Past exam of the mathematics course of the University of Cambridge / 2008 / ii

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

Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2008/PaperII_1.pdf

1H (Number Theory)

Solution

2F (Topics in Analysis)

Solution

3G (Geometry of Group Actions)

Solution

4G (Coding and Cryptography)

Solution

5J (Statistical Modelling)

Solution

6B (Mathematical Biology)

Solution

7A (Dynamical Systems)

i

Solution

8C (Further Complex Methods)

Solution

9A (Classical Dynamics)

Solution

10E (Cosmology)

Solution

11G (Geometry of Group Actions)

Solution

12G (Coding and Cryptography)

Solution

13J (Statistical Modelling)

Solution

14C (Further Complex Methods)

Solution

15E (Cosmology)

i

Solution

ii

Solution

16G (Logic and Set Theory)

Solution

17F (Graph Theory)

i

Solution

ii

Solution

iii

Solution

18H (Galois Theory)

i

Solution

iii

Solution

19G (Representation Theory)

Solution

20G (Number Fields)

a

Solution

b

Solution

21F (Algebraic Topology)

i

Solution

ii

Solution

iii

Solution

22F (Linear Analysis)

Solution

23H (Riemann Surfaces)

Solution

24H (Differential Geometry)

a

Solution

b

Solution

c

Solution

25J (Probability and Measure)

Solution

26I (Applied Probability)

i

Solution

ii

Solution

iii

Solution

iv

Solution

v

Solution

vi

Solution

27I (Principles of Statistics)

Solution

28J (Stochastic Financial Models)

a

Solution

b

Solution

c

Solution

d

Solution

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