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GUIDE TO ADMISSIONS IN MATHEMATICS 1 Cambridge Mathematics The ...
https://www.maths.cam.ac.uk/undergrad/admissions/files/admissions/admissionsguide.pdf30 Apr 2024: In particular, in the case of applicants from groupsthat are currently under-represented at Cambridge1, or those who have had to overcome significanteducational disruption and/or socio-economic disadvantage, some Colleges2 Results that match 1 of 2 words
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15 Number Theory 15.1 Primality Tests (9 units) This ...
https://www.maths.cam.ac.uk/undergrad/catam/II/15pt1.pdf31 Jul 2023: A primality test is an algorithm used to determine whether or not a given integer is prime.In this project we consider several different primality tests, and apply them to numbers ... N. Question 1 Write a program to test for primality using trial -
MAMA/225, NST3AS/225, MAAS/225 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_225.pdf27 Jun 2024: a) Using a function of 1nn. i=1 Xi, give a test of the above hypothesis, and findits properties under the null and alternative hypotheses. ... d) Give a short discussion of the advantages and disadvantages of your threeproposed tests in (a)-(c). -
Public key fingerprints for Maths machines
https://www.maths.cam.ac.uk/computing/remoteaccess/ssh/fingerp.html29 May 2024: Public key fingerprints for Maths machines. Hosts should normally have 2 fingerprints for use with SSH-2 (with RSA and DSA authentication). We no longer support SSH-1 on any of the systems and so no longer provide SSH-1 keys or fingerprint -
Your Cambridge Mathematics alumni newsletter
https://www.maths.cam.ac.uk/friends/files/Maths_alumni_newsletter_June_2023_final_web%20%281%29.html28 Nov 2023: Unlocking the potential of blood tests for public and individual health. -
UNIVERSITY OF CAMBRIDGE Faculty of Mathematics SCHEDULES FOR THE ...
https://www.maths.cam.ac.uk/undergradnst/files/misc/NSTschedules.pdf2 Nov 2023: Convergence of series; comparison and ratio tests. [6]. The integral as the limit of a sum. ... Convergence of series; comparison and ratio tests. Power series of a complex vari-able; circle of convergence. -
MAMA/218, NST3AS/218, MAAS/218 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_218.pdf27 Jun 2024: test_stat <- 2(logLik(model2) - logLik(model1)). > pval <- 1 - pchisq(test_stat, df = 1). ... err.train <- colMeans((Y - Y.hat)2). > err.test <- colMeans((Y.star - Y.hat)2). > -
CST0/MATH/1 NST0 NATURAL SCIENCES TRIPOS Part IA Monday, 12 ...
https://www.maths.cam.ac.uk/undergradnst/files/2023/papernst_ia_1_2023.pdf9 Nov 2023: 3]. Natural Sciences IA, Mathematics Paper 1. 11. 19W. (a) State without proof the ratio test for series convergence. ... 2]. (b) By using any test for series convergence, determine whether the following seriesconverge or diverge:. -
UNIVERSITY OF CAMBRIDGE Faculty of Mathematics SCHEDULES OF LECTURE…
https://www.maths.cam.ac.uk/undergrad/files/schedules.pdf13 Feb 2024: Comparison and ratio tests, alternating series test. [6]. ContinuityContinuity of real- and complex-valued functions defined on subsets of R and C. -
MAMA/221, NST3AS/221, MAAS/221 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_221.pdf27 Jun 2024: 2. 1. Consider a randomized clinical trial to test the efficacy of a new drug. ... Zn given Nz =. ni=1 1{Zi=z},z = 0,1,2. (ii) Describe Fisher’s exact test in the analysis of 2 2 contigency tables. -
MAT1 MATHEMATICAL TRIPOS Part IB Tuesday, 04 June, 2024 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2024/paperib_1_2024.pdf3 Jul 2024: consider the following two tests:. Test 1: Reject H0 if X1 > 0.95;. ... d) Is either Test 1 or Test 2 uniformly most powerful for testing the hypotheses? -
