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Books > Science & Mathematics > Mathematics > Mathematical foundations > Set theory
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A Bridge to Higher Mathematics (Hardcover)
Loot Price: R5,855
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A Bridge to Higher Mathematics (Hardcover)
Series: Textbooks in Mathematics
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A Bridge to Higher Mathematics is more than simply another book to
aid the transition to advanced mathematics. The authors intend to
assist students in developing a deeper understanding of mathematics
and mathematical thought. The only way to understand mathematics is
by doing mathematics. The reader will learn the language of axioms
and theorems and will write convincing and cogent proofs using
quantifiers. Students will solve many puzzles and encounter some
mysteries and challenging problems. The emphasis is on proof. To
progress towards mathematical maturity, it is necessary to be
trained in two aspects: the ability to read and understand a proof
and the ability to write a proof. The journey begins with elements
of logic and techniques of proof, then with elementary set theory,
relations and functions. Peano axioms for positive integers and for
natural numbers follow, in particular mathematical and other forms
of induction. Next is the construction of integers including some
elementary number theory. The notions of finite and infinite sets,
cardinality of counting techniques and combinatorics illustrate
more techniques of proof. For more advanced readers, the text
concludes with sets of rational numbers, the set of reals and the
set of complex numbers. Topics, like Zorn's lemma and the axiom of
choice are included. More challenging problems are marked with a
star. All these materials are optional, depending on the instructor
and the goals of the course.
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