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Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3

www.maths.cam.ac.uk/undergrad/pastpapers/files/2019/paperii_3_2019.pdf

Table of contents 270
- 1I Paper 3 1
  - Solution 1I
- 2H Paper 3 1
  - Solution 2H
- 3G Paper 3 6
  - i 3G 1
    - Solution i
  - ii 3G 1
    - Solution ii
  - iii 3G 1
    - Solution iii
- 4H Paper 3 6
  - a 4H 1
    - Solution a
  - b 4H 1
    - Solution b
  - c 4H 1
    - Solution c
- 5J Paper 3 6
  - a 5J 1
    - Solution a
  - b 5J 1
    - Solution b
  - c 5J 1
    - Solution c
- 6C Paper 3 1
  - Solution 6C
- 7A Paper 3 4
  - a 7A 1
    - Solution a
  - b 7A 1
    - Solution b
- 8E Paper 3 4
  - a 8E 1
    - Solution a
  - b 8E 1
    - Solution b
- 9B Paper 3 1
  - Solution 9B
- 10D Paper 3 4
  - a 10D 1
    - Solution a
  - b 10D 1
    - Solution b
- 11I Paper 3 6
  - a 11I 1
    - Solution a
  - b 11I 1
    - Solution b
  - c 11I 1
    - Solution c
- 12H Paper 3 10
  - a 12H 1
    - Solution a
  - b 12H 1
    - Solution b
  - c 12H 1
    - Solution c
  - d 12H 1
    - Solution d
  - e 12H 1
    - Solution e
- 13C Paper 3 14
  - a 13C 6
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
    - iii a 1
      - Solution iii
  - b 13C 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 14B Paper 3 1
  - Solution 14B
- 15D Paper 3 10
  - a 15D 1
    - Solution a
  - b 15D 1
    - Solution b
  - c 15D 1
    - Solution c
  - d 15D 1
    - Solution d
  - e 15D 1
    - Solution e
- 16I Paper 3 8
  - i 16I 1
    - Solution i
  - ii 16I 1
    - Solution ii
  - iii 16I 1
    - Solution iii
  - iv 16I 1
    - Solution iv
- 17G Paper 3 8
  - a 17G 1
    - Solution a
  - b 17G 1
    - Solution b
  - c 17G 1
    - Solution c
  - d 17G 1
    - Solution d
- 18F Paper 3 1
  - Solution 18F
- 19I Paper 3 9
  - a 19I 1
    - Solution a
  - b 19I 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 20F Paper 3 8
  - a 20F 1
    - Solution a
  - b 20F 1
    - Solution b
  - c 20F 1
    - Solution c
  - d 20F 1
    - Solution d
- 21H Paper 3 8
  - a 21H 1
    - Solution a
  - b 21H 1
    - Solution b
  - c 21H 1
    - Solution c
  - d 21H 1
    - Solution d
- 22H Paper 3 8
  - a 22H 1
    - Solution a
  - b 22H 1
    - Solution b
  - c 22H 1
    - Solution c
  - d 22H 1
    - Solution d
- 23F Paper 3 1
  - Solution 23F
- 24F Paper 3 6
  - a 24F 1
    - Solution a
  - b 24F 1
    - Solution b
  - c 24F 1
    - Solution c
- 25H Paper 3 10
  - a 25H 4
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
  - b 25H 4
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
- 26K Paper 3 10
  - a 26K 1
    - Solution a
  - b 26K 1
    - Solution b
  - c 26K 1
    - Solution c
  - d 26K 1
    - Solution d
  - e 26K 1
    - Solution e
- 27K Paper 3 4
  - a 27K 1
    - Solution a
  - b 27K 1
    - Solution b
- 28J Paper 3 6
  - a 28J 1
    - Solution a
  - b 28J 1
    - Solution b
  - c 28J 1
    - Solution c
- 29K Paper 3 6
  - a 29K 1
    - Solution a
  - b 29K 1
    - Solution b
  - c 29K 1
    - Solution c
- 30A Paper 3 4
  - a 30A 1
    - Solution a
  - b 30A 1
    - Solution b
- 31E Paper 3 10
  - a 31E 1
    - Solution a
  - b 31E 1
    - Solution b
  - c 31E 1
    - Solution c
  - d 31E 1
    - Solution d
  - e 31E 1
    - Solution e
- 32C Paper 3 13
  - a 32C 1
    - Solution a
  - n 32C 1
    - Solution n
  - b 32C 1
    - Solution b
  - c 32C 6
    - i c 1
      - Solution i
    - ii c 1
      - Solution ii
    - iii c 1
      - Solution iii
- 33B Paper 3 6
  - a 33B 1
    - Solution a
  - b 33B 1
    - Solution b
  - c 33B 1
    - Solution c
- 34B Paper 3 1
  - Solution 34B
- 35D Paper 3 1
  - Solution 35D
- 36E Paper 3 1
  - Solution 36E
- 37D Paper 3 12
  - a 37D 6
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
    - iii a 1
      - Solution iii
  - b 37D 4
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
- 38A Paper 3 4
  - a 38A 1
    - Solution a
  - b 38A 1
    - Solution b
- 39A Paper 3 6
  - a 39A 1
    - Solution a
  - b 39A 1
    - Solution b
  - c 39A 1
    - Solution c
- 40C Paper 3 4
  - a 40C 1
    - Solution a
  - b 40C 1
    - Solution b

1I (Number Theory)

Articles: 1

Solution

2H (Topics in Analysis)

Articles: 1

Solution

3G (Coding and Cryptography)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

4H (Automata and Formal Languages)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

5J (Statistical Modelling)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

6C (Mathematical Biology)

Articles: 1

Solution

7A (Further Complex Methods)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

8E (Classical Dynamics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

9B (Cosmology)

Articles: 1

Solution

10D (Quantum Information and Computation)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

11I (Number Theory)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

12H (Automata and Formal Languages)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

13C (Mathematical Biology)

Articles: 14

a

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

14B (Cosmology)

Articles: 1

Solution

15D (Quantum Information and Computation)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

16I (Logic and Set Theory)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

17G (Graph Theory)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

18F (Galois Theory)

Articles: 1

Solution

19I (Representation Theory)

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

20F (Algebraic Topology)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

21H (Linear Analysis)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

22H (Analysis of Functions)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

23F (Riemann Surfaces)

Articles: 1

Solution

24F (Algebraic Geometry)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

25H (Differential Geometry)

Articles: 10

a

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

26K (Probability and Measure)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

27K (Applied Probability)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

28J (Principles of Statistics)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

29K (Stochastic Financial Models)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

30A (Asymptotic Methods)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

31E (Dynamical Systems)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

32C (Integrable Systems)

Articles: 13

a

Articles: 1

Solution

n

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

33B (Principles of Quantum Mechanics)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

34B (Applications of Quantum Mechanics)

Articles: 1

Solution

35D (Statistical Physics)

Articles: 1

Solution

36E (Electrodynamics)

Articles: 1

Solution

37D (General Relativity)

Articles: 12

a

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

38A (Fluid Dynamics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

39A (Waves)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

40C (Numerical Analysis)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

 Ancestors (8)