## Discovering Mathematics with MAPLE by R.J. Stroeker and J.F. Kaashoek (Birkhauser, Boston, 1999)

### Book Contents and Links to Folders of Updated Maple Worksheets:

The Maple R5 worksheets on the CD that comes with the book were originally updated here to Maple 9 Classic worksheets keeping the linalg package, then to Maple 12 Standard worksheets replacing the linalg package by the LinearAlgebra package. These new worksheets should still work through Maple 18 at least.

1 A Tour of Maple V
Introduction * Maple's Windows Interface * Just a Maple Session * Worksheets and Assignments * Exercises * Survey of Used Maple Expressions

2 Functions and Sequences
Introduction * Selected Concepts from Analysis * A Tricky Probability Function * Worksheets and Assignments * Exercises * Survey of Used Maple Expressions

3 Matrices and Vectors
Introduction * Selected Concepts from Linear Algebra * A Least Squares Filter * Worksheets and Assignments * Exercises * Survey of Used Maple Expressions

4 Counting and Summation
Introduction * Selected Concepts from Discrete Mathematics * Binomial Coefficients * Worksheets and Assignments * Exercises * Survey of Used Maple Expressions

5 Derivative and Integral
Introduction * Further Concepts from Analysis * Riemann's Non-differentiable Function * Worksheets and Assignments * Exercises * Survey of Used Maple Expressions

6 Vector Spaces and Linear Mappings
Introduction * Further Concepts from Linear Algebra * Diagonalization and the SVD * Worksheets and Assignments * Exercises * Survey of Used Maple Expressions

A Exercises in Experimentation
Upper Bound for a Parameterized Function * Matrix Differentiation * Chaotic Sequences

Exercises 1.5 * Exercises 2.5 * Exercises 3.5 * Exercises 4.5 * Exercises 5.5 * Exercises 6.5

C Quick Guide to Selected Maple Commands
Linear Algebra * Mathematical Analysis * Statistics * Linear Programming * Mathematical Finance

Bibliography

### File Name conventions by chapter

1. A Tour of Maple V
[tour]
2. Functions and Sequences
[func]
3. Matrices and Vectors
[matr]
4. Counting and Summation
[count]
5. Derivative and Integral
[deriv]
6. Vector Spaces and Linear Mappings
[vec]

Each chapter X folder contains the 5 worksheets whose filenames are built from the [key] given above in the following way

Standard Maple 12

• keySX.mw: A MAPLE "S"ession: MAPLE support for some of the section discussion
• keyWXa.mw, keyWXb.mw: "W"orksheets
• keyAXa.mw, keyAXb.mw: "A"ssignment sheets

Classic Maple 9

• keySX.mws: A MAPLE "S"ession: MAPLE support for some of the section discussion
• keyWXa.mws, keyWXb.mws: "W"orksheets
• keyAXa.mws, keyAXb.mws: "A"ssignment sheets

and some folders contain some extra files explained in the corresponding section. The Classic worksheets are not explicitly linked to the Chapter index web pages, but by adding back in the "s" to the Standard Maple ".mw" URL file extension, one gets those files as well.

### How to do this course

You will have to bring your laptop to class since we do not have a computer classroom. You may help each other in class (cooperative learning) and consult with me on Maple or math problems that stump you.

The operating procedure for this course will be for each chapter:

1) first read the motivating discussion found only in the textbook

2) and then do in sequence the keySX worksheet, then the keyWXa worksheet followed by the assigment keyAXa worksheet,

3) and then repeat for the keyWXb worksheet followed by the assigment keyAXb worksheet.

4) Pick a few problems of your choice from the textbook end of chapter problem list that are sufficiently challenging and in a single worksheet with a Maple section for each such problem, type in a statement of the problem using Maple's typesetting features and then complete the problem with extensive chatter explaining what you are doing as you go along, so that a nice self-contained formal report is the end result for each problem.

5) Repeat this for 2 of the 3 problems in Appendix A.

6) Meanwhile during the course, if you wish to break the grade ceiling of A- based on successful completion of the textbook assignments, you will have to find a mathematical topic of interest to you, of sufficient sophistication that a computer algebra system is needed to solve or investigate the problem, and make a self-contained, fully documented worksheet report of this investigation.

Assignment worksheets will be posted on your student webspace as directed in class. I will download them and include my feedback for you to improve your product and resubmit if necessary by reposting and informing me by email of the link.

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