OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4

www.maths.cam.ac.uk/undergrad/pastpapers/files/2019/paperii_4_2019.pdf

Table of contents 244
- 1I Paper 4 1
  - Solution 1I
- 2H Paper 4 1
  - Solution 2H
- 3G Paper 4 4
  - a 3G 1
    - Solution a
  - b 3G 1
    - Solution b
- 4H Paper 4 9
  - a 4H 6
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
    - iii a 1
      - Solution iii
  - b 4H 1
    - Solution b
- 5J Paper 4 1
  - Solution 5J
- 6C Paper 4 4
  - a 6C 1
    - Solution a
  - b 6C 1
    - Solution b
- 7A Paper 4 6
  - a 7A 1
    - Solution a
  - b 7A 1
    - Solution b
  - c 7A 1
    - Solution c
- 8E Paper 4 6
  - a 8E 1
    - Solution a
  - b 8E 1
    - Solution b
  - c 8E 1
    - Solution c
- 9B Paper 4 1
  - Solution 9B
- 10D Paper 4 4
  - a 10D 1
    - Solution a
  - b 10D 1
    - Solution b
- 11I Paper 4 8
  - a 11I 1
    - Solution a
  - b 11I 1
    - Solution b
  - c 11I 1
    - Solution c
  - d 11I 1
    - Solution d
- 12H Paper 4 4
  - a 12H 1
    - Solution a
  - b 12H 1
    - Solution b
- 13J Paper 4 8
  - a 13J 1
    - Solution a
  - b 13J 1
    - Solution b
  - c 13J 1
    - Solution c
  - d 13J 1
    - Solution d
- 14C Paper 4 8
  - a 14C 1
    - Solution a
  - b 14C 1
    - Solution b
  - c 14C 1
    - Solution c
  - d 14C 1
    - Solution d
- 15E Paper 4 4
  - a 15E 1
    - Solution a
  - b 15E 1
    - Solution b
- 16I Paper 4 1
  - Solution 16I
- 17G Paper 4 1
  - Solution 17G
- 18F Paper 4 4
  - i 18F 1
    - Solution i
  - ii 18F 1
    - Solution ii
- 19I Paper 4 11
  - a 19I 1
    - Solution a
  - b 19I 1
    - Solution b
  - c 19I 6
    - i c 1
      - Solution i
    - ii c 1
      - Solution ii
    - iii c 1
      - Solution iii
- 20G Paper 4 4
  - a 20G 1
    - Solution a
  - b 20G 1
    - Solution b
- 21F Paper 4 4
  - i 21F 1
    - Solution i
  - ii 21F 1
    - Solution ii
- 22H Paper 4 6
  - a 22H 1
    - Solution a
  - b 22H 1
    - Solution b
  - c 22H 1
    - Solution c
- 23H Paper 4 10
  - a 23H 1
    - Solution a
  - b 23H 1
    - Solution b
  - c 23H 1
    - Solution c
  - d 23H 1
    - Solution d
  - e 23H 1
    - Solution e
- 24F Paper 4 16
  - a 24F 6
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
    - iii a 1
      - Solution iii
  - b 24F 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 25H Paper 4 6
  - a 25H 1
    - Solution a
  - b 25H 1
    - Solution b
  - c 25H 1
    - Solution c
- 26K Paper 4 10
  - a 26K 4
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
  - b 26K 4
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
- 27K Paper 4 6
  - a 27K 1
    - Solution a
  - b 27K 1
    - Solution b
  - c 27K 1
    - Solution c
- 28J Paper 4 11
  - a 28J 1
    - Solution a
  - b 28J 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 29K Paper 4 8
  - a 29K 1
    - Solution a
  - b 29K 1
    - Solution b
  - c 29K 1
    - Solution c
  - d 29K 1
    - Solution d
- 30A Paper 4 4
  - a 30A 1
    - Solution a
  - b 30A 1
    - Solution b
- 31E Paper 4 1
  - Solution 31E
- 32B Paper 4 1
  - Solution 32B
- 33B Paper 4 4
  - a 33B 1
    - Solution a
  - b 33B 1
    - Solution b
- 34D Paper 4 4
  - i 34D 1
    - Solution i
  - ii 34D 1
    - Solution ii
- 35E Paper 4 1
  - Solution 35E
- 36D Paper 4 4
  - a 36D 1
    - Solution a
  - b 36D 1
    - Solution b
- 37A Paper 4 9
  - a 37A 1
    - Solution a
  - b 37A 4
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
  - c 37A 1
    - Solution c
- 38A Paper 4 6
  - a 38A 1
    - Solution a
  - b 38A 1
    - Solution b
  - c 38A 1
    - Solution c
- 39C Paper 4 4
  - a 39C 1
    - Solution a
  - b 39C 1
    - Solution b

1I (Number Theory)

Articles: 1

Solution

2H (Topics in Analysis)

Articles: 1

Solution

3G (Coding and Cryptography)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

4H (Automata and Formal Languages)

Articles: 9

a

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

b

Articles: 1

Solution

5J (Statistical Modelling)

Articles: 1

Solution

6C (Mathematical Biology)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

7A (Further Complex Methods)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

8E (Classical Dynamics)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

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: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

12H (Topics in Analysis)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

13J (Statistical Modelling)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

14C (Mathematical Biology)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

15E (Classical Dynamics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

16I (Logic and Set Theory)

Articles: 1

Solution

17G (Graph Theory)

Articles: 1

Solution

18F (Galois Theory)

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

19I (Representation 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

20G (Number Fields)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

21F (Algebraic Topology)

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

22H (Linear Analysis)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

23H (Analysis of Functions)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

24F (Algebraic Geometry)

Articles: 16

a

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

b

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

25H (Differential Geometry)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

26K (Probability and Measure)

Articles: 10

a

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

27K (Applied Probability R)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

28J (Principles of Statistics)

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

29K (Stochastic Financial Models)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

30A (Asymptotic Methods)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

31E (Dynamical Systems)

Articles: 1

Solution

32B (Principles of Quantum Mechanics)

Articles: 1

Solution

33B (Applications of Quantum Mechanics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

34D (Statistical Physics)

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

35E (Electrodynamics)

Articles: 1

Solution

36D (General Relativity)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

37A (Fluid Dynamics)

Articles: 9

a

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

c

Articles: 1

Solution

38A (Waves)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

39C (Numerical Analysis)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

 Ancestors (8)