Models of the U.S. Economy

1977 ◽  
Vol 70 (2) ◽  
pp. 102-110
Author(s):  
Samuel L. Dunn ◽  
Lawrence W. Wright
Keyword(s):  
Probability Theory ◽  
Computer Science ◽  
Linear Algebra ◽  
The U.S

The field of economics provides many opportunities for applying mathematics. The quantification of economics that has occurred in the last thirty years has made it necessary that economists be trained in the uses of higher mathematics. Algebra, geometry, calculus, probability theory and statistics, higher analysis, linear algebra, and computer science are some of the tools being used in contemporary approaches to economics.

scholarly journals Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices

2021 ◽  
Author(s):  
Stefano Massei
Keyword(s):  
Computer Science ◽  
Recent Work ◽  
Linear Algebra ◽  
Optimization Problems ◽  
Approximation Error ◽  
Positive Semidefinite ◽  
Numerical Linear Algebra ◽  
Maximum Volume ◽  
Deterministic Algorithms ◽  
Principal Submatrix

AbstractVarious applications in numerical linear algebra and computer science are related to selecting the $$r\times r$$ r × r submatrix of maximum volume contained in a given matrix $$A\in \mathbb R^{n\times n}$$ A ∈ R n × n . We propose a new greedy algorithm of cost $$\mathcal O(n)$$ O ( n ) , for the case A symmetric positive semidefinite (SPSD) and we discuss its extension to related optimization problems such as the maximum ratio of volumes. In the second part of the paper we prove that any SPSD matrix admits a cross approximation built on a principal submatrix whose approximation error is bounded by $$(r+1)$$ ( r + 1 ) times the error of the best rank r approximation in the nuclear norm. In the spirit of recent work by Cortinovis and Kressner we derive some deterministic algorithms, which are capable to retrieve a quasi optimal cross approximation with cost $$\mathcal O(n^3)$$ O ( n 3 ) .

Gendered Attrition at the Undergraduate Level

2011 ◽  
pp. 714-720 ◽  
Author(s):  
Sandra Katz
Keyword(s):  
Computer Science ◽  
Undergraduate Level ◽  
Men And Women ◽  
Bachelor Of Science ◽  
Post Secondary ◽  
Education Statistics ◽  
Degree Recipients ◽  
The U.S

As Camp showed in her widely cited papers on the “incredible shrinking pipeline” (Camp, 1997; Camp, Miller, & Davies, 2000), women have continuously lagged behind men in earning Bachelor of Science (BS) degrees in computer science (CS) at four-year post-secondary U.S. institutions, despite the fact that the percentage of women earning CS degrees has kept pace with trends in the total number of CS degree recipients. This pattern is illustrated in Figures 1 and 2, which are based on data from the National Center for Education Statistics (National Center for Education Statistics, 2003, Table 282). Our goal is to summarize the proposed causes of, and solutions for, female attrition at the undergraduate level. In times like the present, when the U.S. is experiencing an overall decline in enrollment in undergraduate CS programs (Zweben, 2005), it becomes increasingly important to retain good students—both men and women.

Introduction

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Quantum Mechanics ◽  
Computer Graphics ◽  
Computer Science ◽  
Control Systems ◽  
Linear Algebra ◽  
Mathematical Physics ◽  
Molecular Symmetry ◽  
Research Papers ◽  
Physics Journals

This chapter provides a brief overview of this volume, showing that this book can be used for a variety of ways and can be used to assist the reader toward a better understanding of quaternion linear algebra. Quaternions after all have become increasingly useful for practitioners in research, both in theory and applications. For example, a significant number of research papers on quaternions, perhaps even most of them, appear regularly in mathematical physics journals, and quantum mechanics based on quaternion analysis is mainstream physics. In engineering, quaternions are often used in control systems, and in computer science they play a role in computer graphics. Quaternion formalism is also used in studies of molecular symmetry. Hence, to give the reader a preliminary understanding of quaternions, this chapter also provides some notations and conventions to be used in the remainder of this volume, as well as some standard matrices.

Retention in Computer Science Undergraduate Programs in the U.S.

2018 ◽  
Author(s):  
Chris Stephenson ◽  
Alison Derbenwick Miller ◽  
Christine Alvarado ◽  
Lecia Barker ◽  
Valerie Barr ◽  
...  
Keyword(s):  
Computer Science ◽  
Undergraduate Programs ◽  
The U.S

scholarly journals WEIGHTED AUTOMATA AS COALGEBRAS IN CATEGORIES OF MATRICES

2013 ◽  
Vol 24 (06) ◽  
pp. 709-728 ◽  
Author(s):  
JOSÉ N. OLIVEIRA
Keyword(s):  
Computer Science ◽  
Linear Algebra ◽  
Set Theory ◽  
Matrix Algebra ◽  
Quantitative Methods ◽  
Qualitative Reasoning ◽  
Formal Logic ◽  
Quantitative Reasoning ◽  
Weighted Automata ◽  
Conventional Notation

The evolution from non-deterministic to weighted automata represents a shift from qualitative to quantitative methods in computer science. The trend calls for a language able to reconcile quantitative reasoning with formal logic and set theory, which have for so many years supported qualitative reasoning. Such a lingua franca should be typed, polymorphic, diagrammatic, calculational and easy to blend with conventional notation. This paper puts forward typed linear algebra as a candidate notation for such a unifying role. This notation, which emerges from regarding matrices as morphisms of suitable categories, is put at work in describing weighted automata as coalgebras in such categories. Some attention is paid to the interface between the index-free (categorial) language of matrix algebra and the corresponding index-wise, set-theoretic notation.

Understanding the U.S. domestic computer science Ph.D. pipeline

2015 ◽  
Vol 58 (8) ◽  
pp. 29-32 ◽  
Author(s):  
Susanne Hambrusch ◽  
Ran Libeskind-Hadas ◽  
Eric Aaron
Keyword(s):  
Computer Science ◽  
The U.S

Update on the status of medical computer science programs in the U.S. - 1979

1980 ◽  
Vol 4 (3) ◽  
pp. 7-14 ◽  
Author(s):  
Lynn L. Peterson ◽  
Joan S. Reisch
Keyword(s):  
Computer Science ◽  
Medical Computer ◽  
The Status ◽  
The U.S
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