

Electrical Engineering and Computer Science - Technical Reports

Given an area of storage containing scattered marked nodes, one may wish to rearrange them into a compact mass at one end of the area, meanwhile revising all pointers to marked nodes to show their new locations. An algorithm is here described which accomplishes this task in Iinear time relative to the size of the storage area, and in space of the order of one bit for each pointer. The algorithm operates by reversibly encoding the situation that a collection of locations point to a single location by a linear list, emanating from the pointed-to location, passing through the pointing …

Dual-Mode Combinational Logic For Function-Independent Fault Testing, Sumit Dasgupta

Electrical Engineering and Computer Science - Technical Reports

This paper presents a method of using hardware redundancy to ease the problem of fault testing in combinational logic networks. Combinational logic networks are constructed using dual-mode logic gates. Initially, it is shown that these networks can be tested for all single stuck-at-faults using just two function-independent tests. This method is then extended to detect a large class of multiple faults with the same two function-independent tests.

Software For Linear Elliptic Problems On General Two Dimensional Domains, Elias N. Houstis, John R. Rice

Department of Computer Science Technical Reports

No abstract provided.

Heuristics For Trie Index Minimization, Douglas E. Comer

Department of Computer Science Technical Reports

No abstract provided.

A Compiler Extension Theorem For Lucid, Christoph M. Hoffmann

Department of Computer Science Technical Reports

No abstract provided.

Software For Numerical Computation, John R. Rice

Department of Computer Science Technical Reports

No abstract provided.

Data Base Concepts For System Analysis, Thomas I. M. Ho

Department of Computer Science Technical Reports

No abstract provided.

Comparison Of Fast Direct Methods For Elliptic Problems, Elias N. Houstis, T. S. Papatheordorou

Department of Computer Science Technical Reports

No abstract provided.

Software Engineering, Harlan D. Mills

The Harlan D. Mills Collection

No abstract provided.

Superconcentrators, Nicholas Pippenger

All HMC Faculty Publications and Research

An $n$-superconcentrator is an acyclic directed graph with $n$ inputs and $n$ outputs for which, for every $r \leqq n$, every set of $r$ inputs, and every set of $r$ outputs, there exists an $r$-flow (a set of $r$ vertex-disjoint directed paths) from the given inputs to the given outputs. We show that there exist $n$-superconcentrators with $39n + O(\log n)$ (in fact, at most $40n$) edges, depth $O(\log n)$, and maximum degree (in-degree plus out-degree) 16.

Reliability Growth Apportionment, James K. Byers

Computer Science Faculty Research & Creative Works

A method is presented for apportioning reliability growth to the subsystems that make up a system in order to achieve the required reliability at least cost. Reliability growth apportionment is handled as an s-expected cost minimization problem subject to the constraint of meeting a system reliability requirement. The problem is formulated in terms of Duane's reliability growth model and is solved using geometric programming. The method can be useful in the early stages of system design to determine subsystem reliability growth that will allow a system reliability requirement to be met, and in the latter stages of system design when …

Diagnosis Of Faults In Linear Tree Networks, Sharad C. Seth, K. L. Kodandapani

School of Computing: Faculty Publications

The problem of fault detection and location in tree networks of two input EXCLUSIVE-OR (EOR) gates is considered. The fault model assumes that an EOR gate can change to any other function of its two inputs except the equivalence function. An efficient procedure for single fault location is presented. In the worst case the number of tests necessary to locate single faults is bounded by a linear function of the number of input variables. Constructive upper bounds are obtained for the number of tests to detect multiple faults. Optimality of these bounds is argued and extension of results to other …

Multi-Dimensional Clustering For Data Base Organizations, J. H. Liou, S. B. Yao

Department of Computer Science Technical Reports

No abstract provided.