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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
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Excursions in Number Theory, Algebra, and Analysis (Hardcover, 1st ed. 2022)
Loot Price: R1,504
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Excursions in Number Theory, Algebra, and Analysis (Hardcover, 1st ed. 2022)
Series: Undergraduate Texts in Mathematics
Expected to ship within 12 - 19 working days
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This textbook originates from a course taught by the late Ken
Ireland in 1972. Designed to explore the theoretical underpinnings
of undergraduate mathematics, the course focused on
interrelationships and hands-on experience. Readers of this
textbook will be taken on a modern rendering of Ireland's path of
discovery, consisting of excursions into number theory, algebra,
and analysis. Replete with surprising connections, deep insights,
and brilliantly curated invitations to try problems at just the
right moment, this journey weaves a rich body of knowledge that is
ideal for those going on to study or teach mathematics. A pool of
200 'Dialing In' problems opens the book, providing fuel for active
enquiry throughout a course. The following chapters develop theory
to illuminate the observations and roadblocks encountered in the
problems, situating them in the broader mathematical landscape.
Topics cover polygons and modular arithmetic; the fundamental
theorems of arithmetic and algebra; irrational, algebraic and
transcendental numbers; and Fourier series and Gauss sums. A lively
accompaniment of examples, exercises, historical anecdotes, and
asides adds motivation and context to the theory. Return trips to
the Dialing In problems are encouraged, offering opportunities to
put theory into practice and make lasting connections along the
way. Excursions in Number Theory, Algebra, and Analysis invites
readers on a journey as important as the destination. Suitable for
a senior capstone, professional development for practicing
teachers, or independent reading, this textbook offers insights and
skills valuable to math majors and high school teachers alike. A
background in real analysis and abstract algebra is assumed, though
the most important prerequisite is a willingness to put pen to
paper and do some mathematics.
General
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