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Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4

www.maths.cam.ac.uk/undergrad/pastpapers/files/2020/paperii_4_2020.pdf

Table of contents 277
- 1H Paper 4 1
  - Solution 1H
- 2H Paper 4 1
  - Solution 2H
- 3I Paper 4 4
  - a 3I 1
    - Solution a
  - b 3I 1
    - Solution b
- 4F Paper 4 1
  - Solution 4F
- 5J Paper 4 9
  - a 5J 6
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
    - iii a 1
      - Solution iii
  - b 5J 1
    - Solution b
- 6B Paper 4 6
  - i 6B 1
    - Solution i
  - ii 6B 1
    - Solution ii
  - iii 6B 1
    - Solution iii
- 7E Paper 4 1
  - Solution 7E
- 8B Paper 4 1
  - Solution 8B
- 9D Paper 4 1
  - Solution 9D
- 10C Paper 4 8
  - i 10C 1
    - Solution i
  - ii 10C 1
    - Solution ii
  - iii 10C 1
    - Solution iii
  - iv 10C 1
    - Solution iv
- 11H Paper 4 8
  - a 11H 1
    - Solution a
  - b 11H 1
    - Solution b
  - c 11H 1
    - Solution c
  - d 11H 1
    - Solution d
- 12H Paper 4 9
  - a 12H 1
    - Solution a
  - b 12H 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 13J Paper 4 9
  - a 13J 1
    - Solution a
  - b 13J 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 14B Paper 4 8
  - i 14B 1
    - Solution i
  - ii 14B 1
    - Solution ii
  - iii 14B 1
    - Solution iii
  - iv 14B 1
    - Solution iv
- 15B Paper 4 7
  - a 15B 1
    - Solution a
  - b 15B 1
    - Solution b
  - c 15B 2
    - i c 1
      - Solution i
- 16H Paper 4 11
  - a 16H 1
    - Solution a
  - b 16H 1
    - Solution b
  - c 16H 6
    - i c 1
      - Solution i
    - ii c 1
      - Solution ii
    - iii c 1
      - Solution iii
- 17G Paper 4 1
  - Solution 17G
- 18G Paper 4 4
  - a 18G 1
    - Solution a
  - b 18G 1
    - Solution b
- 19F Paper 4 4
  - a 19F 1
    - Solution a
  - b 19F 1
    - Solution b
- 20G Paper 4 1
  - Solution 20G
- 21F Paper 4 7
  - a 21F 2
    - ii a 1
      - Solution ii
  - b 21F 1
    - Solution b
  - c 21F 1
    - Solution c
- 22I Paper 4 9
  - a 22I 1
    - Solution a
  - b 22I 1
    - Solution b
  - c 22I 4
    - i c 1
      - Solution i
    - ii c 1
      - Solution ii
- 23I Paper 4 6
  - a 23I 1
    - Solution a
  - b 23I 1
    - Solution b
  - c 23I 1
    - Solution c
- 24F Paper 4 1
  - Solution 24F
- 25I Paper 4 11
  - a 25I 1
    - Solution a
  - b 25I 1
    - Solution b
  - c 25I 1
    - Solution c
  - d 25I 4
    - i d 1
      - Solution i
    - ii d 1
      - Solution ii
- 26K Paper 4 9
  - a 26K 1
    - Solution a
  - b 26K 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 27K Paper 4 6
  - i 27K 1
    - Solution i
  - ii 27K 1
    - Solution ii
  - iii 27K 1
    - Solution iii
- 28J Paper 4 1
  - Solution 28J
- 29K Paper 4 10
  - i 29K 1
    - Solution i
  - ii 29K 1
    - Solution ii
  - iii 29K 1
    - Solution iii
  - iv 29K 1
    - Solution iv
  - v 29K 1
    - Solution v
- 30J Paper 4 8
  - i 30J 1
    - Solution i
  - ii 30J 1
    - Solution ii
  - iii 30J 1
    - Solution iii
  - iv 30J 1
    - Solution iv
- 31A Paper 4 8
  - i 31A 1
    - Solution i
  - ii 31A 1
    - Solution ii
  - iii 31A 1
    - Solution iii
  - iv 31A 1
    - Solution iv
- 32E Paper 4 12
  - a 32E 2
    - i a 1
      - Solution i
  - b 32E 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 33A Paper 4 1
  - Solution 33A
- 34C Paper 4 9
  - a 34C 1
    - Solution a
  - b 34C 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 35A Paper 4 6
  - i 35A 1
    - Solution i
  - ii 35A 1
    - Solution ii
  - iii 35A 1
    - Solution iii
- 36D Paper 4 11
  - a 36D 1
    - Solution a
  - b 36D 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 37D Paper 4 8
  - i 37D 1
    - Solution i
  - ii 37D 1
    - Solution ii
  - iii 37D 1
    - Solution iii
  - iv 37D 1
    - Solution iv
- 38B Paper 4 6
  - i 38B 1
    - Solution i
  - ii 38B 1
    - Solution ii
  - iii 38B 1
    - Solution iii
- 39B Paper 4 7
  - a 39B 1
    - Solution a
  - b 39B 4
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
- 40E Paper 4 6
  - a 40E 1
    - Solution a
  - b 40E 1
    - Solution b
  - c 40E 1
    - Solution c

1H (Number Theory)

Articles: 1

Solution

2H (Topics in Analysis)

Articles: 1

Solution

3I (Coding and Cryptography)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

4F (Automata and Formal Languages)

Articles: 1

Solution

5J (Statistical Modelling)

Articles: 9

a

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

b

Articles: 1

Solution

6B (Mathematical Biology)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

7E (Further Complex Methods)

Articles: 1

Solution

8B (Classical Dynamics)

Articles: 1

Solution

9D (Cosmology)

Articles: 1

Solution

10C (Quantum Information and Computation)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

11H (Number Theory)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

12H (Topics in Analysis)

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

13J (Statistical Modelling)

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

14B (Mathematical Biology)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

15B (Classical Dynamics)

Articles: 7

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 2

i

Articles: 1

Solution

16H (Logic and Set Theory)

Articles: 11

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

17G (Graph Theory)

Articles: 1

Solution

18G (Galois Theory)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

19F (Representation Theory)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

20G (Number Fields)

Articles: 1

Solution

21F (Algebraic Topology)

Articles: 7

a

Articles: 2

ii

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

22I (Linear Analysis)

Articles: 9

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

23I (Analysis of Functions)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

24F (Algebraic Geometry)

Articles: 1

Solution

25I (Differential Geometry)

Articles: 11

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

26K (Probability and Measure)

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

27K (Applied Probability)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

28J (Principles of Statistics)

Articles: 1

Solution

29K (Stochastic Financial Models)

Articles: 10

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

v

Articles: 1

Solution

30J (Mathematics of Machine Learning)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

31A (Asymptotic Methods)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

32E (Dynamical Systems)

Articles: 12

a

Articles: 2

i

Articles: 1

Solution

b

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

33A (Principles of Quantum Mechanics)

Articles: 1

Solution

34C (Applications of Quantum Mechanics)

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

35A (Statistical Physics)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

36D (Electrodynamics)

Articles: 11

a

Articles: 1

Solution

b

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

37D (General Relativity)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

38B (Fluid Dynamics II)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

39B (Waves)

Articles: 7

a

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

40E (Numerical Analysis)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

 Ancestors (8)