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A Journey Through The Realm of Numbers - From Quadratic Equations to Quadratic Reciprocity (Paperback, 1st ed. 2020)
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A Journey Through The Realm of Numbers - From Quadratic Equations to Quadratic Reciprocity (Paperback, 1st ed. 2020)
Series: Springer Undergraduate Mathematics Series
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This book takes the reader on a journey from familiar high school
mathematics to undergraduate algebra and number theory. The journey
starts with the basic idea that new number systems arise from
solving different equations, leading to (abstract) algebra. Along
this journey, the reader will be exposed to important ideas of
mathematics, and will learn a little about how mathematics is
really done.Starting at an elementary level, the book gradually
eases the reader into the complexities of higher mathematics; in
particular, the formal structure of mathematical writing
(definitions, theorems and proofs) is introduced in simple terms.
The book covers a range of topics, from the very foundations
(numbers, set theory) to basic abstract algebra (groups, rings,
fields), driven throughout by the need to understand concrete
equations and problems, such as determining which numbers are sums
of squares. Some topics usually reserved for a more advanced
audience, such as Eisenstein integers or quadratic reciprocity, are
lucidly presented in an accessible way. The book also introduces
the reader to open source software for computations, to enhance
understanding of the material and nurture basic programming skills.
For the more adventurous, a number of Outlooks included in the text
offer a glimpse of possible mathematical excursions. This book
supports readers in transition from high school to university
mathematics, and will also benefit university students keen to
explore the beginnings of algebraic number theory. It can be read
either on its own or as a supporting text for first courses in
algebra or number theory, and can also be used for a topics course
on Diophantine equations.
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