5th annual conference in mathematics & statistics service teaching, institute of technology...
TRANSCRIPT
![Page 1: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/1.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
11
Exploring Mathematics Exploring Mathematics usingusing
Mathematical TreatsMathematical Treats
Dr. Michael Brennan, Dr. Michael Brennan,
Department of MathematicsDepartment of Mathematics
Cork Institute of TechnologyCork Institute of Technology
![Page 2: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/2.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
22
![Page 3: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/3.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
33
Student questionStudent question
``What exactly is ? ````What exactly is ? ``
![Page 4: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/4.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
44
What is ?? 3.14159265358979323846 3.14159265358979323846
oror
RatioRatio of the of the circumferencecircumference to the to the diameterdiameter of a of a circlecircle
22
7
355
113
![Page 5: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/5.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
55
![Page 6: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/6.jpg)
Birthday Problem
How large does a group have to be to guarantee a match?
How large does a group have to be so that the chance of a match is greater than 50%
![Page 7: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/7.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
77
Birthday Problem
![Page 8: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/8.jpg)
Examples of TreatsExamples of Treats
Definition of PiDefinition of Pi
ProbabilityProbability
Geometric SeriesGeometric Series
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
88
![Page 9: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/9.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
99
1/4 + 1/16 + 1/64 + 1/256 + · · ·
![Page 10: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/10.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
1010
Geometric Treats
![Page 11: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/11.jpg)
Sum of Series 0 < r < 1Sum of Series 0 < r < 1
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
1111
![Page 12: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/12.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
1212
What is a Mathematical Treat?What is a Mathematical Treat?
DefinitionDefinitionA A Mathematical TreatMathematical Treat is an is an educational resource, e.g. educational resource, e.g.
puzzle,animation,story,image,gamepuzzle,animation,story,image,game that that inspiresinspires and/or adds and/or adds insightinsight into into
a mathematical idea.a mathematical idea.
![Page 13: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/13.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
1313
Mathematical TreatsMathematical Treats
![Page 14: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/14.jpg)
![Page 15: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/15.jpg)
![Page 16: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/16.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
1616
![Page 17: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/17.jpg)
Use of Games Use of Games Bloxorz
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
1717
![Page 18: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/18.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
1818
More Beginnings & EndingsMore Beginnings & Endings
CPU BlogCPU Blog Psychological Principle Primacy-Recency Psychological Principle Primacy-Recency Dr. Lisa Bullard (Active Learning) LIT2009Dr. Lisa Bullard (Active Learning) LIT2009
![Page 19: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/19.jpg)
Active Learning Active Learning
Find Pi using a Find Pi using a Homemade ObjectHomemade Object
Create a Create a Mobius Strip
Devise Birthday Devise Birthday AnalysisAnalysis
Glass Coin Clock Mug
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
1919
![Page 20: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/20.jpg)
Universal Universal Recycle SymbolRecycle Symbol
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2020
![Page 21: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/21.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2121
![Page 22: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/22.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2222
![Page 23: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/23.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2323
Painter’s ParadoxPainter’s Paradox
Gabriels Horn has a Gabriels Horn has a finite volume and finite volume and an infinite surface an infinite surface areaarea
![Page 24: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/24.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2424
Useful ResourcesUseful Resources
ColleaguesColleagues MERLOTMERLOT GeogebraGeogebra Wolfram AlphaWolfram Alpha Math WikipediaMath Wikipedia MathWorldMathWorld Maple ApplicationsMaple Applications
![Page 25: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/25.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2525
Endings...!Endings...!
Use Sparingly*Use Sparingly* Relevancy/ContextRelevancy/Context Encourage EngagementEncourage Engagement SubjectiveSubjective Reaction/Response Reaction/Response
![Page 26: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/26.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2626
![Page 27: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/27.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2727
![Page 28: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/28.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2828
![Page 29: 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Technology Carlow, May 24th-25th 2010. 1 Exploring Mathematics using Mathematical](https://reader035.vdocuments.us/reader035/viewer/2022070407/56649e255503460f94b1464f/html5/thumbnails/29.jpg)
5th Annual Conference in Mathematics & 5th Annual Conference in Mathematics & Statistics Service Teaching, Institute of Statistics Service Teaching, Institute of
Technology Carlow, May 24th-25th 2010.Technology Carlow, May 24th-25th 2010.
2929