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Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3

www.maths.cam.ac.uk/undergrad/pastpapers/files/2020/paperii_3_2020.pdf

Table of contents 252
- 1H Paper 3 1
  - Solution 1H
- 2H Paper 3 1
  - Solution 2H
- 3I Paper 3 1
  - Solution 3I
- 4F Paper 3 4
  - i 4F 1
    - Solution i
  - ii 4F 1
    - Solution ii
- 5J Paper 3 6
  - a 5J 1
    - Solution a
  - b 5J 1
    - Solution b
  - c 5J 1
    - Solution c
- 6B Paper 3 6
  - i 6B 1
    - Solution i
  - ii 6B 1
    - Solution ii
  - iii 6B 1
    - Solution iii
- 7E Paper 3 4
  - i 7E 1
    - Solution i
  - ii 7E 1
    - Solution ii
- 8B Paper 3 1
  - Solution 8B
- 9D Paper 3 1
  - Solution 9D
- 10C Paper 3 8
  - i 10C 1
    - Solution i
  - ii 10C 1
    - Solution ii
  - iii 10C 1
    - Solution iii
  - iv 10C 1
    - Solution iv
- 11H Paper 3 6
  - i 11H 1
    - Solution i
  - ii 11H 1
    - Solution ii
  - iii 11H 1
    - Solution iii
- 12F Paper 3 1
  - Solution 12F
- 13B Paper 3 6
  - i 13B 1
    - Solution i
  - ii 13B 1
    - Solution ii
  - iii 13B 1
    - Solution iii
- 14D Paper 3 6
  - i 14D 1
    - Solution i
  - ii 14D 1
    - Solution ii
  - iii 14D 1
    - Solution iii
- 15C Paper 3 11
  - a 15C 1
    - Solution a
  - b 15C 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 16H Paper 3 1
  - Solution 16H
- 17G Paper 3 8
  - i 17G 1
    - Solution i
  - ii 17G 1
    - Solution ii
  - iii 17G 1
    - Solution iii
  - iv 17G 1
    - Solution iv
- 18G Paper 3 4
  - a 18G 1
    - Solution a
  - b 18G 1
    - Solution b
- 19F Paper 3 1
  - Solution 19F
- 20F Paper 3 6
  - a 20F 1
    - Solution a
  - b 20F 1
    - Solution b
  - c 20F 1
    - Solution c
- 21I Paper 3 8
  - a 21I 1
    - Solution a
  - b 21I 1
    - Solution b
  - c 21I 1
    - Solution c
  - d 21I 1
    - Solution d
- 22I Paper 3 7
  - a 22I 1
    - Solution a
  - b 22I 2
    - iii b 1
      - Solution iii
  - c 22I 1
    - Solution c
- 23F Paper 3 1
  - Solution 23F
- 24F Paper 3 8
  - i 24F 1
    - Solution i
  - ii 24F 1
    - Solution ii
  - iii 24F 1
    - Solution iii
  - iv 24F 1
    - Solution iv
- 25I Paper 3 8
  - a 25I 1
    - Solution a
  - b 25I 1
    - Solution b
  - c 25I 1
    - Solution c
  - d 25I 1
    - Solution d
- 26K Paper 3 11
  - a 26K 1
    - Solution a
  - b 26K 1
    - Solution b
  - c 26K 6
    - i c 1
      - Solution i
    - ii c 1
      - Solution ii
    - iii c 1
      - Solution iii
- 27K Paper 3 1
  - Solution 27K
- 28J Paper 3 4
  - i 28J 1
    - Solution i
  - ii 28J 1
    - Solution ii
- 29K Paper 3 12
  - a 29K 4
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
  - b 29K 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 30D Paper 3 4
  - a 30D 1
    - Solution a
  - b 30D 1
    - Solution b
- 31E Paper 3 11
  - a 31E 1
    - Solution a
  - b 31E 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 32C Paper 3 4
  - a 32C 1
    - Solution a
  - b 32C 1
    - Solution b
- 33A Paper 3 1
  - Solution 33A
- 34C Paper 3 7
  - a 34C 1
    - Solution a
  - b 34C 4
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
- 35A Paper 3 6
  - i 35A 1
    - Solution i
  - ii 35A 1
    - Solution ii
  - iii 35A 1
    - Solution iii
- 36D Paper 3 4
  - i 36D 1
    - Solution i
  - ii 36D 1
    - Solution ii
- 37D Paper 3 9
  - a 37D 1
    - Solution a
  - b 37D 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 38B Paper 3 11
  - a 38B 1
    - Solution a
  - b 38B 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 39B Paper 3 6
  - i 39B 1
    - Solution i
  - ii 39B 1
    - Solution ii
  - iii 39B 1
    - Solution iii
- 40E Paper 3 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: 1

Solution

4F (Automata and Formal Languages)

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

5J (Statistical Modelling)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

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: 4

i

Articles: 1

Solution

ii

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: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

12F (Automata and Formal Languages)

Articles: 1

Solution

13B (Mathematical Biology)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

14D (Cosmology)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

15C (Quantum Information and Computation)

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

16H (Logic and Set Theory)

Articles: 1

Solution

17G (Graph Theory)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

18G (Galois Theory)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

19F (Representation Theory)

Articles: 1

Solution

20F (Algebraic Topology)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

21I (Linear Analysis)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

22I (Analysis of Functions)

Articles: 7

a

Articles: 1

Solution

b

Articles: 2

iii

Articles: 1

Solution

c

Articles: 1

Solution

23F (Riemann Surfaces)

Articles: 1

Solution

24F (Algebraic Geometry)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

25I (Differential Geometry)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

26K (Probability and Measure)

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

27K (Applied Probability)

Articles: 1

Solution

28J (Principles of Statistics)

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

29K (Stochastic Financial Models)

Articles: 12

a

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

30D (Asymptotic Methods)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

31E (Dynamical Systems)

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

32C (Integrable Systems)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

33A (Principles of Quantum Mechanics)

Articles: 1

Solution

34C (Applications of Quantum Mechanics)

Articles: 7

a

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

35A (Statistical Physics)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

36D (Electrodynamics)

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

37D (General Relativity )

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

38B (Fluid Dynamics II)

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

39B (Waves)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

40E (Numerical Analysis)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

 Ancestors (8)