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Fit for students just starting to build a background in
mathematics, this textbook provides an introduction to numerical
methods for linear algebra problems. Introduction to Numerical
Linear Algebra is ideal for a flipped classroom, as it provides
detailed explanations that allow students to read on their own and
instructors to go beyond lecturing, assumes that the reader has
taken a course on linear algebra, but reviews background as needed,
and covers several topics not commonly addressed in related
introductory books, including diffusion, a toy model of computed
tomography, global positioning systems, the use of eigenvalues in
analyzing stability of equilibria, a detailed derivation and
careful motivation of the QR method for eigenvalues starting from
power iteration, a discussion of the use of the SVD for assigning
grades, and multigrid methods. This textbook is appropriate for
undergraduate and beginning graduate students in mathematics and
related fields. It can be used in the following courses: Advanced
Numerical Analysis, Special Topics on Numerical Analysis, Topics on
Data Science, Topics on Numerical Optimization, and Topics on
Approximation Theory
How do you select a winner from a field of candidates? How do you
rank a field of candidates? How do you share a divisible resource
like a cake, or an indivisible one like a pet or a house? These are
the questions addressed in this fun and accessible book that takes
an entertaining look at the choices made by groups of people with
different preferences, needs, and interests. Divided into three
parts, the text first examines voting methods for selecting or
ranking candidates. A brief second part addresses compensation
problems wherein an indivisible item must be assigned to one of
several people who are equally entitled to ownership of the item,
with monetary compensation paid to the others. The third part
discusses the problem of sharing a divisible resource among several
people. Mathematics of Social Choice can be used by mathematics
majors as well as students whose only mathematical background is
elementary algebra. Material geared toward more sophisticated
readers can be skipped without any loss of continuity. The book
includes many elementary and usually simple, but rigorous
mathematical proofs appropriate for beginning mathematics majors.
Students will also find appendices with background material on set
notation, logic, and mathematical induction and solutions to many
of the homework exercises.
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