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An Elementary Transition to Abstract Mathematics
Hardcover
Series: Textbooks in Mathematics
ISBN13: 9780367336936
Publisher: Crc Pr Inc
Published: Oct 28 2019
Pages: 292
Weight: 1.30
Height: 0.90 Width: 6.40 Depth: 9.30
Language: English
An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role.
The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; and the final part focuses on polynomials.
Features:
- The material is presented in many short chapters, so that one concept at a time can be absorbed by the student.
- Two looking back chapters at the outset (pre-calculus and calculus) are designed to start the student's transition by working with familiar concepts.
- Many examples of every concept are given to make the material as concrete as possible and to emphasize the importance of searching for patterns.
- A conversational writing style is employed throughout in an effort to encourage active learning on the part of the student.
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