Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation...
Transcript of Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation...
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Introduction to MAT 402
Parker Glynn-Adey
University of Toronto, Mississauga
January 7, 2020
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What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
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What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
![Page 4: Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation 15% Midterm 20% Exam 30%. The Euclid Project. The Euclid Project Euclid’s Elements](https://reader033.fdocuments.net/reader033/viewer/2022042620/5f4a9f59ee84b4699b4e8f92/html5/thumbnails/4.jpg)
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
![Page 5: Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation 15% Midterm 20% Exam 30%. The Euclid Project. The Euclid Project Euclid’s Elements](https://reader033.fdocuments.net/reader033/viewer/2022042620/5f4a9f59ee84b4699b4e8f92/html5/thumbnails/5.jpg)
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
![Page 6: Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation 15% Midterm 20% Exam 30%. The Euclid Project. The Euclid Project Euclid’s Elements](https://reader033.fdocuments.net/reader033/viewer/2022042620/5f4a9f59ee84b4699b4e8f92/html5/thumbnails/6.jpg)
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
![Page 7: Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation 15% Midterm 20% Exam 30%. The Euclid Project. The Euclid Project Euclid’s Elements](https://reader033.fdocuments.net/reader033/viewer/2022042620/5f4a9f59ee84b4699b4e8f92/html5/thumbnails/7.jpg)
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
![Page 8: Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation 15% Midterm 20% Exam 30%. The Euclid Project. The Euclid Project Euclid’s Elements](https://reader033.fdocuments.net/reader033/viewer/2022042620/5f4a9f59ee84b4699b4e8f92/html5/thumbnails/8.jpg)
Tangible! Playful! Colourful!
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Where does this course lead? (Top dozen posters)
A Celebration of Classical GeometryFields Institute on April 25th 2020
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Where does this course lead? (Top five videos)
Math in Action Journal
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Grade Distribution
Articles 10% + 15% 25%Wiki Improvement 10× 1% 10%Poster + Video Presentation 15%Midterm 20%Exam 30%
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The Euclid Project
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The Euclid Project
Euclid’s Elements was the standard introduction to geometry,number theory, and mathematics, from antiquity until moderntimes.
We are going to read it and write about it.
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The Euclid Project
Euclid’s Elements was the standard introduction to geometry,number theory, and mathematics, from antiquity until moderntimes. We are going to read it and write about it.
![Page 15: Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation 15% Midterm 20% Exam 30%. The Euclid Project. The Euclid Project Euclid’s Elements](https://reader033.fdocuments.net/reader033/viewer/2022042620/5f4a9f59ee84b4699b4e8f92/html5/thumbnails/15.jpg)
The Explorations
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The Explorations
During the Explorations part of the course,we will explore classical geometry post-Euclid.
The explorations will feature problems, puzzles, and tricks. Thepurpose of the Explorations is to develop your sense of the richnessof geometry. There is a rich body of folk lore geometry.
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The Explorations
During the Explorations part of the course,we will explore classical geometry post-Euclid.
The explorations will feature problems, puzzles, and tricks. Thepurpose of the Explorations is to develop your sense of the richnessof geometry.
There is a rich body of folk lore geometry.
![Page 18: Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation 15% Midterm 20% Exam 30%. The Euclid Project. The Euclid Project Euclid’s Elements](https://reader033.fdocuments.net/reader033/viewer/2022042620/5f4a9f59ee84b4699b4e8f92/html5/thumbnails/18.jpg)
The Explorations
During the Explorations part of the course,we will explore classical geometry post-Euclid.
The explorations will feature problems, puzzles, and tricks. Thepurpose of the Explorations is to develop your sense of the richnessof geometry. There is a rich body of folk lore geometry.
![Page 19: Introduction to MAT 402 - pgadey.ca€¦ · Wiki Improvement 10 1% 10% Poster + Video Presentation 15% Midterm 20% Exam 30%. The Euclid Project. The Euclid Project Euclid’s Elements](https://reader033.fdocuments.net/reader033/viewer/2022042620/5f4a9f59ee84b4699b4e8f92/html5/thumbnails/19.jpg)
(2,3,6) Kaleidoscope
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Circle Limit III – Escher, 1959
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Tangible Mathematics
Martin Schilling 1864 → Brown University 1973 → Smithsonian
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Tangible Mathematics
Martin Schilling 1864 → Brown University 1973 → Smithsonian
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Mural Mosaic in The Alhambra – Escher, 1922
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Geometry: Art, Education, Research #GEAR2020
Friday October 9th to Sunday October 11th 2020 @ [email protected]