MAMA/327, NST3AS/327, MAAS/327 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_327.pdf27 Jun 2024: Part III, Paper 327. 3. 2 Define the space of test functions D(Rn) and the space of distributions D′(Rn),defining the notion of convergence on each. ... 0 for each sequence of test functions {φm}m1 that converge to zero in D(Rn). -
MAT1 MATHEMATICAL TRIPOS Part IB Wednesday, 05 June, 2024 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2024/paperib_2_2024.pdf3 Jul 2024: i) Suppose the gambler wishes to test the hypothesis that the die is fair. ... What arethe null and alternative hypotheses? (ii) Describe Pearson’s test. What is the limiting distribution of the Pearson statisticunder the null hypothesis? -
MAMA/325, NST3AS/325, MAAS/325 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_325.pdf27 Jun 2024: carefully what Page and Geilker intended the experiment to test, beyond whatwas previously implied by experiment and observation. ... h = 6.6 1034 m2kg s1, mn = 1.67 1027kg.)(c) Does the Page-Geilker experiment test anything (however implausible) not -
MATHEMATICAL TRIPOS Part IB 2024 List of Courses Analysis ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2024/list_ib.pdf3 Jul 2024: MATHEMATICAL TRIPOS Part IB 2024. List of Courses. Analysis and Topology. Complex Analysis. Complex Analysis or Complex Methods. Complex Methods. Electromagnetism. Fluid Dynamics. Geometry. Groups, Rings and Modules. Linear Algebra. Markov Chains. -
MAMA/316, NST3AS/316, MAAS/316 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_316.pdf27 Jun 2024: ii) The test particle’s equation of motion can be written ẍ2ẏ = F and ÿ2ẋ = G,where. ... Explain how these equations result in5 equilibrium points for the test particle’s motion. -
15 Number Theory 15.10 The Continued Fraction Method for ...
https://www.maths.cam.ac.uk/undergrad/catam/II/15pt10.pdf31 Jul 2023: Question 1 Write a program, using trial division, to test whether N is a product ofprimes in B (we say that N is B-smooth), and if so to give the ... Write a procedure that given x, y, N 6 1015 tests whether x2 Ny2 = 1, being carefulto avoid integer -
MAMA/349, NST3AS/349, MAAS/349 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_349.pdf27 Jun 2024: problem. Test if such a modification of theClosed Box model actually works by introducing yield linearly dependent on metallicity,i.e. -
MATHEMATICAL TRIPOS 2023-24 GUIDE TO COURSES IN PART IB ...
https://www.maths.cam.ac.uk/undergrad/files/coursesIB.pdf22 Aug 2023: test. Building on Part IA Probability, this course willpresent basic techniques of inference, together with their theoretical justification. ... understand and be able to apply the ideas of hypothesis testing, including the Neyman–Pearsonlemma, and -
10 Statistics 10.16 The Tennis Modelling Challenge (8 units) ...
https://www.maths.cam.ac.uk/undergrad/catam/II/10pt16.pdf31 Jul 2023: Fit the model using the data from 2000–2014 and compare to the model fitin Question 2 using the logistic loss incurred on training and test data. ... Question 5 Perform a formal hypothesis test which might allow you to reject themodel in Question 2 in -
MAMA/207, NST3AS/207, MAAS/207 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2023/Paper_207.pdf12 Jul 2023: nk. Let the allocation ratiobe defined as R = n0n1. (a) The Z-test (Wald test) is based on a statistic Z = θ̂ p0n0(1p0). ... Person 1, doesn’t have the risk factor: positive test 1 week after the start ofthe study, and a negative test 2 weeks after -
Introduction 1 General Please read the whole of this ...
