Results from Linear Algebra, Probability Theory and Statistics

2011 ◽  
pp. 199-213
Keyword(s):  
Probability Theory ◽  
Linear Algebra

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 КОМП’ЮТЕРНО-ОРІЄНТОВАНІ ЕЛЕМЕНТИ НАВЧАННЯ МАТЕМАТИЧНИХ ДИСЦИПЛІН МАЙБУТНІХ УЧИТЕЛІВ МАТЕМАТИКИ

2021 ◽  
Vol 1 (2) ◽  
pp. 255-262
Author(s):  
O. B. KRASNOZHON ◽  
◽  
V. V. MATSIUK ◽  
Keyword(s):  
Probability Theory ◽  
Secondary Education ◽  
Euclidean Space ◽  
Least Squares ◽  
Linear Algebra ◽  
Least Squares Method ◽  
Mathematical Statistics ◽  
Academic Disciplines ◽  
Educational Institutions ◽  
Teaching Mathematics

The article is devoted to the issues of constructing effective computer-oriented components of the methodological system of teaching the disciplines «Linear Algebra» and «Probability Theory with Elements of Mathematical Statistics» provided for in the educational and professional program «Secondary Education (Mathematics)» of the first level of higher education in the specialty 014 Secondary Education (Mathematics). The article analyzes the methodological aspects of the effective organization of computations when finding the angle between a given vector and a nonzero subspace of Euclidean space, as well as using the least squares method for processing experimental data. The theoretical and practical information known to students-mathematicians from the corresponding sections of these academic disciplines is briefly presented. Analyzed educational, methodological and scientific literature used in teaching linear algebra and probability theory with elements of mathematical statistics; the expediency of using computer-oriented elements of teaching mathematical disciplines of future mathematics teachers has been substantiated. The authors proposed the use of computer-oriented learning elements in the processing of the content of disciplines and the development of test tasks of different levels of complexity in linear algebra and probability theory with elements of mathematical statistics in order to objectively assess the level of students' knowledge and timely correct individual educational trajectories. The article provides examples of the application of computer-oriented elements of teaching linear algebra and probability theory with elements of mathematical statistics, and also analyzes the methodological features of the organization of calculations in the software mathematical environment Mathcad. The methodological and practical materials presented in the article can be useful for students to organize and activate independent scientific and pedagogical activities, teachers of secondary educational institutions, heads of optional and circle work of students, teachers of linear algebra and probability theory courses with elements of mathematical statistics of pedagogical higher educational institutions. Key words: methods of teaching mathematics, computer-oriented elements of teaching mathematics, linear algebra, probability theory, mathematical statistics, Euclidean space, non-zero subspace of Euclidean space, least squares method.

Matrix Completions, Moments, and Sums of Hermitian Squares

2011 ◽  
Author(s):  
Mihály Bakonyi ◽  
Hugo J. Woerdeman
Keyword(s):  
Linear Algebra ◽  
Undergraduate Students ◽  
Complex Analysis ◽  
Measure Theory ◽  
Complex Function ◽  
Complex Function Theory ◽  
Extensive Discussion ◽  
The Subject ◽  
Processing Control ◽  
Developing Area

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.

Topics in Quaternion Linear Algebra

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Linear Algebra ◽  
Complex Analysis ◽  
Dimensional Space ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Number System ◽  
Graduate Course ◽  
Open Problems ◽  
Unpublished Research ◽  
Reference Tool

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

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