A transition to Advanced Mathematics

Maurice Eggen, Douglas Smith, Richard St. Andre

372 pages, parution le 15/11/2005 (6^eme édition)

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Résumé

Transition to advanced mathematics bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically-to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Second, it provides a firm foundation of the basic concepts and methods needed for continued work. Finally, it provides introductions to concepts of modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics. The text will improve the student's ability to think and write in a mature mathematical fashion and provide a solid understanding of the material most useful for advanced courses.

Benefits

The text emphasizes enhancing the student's ability to write and understand proofs in the coverage of sets, relations, and functions (Chapters 2, 3, and 4). The pace is deliberate while the rigorous approach requires the student to deal precisely with these concepts.
The chapters on cardinality, concepts of algebra, and concepts of analysis (Chapters 5, 6, and 7) make use of the skills and techniques the student acquired in the first half of the book. These chapters are a cut above the earlier chapters in terms of level and rigor.
"Proofs to Grade" are a special feature of most of the exercise sets. A list of claims with alleged proofs is presented, and the student is asked to assign a letter grade to each "proof" and to justify the grade assigned. These exercises reemphasize the theorems and counterexamples in the text and also provide the student with an experience similar to grading papers.
The authors follow a logical development of topics, and write in a readable style that is concise, but complete.
Discussions of sequences and real analysis concepts are tied to students' experience in elementary calculus.
Worked examples and exercises throughout the text, ranging from the routine to the challenging, reinforce the concepts.

L'auteur - Douglas Smith

Douglas K. Smith is a consultant and writer concerned with organization performance and change. He works with leading organizations that span the spectrum non profit-making, profit-making and governments. He is co-creator of the 'horizontal organization' and author of TAKING CHARGE OF CHANGE and MANAGING PERFORMANCE.

Sommaire

Logic and proofs
Set theory
Relations
Functions
Cardinality
Concepts of algebra: groups (optional)
Concepts of analysis: completeness of the real numbers

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Thomson
Auteur(s)	Maurice Eggen, Douglas Smith, Richard St. Andre
Parution	15/11/2005
Édition	6^eme édition
Nb. de pages	372
Format	18,5 x 23
Couverture	Broché
Poids	565g
Intérieur	Noir et Blanc
EAN13	9780534410193
ISBN13	978-0-534-41019-3