https://www.maths.cam.ac.uk/undergrad/catam/IB/IBintro.pdf29 Aug 2023: For example, use of a command to test whether an integer is prime would notbe allowed in a project which required you to write a program to find prime numbers. ... you must write and test all programs yourself, and all reports must be writtenindependently -
MAMA/205, NST3AS/205, MAAS/205 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2023/Paper_205.pdf20 Jul 2023: Describe the closed testing procedure, introducing any other tests that are neededin order for it to work. ... observations(xi,yi,zi) RRRp for i = 1,. ,n. We wish to test the null hypothesis H0: x1 y1 |z1using the test statistic. -
Mathematical Tripos Part IB Computational Projects 2023/2024 CATAM…
https://www.maths.cam.ac.uk/undergrad/catam/IB/IBmanual.pdf28 Nov 2023: For example, use of a command to test whether an integer is prime would notbe allowed in a project which required you to write a program to find prime numbers. ... you must write and test all programs yourself, and all reports must be writtenindependently -
MAT0 MATHEMATICAL TRIPOS Part IA Thursday, 1 June, 2023 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/paperia_1_2023.pdf7 Jul 2023: Justify your answers. Part IA, Paper 1. 3. 4E AnalysisState the comparison test. ... Show that limn Pn/Nn = 1. State the alternating series test. -
MATHEMATICAL TRIPOS Part IB 2022 List of Courses Analysis ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/list_ib.pdf7 Jul 2023: MATHEMATICAL TRIPOS Part IB 2022. List of Courses. Analysis and Topology. Complex Analysis. Complex Analysis or Complex Methods. Complex Methods. Electromagnetism. Fluid Dynamics. Geometry. Groups, Rings and Modules. Linear Algebra. Markov Chains. -
Causal Inference (M16) Dr. Q. Zhao From its onset, ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Statistics/casual_inference_zhao.pdf21 Feb 2024: 1. Motivations:. • Principles of causal inference: motivations; historical perspectives; basic concepts.• Randomized experiments: randomization tests, regression adjustment and its asymp-totic inference. • -
MAT1 MATHEMATICAL TRIPOS Part IB Thursday, 08 June, 2023 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/paperib_3_2023.pdf7 Jul 2023: 18H Statistics(a) Define a uniformly most powerful (UMP) test when X f(|θ) for θ Θ, and. ... ii) Prove that the test in part (i) is UMP of size α for testing H0 : θ 6 0versus H1 : θ > 0. -
MAT1 MATHEMATICAL TRIPOS Part IB Tuesday, 06 June, 2023 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/paperib_1_2023.pdf7 Jul 2023: 6H Statistics(a) Define the generalized likelihood ratio test statistic and state Wilks’ Theorem. ... What isan appropriate statistic and what is the critical region for a test of size α? -
MAMA/116, NST3AS/116, MAAS/116 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2023/Paper_116.pdf12 Jul 2023: Justify your claims for all parts of the question. [You may use the Tarski-Vaught test for elementarity without proof. -
17 Combinatorics 17.3 Hamiltonian cycles (5 units) This project ...
https://www.maths.cam.ac.uk/undergrad/catam/II/17pt3.pdf31 Jul 2023: Test your program on a few particular graphs; and then use iton a selection of graphs from G(n, p) with n up to 21 and p firstly varying from -
MAMA/218, NST3AS/218, MAAS/218 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2023/Paper_218.pdf12 Jul 2023: Give an interpretation of the estimated gender coefficient. The researcher then performed a statistical test and fitted a second model. > ... 3. (b) Explain the statistical test performed by the researcher. State the phenomenonbehind the researcher’s -
MAMA/107, NST3AS/107, MAAS/107 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2023/Paper_107.pdf12 Jul 2023: i) By constructing a suitable test function, prove that weak solutions of (1)satisfy. -
MATHEMATICAL TRIPOS Part IA 2023 List of Courses Analysis ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/list_ia.pdf7 Jul 2023: Justify your answers. Paper 1, Section I. 4E AnalysisState the comparison test. ... Show that limnPn/Nn = 1. State the alternating series test. -
Statistical Learning in Practice (L24) Dr R. Altmeyer Statistical ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Statistics/Stats_Learning_Practice_Altmeyer.pdf21 Feb 2024: Principal component analysis. • Introduction to time series. Prerequisites. Elementary probability theory, maximum likelihood estimation, hypothesis tests and confidenceintervals, linear models. -
Advanced Stellar Evolution (L16) Non-Examinable (Graduate Level) Dr…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Astrophysics/Advanced_Stellar_Evolution_Zytkow.pdf21 Feb 2024: Theonly way in which we may test stellar structure and evolution theory is through the comparisonof theoretical results to observations. -
