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Like other introductions to number theory, this one includes the
usual curtsy to divisibility theory, the bow to congruence, and the
little chat with quadratic reciprocity. It also includes proofs of
results such as Lagrange's Four Square Theorem, the theorem behind
Lucas's test for perfect numbers, the theorem that a regular n-gon
is constructible just in case phi(n) is a power of 2, the fact that
the circle cannot be squared, Dirichlet's theorem on primes in
arithmetic progressions, the Prime Number Theorem, and Rademacher's
partition theorem. We have made the proofs of these theorems as
elementary as possible. Unique to The Queen of Mathematics are its
presentations of the topic of palindromic simple continued
fractions, an elementary solution of Lucas's square pyramid
problem, Baker's solution for simultaneous Fermat equations, an
elementary proof of Fermat's polygonal number conjecture, and the
Lambek-Moser-Wild theorem.
This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures actually used by famous mathematicians, giving more mathematically talented students a greater opportunity to learn the history and philosophy by way of problem solving. Several important philosophical topics are pursued throughout the text, giving the student an opportunity to come to a full and consistent knowledge of their development. These topics include infinity, the nature of motion, and Platonism. This book offers, in fewer pages, a deep penetration into the key mathematical and philosophical aspects of the history of mathematics.
The authors' novel approach to some interesting mathematical concepts - not normally taught in other courses - places them in a historical and philosophical setting. Although primarily intended for mathematics undergraduates, the book will also appeal to students in the sciences, humanities and education with a strong interest in this subject. The first part proceeds from about 1800 BC to 1800 AD, discussing, for example, the Renaissance method for solving cubic and quartic equations and providing rigorous elementary proof that certain geometrical problems posed by the ancient Greeks cannot be solved by ruler and compass alone. The second part presents some fundamental topics of interest from the past two centuries, including proof of G del's incompleteness theorem, together with a discussion of its implications.
This is a concise introductory textbook for a one-semester
(40-class) course in the history and philosophy of mathematics. It
is written for mathemat ics majors, philosophy students, history of
science students, and (future) secondary school mathematics
teachers. The only prerequisite is a solid command of precalculus
mathematics. On the one hand, this book is designed to help
mathematics majors ac quire a philosophical and cultural
understanding of their subject by means of doing actual
mathematical problems from different eras. On the other hand, it is
designed to help philosophy, history, and education students come
to a deeper understanding of the mathematical side of culture by
means of writing short essays. The way I myself teach the material,
stu dents are given a choice between mathematical assignments, and
more his torical or philosophical assignments. (Some sample
assignments and tests are found in an appendix to this book. ) This
book differs from standard textbooks in several ways. First, it is
shorter, and thus more accessible to students who have trouble
coping with vast amounts of reading. Second, there are many
detailed explanations of the important mathematical procedures
actually used by famous mathe maticians, giving more mathematically
talented students a greater oppor tunity to learn the history and
philosophy by way of problem solving.
Like other introductions to number theory, this one includes the
usual curtsy to divisibility theory, the bow to congruence, and the
little chat with quadratic reciprocity. It also includes proofs of
results such as Lagrange's Four Square Theorem, the theorem behind
Lucas's test for perfect numbers, the theorem that a regular n-gon
is constructible just in case phi(n) is a power of 2, the fact that
the circle cannot be squared, Dirichlet's theorem on primes in
arithmetic progressions, the Prime Number Theorem, and Rademacher's
partition theorem. We have made the proofs of these theorems as
elementary as possible. Unique to The Queen of Mathematics are its
presentations of the topic of palindromic simple continued
fractions, an elementary solution of Lucas's square pyramid
problem, Baker's solution for simultaneous Fermat equations, an
elementary proof of Fermat's polygonal number conjecture, and the
Lambek-Moser-Wild theorem.
The authors' novel approach to some interesting mathematical
concepts - not normally taught in other courses - places them in a
historical and philosophical setting. Although primarily intended
for mathematics undergraduates, the book will also appeal to
students in the sciences, humanities and education with a strong
interest in this subject. The first part proceeds from about 1800
BC to 1800 AD, discussing, for example, the Renaissance method for
solving cubic and quartic equations and providing rigorous
elementary proof that certain geometrical problems posed by the
ancient Greeks cannot be solved by ruler and compass alone. The
second part presents some fundamental topics of interest from the
past two centuries, including proof of G del's incompleteness
theorem, together with a discussion of its implications.
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