beamer, tikz graphics, and flash applets in the classroom
TRANSCRIPT
Beamer, TikZ graphics, and Flash applets in the classroomBeamer,
TikZ graphics, and Flash applets in the classroom
Anders O.F. Hendrickson
MathFest 2012 Madison, Wisconsin
Beamer
Since its release in 2003, the Beamer package has transformed mathematics conference talks. LATEX source code yields PDF files suitable for projectors. Overlay specifications like \item<3-> permit step-by-step uncovering of items
or making them visible.
Beamer
Since its release in 2003, the Beamer package has transformed mathematics conference talks. LATEX source code yields PDF files suitable for projectors. Overlay specifications like \item<3-> permit step-by-step uncovering of items
or making them visible.
Beamer
Since its release in 2003, the Beamer package has transformed mathematics conference talks. LATEX source code yields PDF files suitable for projectors. Overlay specifications like \item<3-> permit step-by-step uncovering of items
or making them visible.
Beamer
Since its release in 2003, the Beamer package has transformed mathematics conference talks. LATEX source code yields PDF files suitable for projectors. Overlay specifications like \item<3-> permit step-by-step uncovering of items or making them visible.
Beamer TikZ animate Flash Builder Conclusion
Beamer in the classroom
The use of slideshows in the classroom is nothing new. My objective today is to spread the word about three packages that can make Beamer even more useful pedagogically:
TikZ graphics The animate package Inclusion of Flash applets
Beamer TikZ animate Flash Builder Conclusion
TikZ graphics
Till Tantau, the author of Beamer, also wrote the PGF graphics package and the TikZ frontend to it. TikZ is “graphics in the spirit of LATEX.” The basic elements of TikZ are nodes and paths.
Beamer TikZ animate Flash Builder Conclusion
TikZ graphics
Till Tantau, the author of Beamer, also wrote the PGF graphics package and the TikZ frontend to it. TikZ is “graphics in the spirit of LATEX.” The basic elements of TikZ are nodes and paths.
Beamer TikZ animate Flash Builder Conclusion
TikZ graphics
Till Tantau, the author of Beamer, also wrote the PGF graphics package and the TikZ frontend to it. TikZ is “graphics in the spirit of LATEX.” The basic elements of TikZ are nodes and paths.
Beamer TikZ animate Flash Builder Conclusion
Example 1: Definition of a Graph
Definition A graph is a collection of vertices (points) connected by edges (lines or curves).
Example
A
BC
D
E
My source code
Source code in LATEX file Output \usepackage{tikz}
\begin{tikzpicture}[very thick] \vertex[label=135:$A$] (A) at (2,0) {}; \vertex[label= 0:$B$] (B) at (4,2) {}; \vertex[label=135:$C$] (C) at (0,1) {}; \vertex[label=135:$D$] (D) at (2,4) {}; \vertex[label= 0:$E$] (E) at (6,3) {}; \draw (A)--(B); \draw (B)--(D); \draw (C) to[bend left=30] (D); \draw (E) to[bend right=20] (C); \draw (D) to[out=30, in=30] (E);
\end{tikzpicture} A
My source code
Source code in LATEX file Output \usepackage{tikz}
\begin{tikzpicture}[very thick] \vertex[label=135:$A$] (A) at (2,0) {}; \vertex[label= 0:$B$] (B) at (4,2) {}; \vertex[label=135:$C$] (C) at (0,1) {}; \vertex[label=135:$D$] (D) at (2,4) {}; \vertex[label= 0:$E$] (E) at (6,3) {}; \draw (A)--(B); \draw (B)--(D); \draw (C) to[bend left=30] (D); \draw (E) to[bend right=20] (C); \draw (D) to[out=30, in=30] (E);
\end{tikzpicture} A
V1 V2W1 W2
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
{AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
{AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
{AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
{AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,AB,AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,AB,AB,CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,AB,AB,CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in Reduced REF
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5 ·
4
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5 · 4 ·
3 = 60
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5 · 4 · 3
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5 · 4 · 3 = 60
Example 4: Combinations
ABC ABD ABE ACB ACD ACE ADB ADC ADE AEB AEC AED
BAC BAD BAE BCA BCD BCE BDA BDC BDE BEA BEC BED
CAB CAD CAE CBA CBD CBE CDA CDB CDE CEA CEB CED
DAB DAC DAE DBA DBC DBE DCA DCB DCE DEA DEB DEC
EAB EAC EAD EBA EBC EBD ECA ECB ECD EDA EDB EDC
Beamer TikZ animate Flash Builder Conclusion
Example 4: Combinations
Example 4: Combinations
{A,B,C} {A,B,D} {A,B,E} {A,C,D} {A,C,E} {A,D,E} {B,C,D} {B,C,E} {B,D,E} {C,D,E}
Beamer TikZ animate Flash Builder Conclusion
Example 4: Combinations
{A,B,C} {A,B,D} {A,B,E} {A,C,D} {A,C,E} {A,D,E} {B,C,D} {B,C,E} {B,D,E} {C,D,E}
60 6
= 10 = (5
The animate package
That example was made using the animate package. \usepackage{animate} The code for making it is not too intricate:
\begin{animateinline}[poster=first, autoplay]{30}% \multiframe{101}{i=0+1}{%
\pgfmathsetmacro{\t}{\i/100}% \DrawBigListOfPermutations
}% \end{animateinline}%
Here \DrawBigListOfPermutations is a macro which draws what the list should look like at time \t∈ [0,1]. This code creates a for-loop during which \i runs from 0 to 100 and \t runs from 0 to 1.
