This lecture builds hyperbolic geometry using only calculus and linear algebra. After defining distance via curve length and tangent-vector speeds, we motivate negative curvature through familiar surfaces, culminating in an explicit treatment of the pseudosphere. We then introduce four equivalent models of the hyperbolic plane and prove the main isometry statements connecting them, highlighting Mรถbius transformations, the Cayley transform, and Lorentz symmetries. We end with cross-ratio computations and Kleinโs transformation-group viewpoint, explaining geometrically why the Euclidean parallel postulate does not hold.
3:00pm- 3:40 pm :ย ํ์ ๋ฐํ ๋ฐ ํ ์
์ก๊ธฐ์ค:ย Two perspectives on matrix : Linear Transformation and Change of basis
์ง๋ 1๋ ๋์ ๋ฐฐ์ด ์ ํ๋์ํ์ ๊ฐ๋ ์ค ํ๋ ฌ์ ๋ฐ๋ผ๋ณด๋ ๋ ๊ฐ์ง์ ๊ด์ ์ ๋ํด์ ๋ฐํํ ๊ฒ ์ ๋๋ค. ํ๊ธฐ ์ ํ๋์์์ ๋ฐฐ์ด ์ ํ๋ณํ๊ณผ, 2ํ๊ธฐ์๋ ๊ธฐ์ ๋ณํ์ ํตํฉํ์ฌ ํ๋ ฌ์ ์ฌ์ค ์ด์ค์ ์๋ฏธ๋ก ๋ณผ ์ ์์ ๊ณ ์ฐฐํ๊ณ ์ด๋ฅผ ๋ฐํ์ผ๋ก ํ๋ ฌ์ ์ฌ๊ตฌ์ฑํ์ฌ ๋ฎ์ ๊ด๊ณ๋ฅผ ์ดํดํ ์ ์์์ ๋ณด์ผ ๊ฒ ์ ๋๋ค.
ํ์์ฐฌ: Definition and examples of the Poisson processย
I will explain the definition and properties of the Poisson process and look at examples of the Poisson processย
๊นํ์ฃผ: TBA