A Bridge to Higher Mathematics

Name: A Bridge to Higher Mathematics
Brand: Taylor & Francis
SKU: 9781138441637
Price: 16601.0 INR
Availability: InStock

by Valentin Deaconu

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ISBN13: 9781138441637
Binding: Hardcover
Subject: N/A
Publisher: Taylor & Francis
Publisher Imprint: CRC Press
Publication Date: July 11, 2017
Pages: 220
Original Price: GBP 200.0
Language: English
Edition: N/A
Item Weight: 570 grams
BISAC Subject(s): Set Theory, Functional Analysis, and Logic

About The Book

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.

About The Author

Valentin Deaconu teaches at University of Nevada, Reno.

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