Planetary System Dynamics (M24) Professor M. Wyatt This course ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Astrophysics/Planetary_System_Dynamics_Wyatt.pdf21 Feb 2024: Secular perturbations: Laplace coefficients, Laplace-Lagrange theory, test particles, secu-lar resonances, Kozai cycles, hierarchical systems. • -
Faculty of Mathematics Part III Essays: 2023-24 Titles 1 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/essays/essays.pdf9 Feb 2024: Faculty of Mathematics. Part III Essays: 2023-24. Titles 1 – 54. Department of Pure Mathematics& Mathematical Statistics. Titles 55 – 93. Department of Applied Mathematics& Theoretical Physics. Titles 94 – 118. Additional Essays. i. -
Statistics in Medicine (3 units) Statistics in Medical Practice ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Statistics/Statistics_Medicine_Jackson_Treasure.pdf21 Feb 2024: Methods for comparing two time-to-eventdistributions (as in a clinical trial of an active treatment versus a placebo) are derived(log-rank test). -
14 General Relativity 14.5 Cosmological distances (8 units) Although…
https://www.maths.cam.ac.uk/undergrad/catam/II/14pt5.pdf31 Jul 2023: 12). A method to test whether a sample of objects has a uniform comoving density and luminositywhich does not change with cosmic time is to use the < V/Vmax > test. -
MAT2 MATHEMATICAL TRIPOS Part II Friday, 09 June, 2023 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/paperii_4_2023.pdf7 Jul 2023: If not, whatis the name of the statistical procedure you can use to test this hypothesis? > ... iv) An analyst fitted the following model to test H1. Does the model fit suggest evidenceagainst H1? -
General Relativity (M24) Professor C. Warnick General Relativity is…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Relativity%20and%20Cosmology/General_Relativity_Warnick.pdf21 Feb 2024: the solar system tests of GR, will not be covered in this course. -
MAT2 MATHEMATICAL TRIPOS Part II Monday, 05 June, 2023 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/paperii_1_2023.pdf7 Jul 2023: c) Suppose k 6 p. For a fixed θ Θ, suppose we wish to test the null hypothesis. ... Deduce an asymptotically valid level-α hypothesis test basedon the statistic. [You may quote any result from the lectures that you need, without proof.]. -
Mathematical Tripos Part III Handbook 2023-24 Contents 1.…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/Part%20III%20Handbook%202023-24.pdf22 Jan 2024: Mathematical Tripos. Part III Handbook 2023-24. Contents 1. Introduction. 1. 2. Introductory and Welcome Meetings. 1. 3. Departmental Registration. 2. 4. Points of Contact. 2. 5. Lectures. 4. 6. Examples Classes. 5. 7. Recordings. 7. 8. Managing -
Model Theory and Non-Classical Logic (M24) Dr J. Siqueira ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Foundations/Model_Theory_Non-Classical_Logic_Siqueira.pdf21 Feb 2024: We will cover most or all of the following topics:. • Definable sets, elementary substructures, and the Tarski-Vaught test;. • -
MATHEMATICAL TRIPOS Part II 2022 List of Courses Algebraic ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/list_ii.pdf7 Jul 2023: MATHEMATICAL TRIPOS Part II 2022. List of Courses. Algebraic Geometry. Algebraic Topology. Analysis of Functions. Applications of Quantum Mechanics. Applied Probability. Asymptotic Methods. Automata and Formal Languages. Classical Dynamics. Coding -
MAT1 MATHEMATICAL TRIPOS Part IB Thursday, 06 June, 2024 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2024/paperib_3_2024.pdf3 Jul 2024: sample from a N(µ,1) population, and we wish to. test the hypothesisH0 : µ = 0 against H1 : µ ̸= 0. ... a) Define a level-α hypothesis test based on X̄ = 1nn. -
Distribution Theory and Applications (L16) Dr. A. Ashton This ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Applied%20and%20computstional%20analysis/Distribution_Theory_Ashton.pdf21 Feb 2024: First we will cover the basic definitions for distributions and related spaces of test functions.Then we look at operations such as differentiation, translation, convolution and the Fouriertransform. -
17 Combinatorics 17.1 Graph Colouring (7 units) This project ...
https://www.maths.cam.ac.uk/undergrad/catam/II/17pt1.pdf31 Jul 2023: Test your program on ten members of G(70, 0.5), andcompare the number of colours used when the vertices are ordered in the following ways:(i) by increasing degree, (ii) -
Contents Units Introduction 1 Numerical Methods 1.1 Fourier…
https://www.maths.cam.ac.uk/undergrad/catam/II/IIcontents.pdf31 Jul 2023: 15 Number Theory. 15.1 Primality Tests 9. 15.10 The Continued Fraction Method for Factorisation 8.
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