A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics

Front Matter......Page 1
Contents......Page 6
Preface......Page 10
I. The Study and Practice of Modern Mathematics......Page 11
Introduction......Page 12
1.1 Why learn mathematics?......Page 13
1.2 Studying mathematics......Page 14
1.3 Homework assignments and problem solving......Page 15
1.5 Inspiration......Page 18
Exercises......Page 19
2.1 What is the goal of mathematical writing?......Page 20
2.3 Writing mathematical sentences......Page 21
2.4 Avoiding errors......Page 22
2.5 Writing mathematical solutions and proofs......Page 23
2.7 The revision process......Page 26
Exercises......Page 27
3.1 What is mathematical research?......Page 29
3.3 General advice......Page 30
3.5 Fixing common problems......Page 31
3.6 Using computer resources......Page 32
Exercises......Page 33
4.1 Why give a presentation of mathematics?......Page 35
4.3 DOs and DON\'Ts......Page 36
4.6 Publishing your research......Page 37
Exercises......Page 38
5. Looking Ahead: Taking Professional Steps......Page 40
Exercises......Page 43
6. What is it Like Being a Mathematician?......Page 44
Exercises......Page 47
7. Guide to Web Resources......Page 49
Exercises......Page 52
8.1 Mathematicians......Page 53
8.2 Mathematical concepts......Page 54
8.3 Mathematical challenges......Page 55
8.4 Mathematical culture......Page 56
8.5 Mathematical fun......Page 57
II. The Tools of Modern Mathematics......Page 59
Introduction......Page 60
9.1 What is TEX?......Page 61
9.4 How to create and typeset a simple LATEX document......Page 62
9.5 How to add basic information to your document......Page 63
9.6 How to do elementary mathematical typesetting......Page 65
9.7 How to do advanced mathematical typesetting......Page 68
9.8 How to use graphics......Page 71
Exercises......Page 74
10.1 What is PSTricks?......Page 79
10.2 How to make simple pictures......Page 80
10.3 How to plot functions......Page 84
10.4 How to make pictures with nodes......Page 87
Exercises......Page 90
11.1 What is Beamer?......Page 93
11.3 How to set up a Beamer document......Page 94
11.4 How to enhance a Beamer presentation......Page 96
Exercises......Page 97
12.1 What is a computer algebra system?......Page 98
12.2 How to use a CAS as a calculator......Page 99
12.3 How to compute functions......Page 107
12.4 How to make graphs......Page 115
12.5 How to do simple programming......Page 121
Exercises......Page 125
13.1 What are MATLAB and Octave?......Page 129
13.2 How to explore Linear Algebra......Page 131
13.3 How to plot a curve in two dimensions......Page 136
13.4 How to plot a surface in three dimensions......Page 138
13.5 How to manipulate the appearance of plots......Page 142
13.6 Other considerations......Page 144
Exercises......Page 145
14.1 What is R?......Page 148
14.2 How to use R as a calculator......Page 149
14.3 How to explore and describe data......Page 151
14.4 How to explore relationships......Page 154
14.5 How to test hypotheses......Page 157
14.6 How to generate table values and simulate data......Page 158
14.7 How to make a plot ready to print......Page 159
Exercises......Page 160
15.1 What is HTML?......Page 162
15.2 How to create a simple Web page......Page 163
15.4 How to add links to your Web pages......Page 168
15.5 How to design your Web pages......Page 170
Exercises......Page 171
16.1 What are Geometer\'s Sketchpad and GeoGebra?......Page 173
16.2 How to use Geometer\'s Sketchpad......Page 174
16.3 How to use GeoGebra......Page 178
16.4 How to do more elaborate sketches in Geometer\'s Sketchpad......Page 181
16.5 How to do more elaborate sketches in GeoGebra......Page 185
Exercises......Page 189
17.1 What is PostScript?......Page 192
17.2 How to use the stack......Page 193
17.3 How to make simple pictures......Page 194
17.4 How to add text to pictures......Page 201
17.5 How to use programming constructs......Page 202
17.6 How to add color to pictures......Page 207
17.7 More examples......Page 210
Exercises......Page 215
18.1 Why program?......Page 218
18.2 How to choose a language......Page 219
Exercises......Page 224
19.1 What is free and open source software?......Page 226
19.2 Why use free and open source software?......Page 227
19.3 What is Linux?......Page 228
19.4 How to install Linux......Page 229
19.5 Where to get Linux applications......Page 230
19.6 How is Linux familiar?......Page 231
19.7 How is Linux different?......Page 232
19.8 How to learn more......Page 234
Exercises......Page 235
20. Putting it All Together......Page 237
Exercises......Page 238
Bibliography......Page 240