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  2. Partial Solutions for Exercises inWhere do Numbers Come From? ...

    https://www.dpmms.cam.ac.uk/~twk/Ansnumber.pdf
    7 Jan 2023: 24. Exercise 3.2.6. (i) a 1 = a 1 so (a, a) (1, 1) and [a, a] = [1, 1].Using the associative law of addition, (a 1) 1 = a (1
  3. Modular curves and Ne19 eron models of generalized Jacobians

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/neronfinal.pdf
    10 Feb 2023: Some of our results in this case are then subsumedby the works [24–26] on Picard schemes of semifactorial curves.
  4. Automata & Formal LanguagesMichaelmas Term 2023 Part II of ...

    https://www.dpmms.cam.ac.uk/study/II/AutomataAndFormalLanguages/2023-2024/M23_AFL_ES2.corrected.pdf
    23 Oct 2023: 24) Give a context-free grammar in Chomsky normal form for the languages {amb2mck ; m, k 1} and{ambkam ; m, k 1}.
  5. HX1Lycée Louis le Grand 2015-2016 Mathématiques Classe de…

    https://www.dpmms.cam.ac.uk/~aptm3/docs/lecture-notes/Mathematiques-Sup.pdf
    31 Aug 2023: Proposition 1.24 (Linéarisation de cosn θ). n N, θ R. cosn θ =(eiθ eiθ. ... Proposition 3.24. L’applicationP(E) {0, 1}. E. A 7 1Aest une bijection.
  6. HX1Lycée Louis le Grand 2015-2016 Physique Classe de Mathématiques ...

    https://www.dpmms.cam.ac.uk/~aptm3/docs/lecture-notes/Physique-Sup.pdf
    31 Aug 2023: 93III Action d’un champ magnétique sur un moment magnétique. 94. 24 Induction 97I Lois de l’induction. ... R2. Req. Vocabulaire 6.24. On dit que le pont est équilibré lorsque la tension aux bornes de ()est nulle.
  7. MP∗2Lycée Louis le Grand 2016-2017 Mathématiques Classe de…

    https://www.dpmms.cam.ac.uk/~aptm3/docs/lecture-notes/Mathematiques-Spe.pdf
    31 Aug 2023: 24 Anneaux 126I Généralités. 126II L’anneau Z/nZ. 127III Caractéristique d’un corps. ... Alors XY Z (XY. )Z. Proposition 6.24. C0 (R,R) R. Démonstration.
  8. Geometric inverse problems with emphasis on two dimensions Gabriel ...

    https://www.dpmms.cam.ac.uk/~gpp24/GIP2D_driver.pdf
    1 Feb 2023: Geometric inverse problems. with emphasis on two dimensions. Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann. iii. To our families and all who have supported us. This material has been published by Cambridge University Press & Assessment
  9. INDEPENDENCE OF ` FOR FROBENIUS CONJUGACY CLASSES ATTACHED TO ...

    https://www.dpmms.cam.ac.uk/~rz240/l-indep_v2.pdf
    23 Jan 2023: INDEPENDENCE OF FOR FROBENIUS CONJUGACY. CLASSES ATTACHED TO ABELIAN VARIETIES. MARK KISIN AND RONG ZHOU. Abstract. Let A be an abelian variety over a number field E C and let Gdenote the Mumford–Tate group of A. After replacing E by a finite
  10. Number Fields IID, Lent 2020* Comments/corrections to…

    https://www.dpmms.cam.ac.uk/~ajs1005/nf2d/number_fields_notes.pdf
    1 Feb 2023: 24. Proposition 11.3. If R |dK|1/2, there are infinitely many elements of oK withNK/Q(α) R.Let’s assume this.
  11. Department of Pure Mathematics and Mathematical Statistics

    https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/previous.html
    17 Oct 2023: Example sheet 3 updated Jan 24, 2011.

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