Beamer TikZ animate Flash Builder Conclusion
On to interactivity!
Everything so far has been pre-scripted. Another dimension can be added through embedding interactive applets into your Beamer PDF files. I use the flashmovie package to embed Flash applets. Q: How do you make Flash applets? A: Adobe’s Flash Builder software is free to educators!
Beamer TikZ animate Flash Builder Conclusion
On to interactivity!
Everything so far has been pre-scripted. Another dimension can be added through embedding interactive applets into your Beamer PDF files. I use the flashmovie package to embed Flash applets. Q: How do you make Flash applets? A: Adobe’s Flash Builder software is free to educators!
Beamer TikZ animate Flash Builder Conclusion
On to interactivity!
Everything so far has been pre-scripted. Another dimension can be added through embedding interactive applets into your Beamer PDF files. I use the flashmovie package to embed Flash applets. Q: How do you make Flash applets? A: Adobe’s Flash Builder software is free to educators!
Beamer TikZ animate Flash Builder Conclusion
On to interactivity!
Everything so far has been pre-scripted. Another dimension can be added through embedding interactive applets into your Beamer PDF files. I use the flashmovie package to embed Flash applets. Q: How do you make Flash applets? A: Adobe’s Flash Builder software is free to educators!
Beamer TikZ animate Flash Builder Conclusion
Beamer TikZ animate Flash Builder Conclusion
Example 5: When are Two Graphs the Same?
Definition Two graphs are the same if the vertices of one correspond to the vertices of another in such a way that the edges also correspond.
\flashmovie[width=10cm,height=6cm]{GraphIsomorphism.swf}
Beamer TikZ animate Flash Builder Conclusion
Example 5: When are Two Graphs the Same?
Definition Two graphs are the same if the vertices of one correspond to the vertices of another in such a way that the edges also correspond.
\flashmovie[width=10cm,height=6cm]{GraphIsomorphism.swf}
Beamer TikZ animate Flash Builder Conclusion
Example 6: Degree of a Vertex
Definition The degree of a vertex is how many lines come into it.
A loop contributes 2 towards the degree of its vertex.
Beamer TikZ animate Flash Builder Conclusion
Example 6: Degree of a Vertex
Definition The degree of a vertex is how many lines come into it.
A loop contributes 2 towards the degree of its vertex.
Beamer TikZ animate Flash Builder Conclusion
Example 7: Cayley Tables
Two Advantages
Beamer slideshows, especially with graphics and interactivity, can bring at least two great advantages into the classroom:
You can display and manipulate larger examples than could be written on the board. Interactive examples reinforce the objectivity of mathematics.
Beamer TikZ animate Flash Builder Conclusion
Questions?
Resources
Beamer Search for beameruserguide.pdf TikZ Search for pgfmanual.pdf
animate Search for animate.pdf Flash To get Flash Builder, go to
http://freeriatools.adobe.com/flex To embed in PDF’s, search for test-flv.pdf or flashmovie.sty This MathFest: Applets in WeBWorK Barbara Margolius, Dan Gries, & Felipe Martins (Minicourse; GCPS 7, Friday 1:30pm) www.flashandmath.com
For my daughter
Anders O.F. Hendrickson
MathFest 2012 Madison, Wisconsin
Beamer
Since its release in 2003, the Beamer package has transformed mathematics conference talks. LATEX source code yields PDF files suitable for projectors. Overlay specifications like \item<3-> permit step-by-step uncovering of items
or making them visible.
