eBook ISBN:  9781470458355 
Product Code:  CLRM/20.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
eBook ISBN:  9781470458355 
Product Code:  CLRM/20.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 

Book DetailsClassroom Resource MaterialsVolume: 20; 2003; 160 pp
This text supplement contains 12 exploratory exercises designed to facilitate students' understanding of the most elemental concepts encountered in a first real analysis course: notions of boundedness, supremum/infimum, sequences, continuity and limits, limit suprema/infima, and pointwise and uniform convergence. In designing the exercises, the authors ask students to formulate definitions, make connections between different concepts, derive conjectures, or complete a sequence of guided tasks designed to facilitate concept acquisition. Each exercise has three basic components: making observations and generating ideas from handson work with examples, thinking critically about the examples, and answering additional questions for reflection.
The exercises can be used in a variety of ways: to motivate a lecture, to serve as a basis for inclass activities, or to be used for lab sessions, where students work in small groups and submit reports of their investigations. While the exercises have been useful for real analysis students of all ability levels, the authors believe this resource might prove most beneficial in the following scenarios:
A twosemester sequence in which the following topics are covered: properties of the real numbers, sequences, continuity, sequences and series of functions, differentiation, and integration.
A class of students for whom analysis is their first upper division course.
A group of students with a wide range of abilities for whom a cooperative approach focusing upon fundamental concepts could help to close the gap in skill development and concept acquisition.
An independent study or private tutorial in which the student receives a minimal level of instruction.
A resource for an instructor developing a cooperative, interactive course that does not involve the use of a standard text.
Ancillary materials, including Visual Guide Sheets for those exercises that involve the use of technology and Report Guides for a lab session approach are provided online at: http:www.saintmarys.edu/~jsnow.
In designing the exercise, the authors were inspired by Ellen Parker's book, Laboratory Experiences in Group Theory, also published by the MAA.

Table of Contents

Chapters

1. Boundedness of Sets

2. Introducing the “Epsilon Definition” of Least Upper Bound

3. Introduction to the Formal Definition of Convergence

4. Experience with the Definition of the Limit of a Sequence

5. Experience with the Negation of the Definition of Convergence

6. Algebraic Combinations of Sequences

7. Conditions Related to Convergence

8. Understanding the Limit Superior and the Limit Inferior

9. Continuity and Sequences

10. Another Definition of Continuity

11. Experience with the $\epsilon \delta $ Definitions of Continuity and Limit

12. Uniform Convergence of a Sequence of Functions


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This text supplement contains 12 exploratory exercises designed to facilitate students' understanding of the most elemental concepts encountered in a first real analysis course: notions of boundedness, supremum/infimum, sequences, continuity and limits, limit suprema/infima, and pointwise and uniform convergence. In designing the exercises, the authors ask students to formulate definitions, make connections between different concepts, derive conjectures, or complete a sequence of guided tasks designed to facilitate concept acquisition. Each exercise has three basic components: making observations and generating ideas from handson work with examples, thinking critically about the examples, and answering additional questions for reflection.
The exercises can be used in a variety of ways: to motivate a lecture, to serve as a basis for inclass activities, or to be used for lab sessions, where students work in small groups and submit reports of their investigations. While the exercises have been useful for real analysis students of all ability levels, the authors believe this resource might prove most beneficial in the following scenarios:
A twosemester sequence in which the following topics are covered: properties of the real numbers, sequences, continuity, sequences and series of functions, differentiation, and integration.
A class of students for whom analysis is their first upper division course.
A group of students with a wide range of abilities for whom a cooperative approach focusing upon fundamental concepts could help to close the gap in skill development and concept acquisition.
An independent study or private tutorial in which the student receives a minimal level of instruction.
A resource for an instructor developing a cooperative, interactive course that does not involve the use of a standard text.
Ancillary materials, including Visual Guide Sheets for those exercises that involve the use of technology and Report Guides for a lab session approach are provided online at: http:www.saintmarys.edu/~jsnow.
In designing the exercise, the authors were inspired by Ellen Parker's book, Laboratory Experiences in Group Theory, also published by the MAA.

Chapters

1. Boundedness of Sets

2. Introducing the “Epsilon Definition” of Least Upper Bound

3. Introduction to the Formal Definition of Convergence

4. Experience with the Definition of the Limit of a Sequence

5. Experience with the Negation of the Definition of Convergence

6. Algebraic Combinations of Sequences

7. Conditions Related to Convergence

8. Understanding the Limit Superior and the Limit Inferior

9. Continuity and Sequences

10. Another Definition of Continuity

11. Experience with the $\epsilon \delta $ Definitions of Continuity and Limit

12. Uniform Convergence of a Sequence of Functions