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30 Mar 2022: 42. 7.3 Some stacks. 44. 7.4 Orbits of square-free discriminant. 46. ... We then recall and extend some of its basic properties in 3.2–3.6.In 3.7 we introduce the corresponding family of curves C B and in 3.8

6 Jul 2022: Thennecessarily ρ(0) = idV , and ρ(1) is some invertible linear map α on V. ... Say ρ(1) = A then Aei =λei ei1 for some non-zero λ and i = 1,.

29 Nov 2022: Thennecessarily ρ(0) = idV , and ρ(1) is some invertible linear map α on V. ... Say ρ(1) = A then Aei =λei ei1 for some non-zero λ and i = 1,.

30 Aug 2022: αpj α1q1jie. pjqj 1α2. Thus A can bet on some horse with B if and only if. ... maxj. pjqj 1α2. Similarly B can bet on some horse with A if and only if.

12 Dec 2022: Proofs for some results inTopics in Analysis. T. W. Körner. October 4, 2022. ... Now P(z) = 0 if and only if z = ajfor some 1 j m.

18 Nov 2022: thefact that θ is holomorphic) and some kind of invariance property under anarithmetic group such as Γ. ... The last two bullet points rely on some of the most important advances inarithmetic geometry of the 20th century.

11 Dec 2022: 1.1 Some Puzzles to Get You StartedDon’t look down on puzzles:. ... 2.2 Here are some things you will needEXERCISE 16. 1. Factorise x2 y2.

24 May 2022: 1.6 Some examples of ordinals that aren’t too big. 231.7 Some worked exercises. ... Fortunately ω2 does have some naturalmanifestations: IN IN ordered lexicographically is of length ω2.