Beamer
Since its release in 2003, the Beamer package has transformed mathematics conference talks. LATEX source code yields PDF files suitable for projectors. Overlay specifications like \item<3-> permit step-by-step uncovering of items
or making them visible.
Beamer
Since its release in 2003, the Beamer package has transformed mathematics conference talks. LATEX source code yields PDF files suitable for projectors. Overlay specifications like \item<3-> permit step-by-step uncovering of items
or making them visible.
Beamer
Since its release in 2003, the Beamer package has transformed mathematics conference talks. LATEX source code yields PDF files suitable for projectors. Overlay specifications like \item<3-> permit step-by-step uncovering of items or making them visible.
Beamer TikZ animate Flash Builder Conclusion
Beamer in the classroom
The use of slideshows in the classroom is nothing new. My objective today is to spread the word about three packages that can make Beamer even more useful pedagogically:
TikZ graphics The animate package Inclusion of Flash applets
Beamer TikZ animate Flash Builder Conclusion
TikZ graphics
Till Tantau, the author of Beamer, also wrote the PGF graphics package and the TikZ frontend to it. TikZ is “graphics in the spirit of LATEX.” The basic elements of TikZ are nodes and paths.
Beamer TikZ animate Flash Builder Conclusion
TikZ graphics
Till Tantau, the author of Beamer, also wrote the PGF graphics package and the TikZ frontend to it. TikZ is “graphics in the spirit of LATEX.” The basic elements of TikZ are nodes and paths.
Beamer TikZ animate Flash Builder Conclusion
TikZ graphics
Till Tantau, the author of Beamer, also wrote the PGF graphics package and the TikZ frontend to it. TikZ is “graphics in the spirit of LATEX.” The basic elements of TikZ are nodes and paths.
Beamer TikZ animate Flash Builder Conclusion
Example 1: Definition of a Graph
Definition A graph is a collection of vertices (points) connected by edges (lines or curves).
Example
A
BC
D
E
My source code
Source code in LATEX file Output \usepackage{tikz}
\begin{tikzpicture}[very thick] \vertex[label=135:$A$] (A) at (2,0) {}; \vertex[label= 0:$B$] (B) at (4,2) {}; \vertex[label=135:$C$] (C) at (0,1) {}; \vertex[label=135:$D$] (D) at (2,4) {}; \vertex[label= 0:$E$] (E) at (6,3) {}; \draw (A)--(B); \draw (B)--(D); \draw (C) to[bend left=30] (D); \draw (E) to[bend right=20] (C); \draw (D) to[out=30, in=30] (E);
\end{tikzpicture} A
My source code
Source code in LATEX file Output \usepackage{tikz}
\begin{tikzpicture}[very thick] \vertex[label=135:$A$] (A) at (2,0) {}; \vertex[label= 0:$B$] (B) at (4,2) {}; \vertex[label=135:$C$] (C) at (0,1) {}; \vertex[label=135:$D$] (D) at (2,4) {}; \vertex[label= 0:$E$] (E) at (6,3) {}; \draw (A)--(B); \draw (B)--(D); \draw (C) to[bend left=30] (D); \draw (E) to[bend right=20] (C); \draw (D) to[out=30, in=30] (E);
\end{tikzpicture} A
V1 V2W1 W2
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Advantages of TikZ
Place objects intuitively using Cartesian coordinates. No need to manage separate graphics files; source code resides in your own LATEX document. Can include any LATEX code within the picture. Several programs can export graphics to TikZ, including Geogebra, Inkscape, MATLAB, and R. TikZ commands also accept Beamer overlay specifications, such as \draw<2-> (A) to (B);
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
{AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
{AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
{AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
{AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,
BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,
AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,AB,
AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,AB,AB,
CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,AB,AB,CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 2: Vertex and Edge Sets
Example
A
The vertex set is: {A,B,C} The edge (multi)set is: {AC,BC,AB,AB,CC}
\alt<6>{\draw[ultra thick, red] (B) to (C);} {\draw[thick] (B) to (C);}
Beamer TikZ animate Flash Builder Conclusion
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3: Gauss-Jordan Reduction
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in REF
Example 3 in Reduced REF
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5 ·
4
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5 · 4 ·
3 = 60
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5 · 4 · 3
