
Transition to Higher Mathematics: Structure and Proof - Second Edition
Bob A Dumas, University of Washington - Seattle Campus
John E McCarthy, Washington University in St Louis
Año de Copyright:
ISBN 13: 9781941823033
Publisher: Open Scholarship
Language: English
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Condiciones de Uso
Attribution
CC BY
Comentarios
Opinión de Christina Eubanks-Turner, Professor, Loyola Marymount University on 3/18/22
The text covers the areas and ideas of the subject appropriately. It also provides an index and appendices. The table of contents is organized and easy to use to navigate between the topics. The inclusion of more hints or solutions to some... lee mas
Opinión de Christina Eubanks-Turner, Professor, Loyola Marymount University on 3/18/22
Exhaustividad
The text covers the areas and ideas of the subject appropriately. It also provides an index and appendices. The table of contents is organized and easy to use to navigate between the topics. The inclusion of more hints or solutions to some exercises would be helpful to both students and instructors. The text should include more examples to help clarify concepts for students.
Precisión de contenido
The content seems mostly accurate. There is an adequate number of examples and justifications in the proofs of statements.
Relevancia / Longevidad
The content is presented in a traditional way. The text is written in such a way that necessary updates will be straightforward to implement.
Claridad
The language in the text is clear. There are some transitional explanation paragraphs, which aid in student understanding of mathematics in the text.
Consistencia
The text is consistent in writing and terminology.
Modularidad
Each chapter of the book includes several subsections, which makes the content easier to understand.
Organización / Estructura / Flujo
The topics in the text are presented in a logical manner. The table of contents should be made clickable for ease of use.
Interfaz
The text and images are displayed in a clear and orderly manner.
Errores gramaticales
I found no grammatical errors.
Relevancia cultural
There is no inclusion of any culturally relevant pieces, which is consistent with introductory proof textbooks. More examples related to applications of the content could have been included to make the content more culturally relevant.
Table of Contents
- Chapter 0. Introduction
- Chapter 1. Preliminaries
- Chapter 2. Relations
- Chapter 3. Proofs
- Chapter 4. Principle of Induction
- Chapter 5. Limits
- Chapter 6. Cardinality
- Chapter 7. Divisibility
- Chapter 8. The Real Numbers
- Chapter 9. Complex Numbers
Acerca del libro
This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter 5: Limits, Chapter 6: Cardinality, Chapter 7: Divisibility, Chapter 8: The Real Numbers, Chapter 9: Complex Numbers. The last 4 chapters can also be used as independent introductions to four topics in mathematics: Cardinality; Divisibility; Real Numbers; Complex Numbers.
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Authors
Bob A. Dumas, University of Washington - Seattle Campus
John E. McCarthy, Washington University in St Louis