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Holly Krieger — Cambridge
https://www.dpmms.cam.ac.uk/~hk439/research.html9 May 2023: Juul, N. Looper, M. Manes, B. Thompson, L. Walton), Research Directions in Number Theory, Association for Women in Mathematics Series, Vol. ... Some consequences of Schanuel's conjecture (with C. Cheng, B. Dietel, M. -
The Cauchy-Schwarz inequality
https://www.dpmms.cam.ac.uk/~wtg10/csineq.html4 Oct 2001: 1. /b. 1. rather than some other a. i. /b. i. , ... i. are equal. This still leaves a minor problem that some of the b. -
Recent papers and preprints
https://www.dpmms.cam.ac.uk/~ik355/pubs.html17 May 2024: pdf]. I. Kontoyiannis. "Some information-theoretic computations related to the distribution of prime numbers." In Festschrift in Honor of Jorma Rissanen, (P. ... Mutual information, synergy, and some curious phenomena for simple channels." 2005 IEEE -
Lent 2024 LOGIC AND SET THEORY – EXAMPLES 4 ...
https://www.dpmms.cam.ac.uk/study/II/Logic/2023-2024/sheet4.pdf3 Apr 2024: Show further that if f : X Y is a continuous function between Polish spacesand f is injective on a Borel set B X, then f(B) is Borel. ... 14. Prove that a set A (in some Polish space) is analytic if and only if there exist closedsets An1,.,nk (indexed by -
Henkin on ω-consistency and ω-completeness JSL 1954 and 1957: ...
https://www.dpmms.cam.ac.uk/~tef10/henkin.pdf8 Jan 2021: After allT might prove φ(a) for every a in Γ and yet prove φ(b) for some constant bnot in Γ. ... We need some definitions. DEFINITION 4. A theory T is Γn-complete iff whenever φ(x1,. -
slide 0 Modular formsand motivesA J Scholl slide 1 ...
https://www.dpmms.cam.ac.uk/~ajs1005/preprints/banff.pdf29 Jan 2010: slide 12. Lemma j = isomn on HM(;)(") Z[ 12k!].(each component of complement is xedby some with "( ) = 1.)[D]ix(pr0#D [ [prk#D)(") 7!y2 2Hk1M (Uky ;k 1)(")'Hk1M ... E fyg)k;k 1)(")Eisenstein symbol (B)ny = 0, some n > 1[n]y 2 Hk1M ((E 0)k;k 1)(")?yoHk1M -
DIFFERENTIAL GEOMETRY (PART III) MICHAELMAS 2021 EXAMPLE SHEET 2 ...
https://www.dpmms.cam.ac.uk/files/study/III/DifferentialGeometry/2021-2022/DGSheet2.pdf1 Nov 2021: Show that M M is trivial.(b) Show that for all n we have TSn R = Rn1 over Sn. ... 4.† Let α be a nowhere-zero 1-form on a manifold X, and let β be a p-form.(a) Show that if β = α γ for some (p -
Publications | Department of Pure Mathematics and Mathematical…
https://www.dpmms.cam.ac.uk/publications?page=18718 Jul 2024: 753,. 442. Set colourings of graphs. B BOLLOBAS, A THOMASON. – Discrete Mathematics. ... SOME MISLEADING ARGUMENTS INVOLVING CONDITIONAL INDEPENDENCE. AP DAWID. – JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL. -
The existence of root two
https://www.dpmms.cam.ac.uk/~wtg10/roottwo.html20 Sep 2001: We know that some numbers are irrational, but we can still describe them, by means of their decimal expansions. ... 2. in some way, consistent with the principle that 0 < a < b implies that a. -
Mich. 2023 ANALYSIS AND TOPOLOGY—EXAMPLES 4 PAR 1. Let ...
https://www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2023-2024/4.pdf24 Nov 2023: 10. Let f: R2 R and (a,b) R2. (a) Suppose that D1f exists and is continuous in some open ball around (a,b), and that. ... b) Suppose instead that D1f exists and is bounded on some open ball around (a,b), and. -
Holly Krieger - vita
https://www.dpmms.cam.ac.uk/~hk439/CV.pdf19 Apr 2023: Juul, N. Looper, M. Manes, B. Thompson, L. WaltonTo appear in Research Directions in Number Theory - Women in Numbers 4. ... 23, 5498-5525. 2. 2009 Some Consequences of Schanuel’s Conjecture,with C. Cheng, B. -
problemsPDE
https://www.dpmms.cam.ac.uk/files/study/III/AnalysisPDE/2021-2022/Sheet1.pdf14 Oct 2021: Show that ifeb|k|f̂(k) L2(R) for some b > 0 then f is real analytic at each point in R. ... u1. 1We write A B to mean that there exists a universal constant C such that A CB. -
Definitions
https://www.dpmms.cam.ac.uk/~wtg10/definition.html24 Nov 2001: In the end, in order to do this one is forced to come up with some non-canonical construction that satisfies the axiom. ... four times, being periodic with period some number (defined to be 2 pi), satisfying the addition law -
Lent 2024 Number Fields – Example Sheet 3 P.P. ...
https://www.dpmms.cam.ac.uk/study/II/NumberFields/2023-2024/example3.pdf23 Feb 2024: 2(1. 71). Find an element of OK with norm 2a 3b 5 for some. ... a,b 0. Hence prove that the class group of K is cyclic and find its order. -
Fermat's little theorem
https://www.dpmms.cam.ac.uk/~wtg10/fermat.html6 Mar 2002: b in B (that is, some non-zero b (mod p)) such that the set of all bx. ... Hence, if we can find some b that does not belong to A, then we have constructed the desired injection. -
MATHEMATICAL TRIPOS: PART IA Lent 2024 PROBABILITY JRNExample Sheet…
https://www.dpmms.cam.ac.uk/study/IA/Probability/2023-2024/pex1.pdf11 Jan 2024: 6. Let (An : n N) be a sequence of events in some probability space (, F, P). ... Set. A = {ω : ω An infinitely often}, B = {ω : ω An for all sufficiently large n}. -
Riemann SurfacesExample Sheet 1 Michaelmas 2023 Please send any ...
https://www.dpmms.cam.ac.uk/study/II/Riemann/2023-2024/RS1M23.pdf12 Oct 2023: 6. By considering the singularity at or otherwise, show that any injective holo-morphic map f C C has the form f(z) = az b, for some a C and b ... 0,1,a} to be conformallyequivalent to C{0,1,b}, where a,b C{0,1}.[Don’t forget the cross ratio from IB - -
The fundamental theorem of arithmetic
https://www.dpmms.cam.ac.uk/~wtg10/FTA.html15 Jun 2000: The definition is that it is not divisible by 2. However, another, more positive definition is that a can be written 2b1 for some integer b. ... b. Having had some success with addition, we could try multiplication. What happens if we replace a by ha? -
Mich. 2023 ANALYSIS AND TOPOLOGY—EXAMPLES 1 PAR 1. Let ...
https://www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2023-2024/1.pdf12 Oct 2023: a, b], and suppose that fn converges pointwise to a continuous function f. ... Show that there is some subinterval [a, b] of [0, 1] with a < b on which (fn) is uniformly. -
The mean value theorem
https://www.dpmms.cam.ac.uk/~wtg10/meanvalue.html13 Dec 2001: Then there is some point c in (a,b) such that f'(c) equals (f(b)-f(a))/(b-a). ... Here, I take f to be real valued and defined on some interval of real numbers.
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