Example 4: Combinations
Example How many ways are there to choose a three-member committee from senators A, B, C, D, and E? We start by choosing the committee members one by one:
5 · 4 · 3 = 60
Example 4: Combinations
ABC ABD ABE ACB ACD ACE ADB ADC ADE AEB AEC AED
BAC BAD BAE BCA BCD BCE BDA BDC BDE BEA BEC BED
CAB CAD CAE CBA CBD CBE CDA CDB CDE CEA CEB CED
DAB DAC DAE DBA DBC DBE DCA DCB DCE DEA DEB DEC
EAB EAC EAD EBA EBC EBD ECA ECB ECD EDA EDB EDC
Beamer TikZ animate Flash Builder Conclusion
Example 4: Combinations
Example 4: Combinations
{A,B,C} {A,B,D} {A,B,E} {A,C,D} {A,C,E} {A,D,E} {B,C,D} {B,C,E} {B,D,E} {C,D,E}
Beamer TikZ animate Flash Builder Conclusion
Example 4: Combinations
{A,B,C} {A,B,D} {A,B,E} {A,C,D} {A,C,E} {A,D,E} {B,C,D} {B,C,E} {B,D,E} {C,D,E}
60 6
= 10 = (5
The animate package
That example was made using the animate package. \usepackage{animate} The code for making it is not too intricate:
\begin{animateinline}[poster=first, autoplay]{30}% \multiframe{101}{i=0+1}{%
\pgfmathsetmacro{\t}{\i/100}% \DrawBigListOfPermutations
}% \end{animateinline}%
Here \DrawBigListOfPermutations is a macro which draws what the list should look like at time \t∈ [0,1]. This code creates a for-loop during which \i runs from 0 to 100 and \t runs from 0 to 1.
Beamer TikZ animate Flash Builder Conclusion
On to interactivity!
Everything so far has been pre-scripted. Another dimension can be added through embedding interactive applets into your Beamer PDF files. I use the flashmovie package to embed Flash applets. Q: How do you make Flash applets? A: Adobe’s Flash Builder software is free to educators!
Beamer TikZ animate Flash Builder Conclusion
On to interactivity!
Everything so far has been pre-scripted. Another dimension can be added through embedding interactive applets into your Beamer PDF files. I use the flashmovie package to embed Flash applets. Q: How do you make Flash applets? A: Adobe’s Flash Builder software is free to educators!
Beamer TikZ animate Flash Builder Conclusion
On to interactivity!
Everything so far has been pre-scripted. Another dimension can be added through embedding interactive applets into your Beamer PDF files. I use the flashmovie package to embed Flash applets. Q: How do you make Flash applets? A: Adobe’s Flash Builder software is free to educators!
Beamer TikZ animate Flash Builder Conclusion
On to interactivity!
Everything so far has been pre-scripted. Another dimension can be added through embedding interactive applets into your Beamer PDF files. I use the flashmovie package to embed Flash applets. Q: How do you make Flash applets? A: Adobe’s Flash Builder software is free to educators!
Beamer TikZ animate Flash Builder Conclusion
Beamer TikZ animate Flash Builder Conclusion
Example 5: When are Two Graphs the Same?
Definition Two graphs are the same if the vertices of one correspond to the vertices of another in such a way that the edges also correspond.
\flashmovie[width=10cm,height=6cm]{GraphIsomorphism.swf}
Beamer TikZ animate Flash Builder Conclusion
Example 5: When are Two Graphs the Same?
Definition Two graphs are the same if the vertices of one correspond to the vertices of another in such a way that the edges also correspond.
\flashmovie[width=10cm,height=6cm]{GraphIsomorphism.swf}
Beamer TikZ animate Flash Builder Conclusion
Example 6: Degree of a Vertex
Definition The degree of a vertex is how many lines come into it.
A loop contributes 2 towards the degree of its vertex.
Beamer TikZ animate Flash Builder Conclusion
Example 6: Degree of a Vertex
Definition The degree of a vertex is how many lines come into it.
A loop contributes 2 towards the degree of its vertex.
Beamer TikZ animate Flash Builder Conclusion
Example 7: Cayley Tables
Two Advantages
Beamer slideshows, especially with graphics and interactivity, can bring at least two great advantages into the classroom:
You can display and manipulate larger examples than could be written on the board. Interactive examples reinforce the objectivity of mathematics.
Beamer TikZ animate Flash Builder Conclusion
Questions?
Resources
Beamer Search for beameruserguide.pdf TikZ Search for pgfmanual.pdf
animate Search for animate.pdf Flash To get Flash Builder, go to
http://freeriatools.adobe.com/flex To embed in PDF’s, search for test-flv.pdf or flashmovie.sty This MathFest: Applets in WeBWorK Barbara Margolius, Dan Gries, & Felipe Martins (Minicourse; GCPS 7, Friday 1:30pm) www.flashandmath.com
For my daughter