Past exam of the mathematics course of the University of Cambridge / 2010 / ii

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

Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2010/PaperII_1.pdf

1G (Number Theory)

i

Solution

ii

Solution

2F (Topics in Analysis)

i

Solution

ii

Solution

3F (Geometry of Group Actions)

Solution

4H (Coding and Cryptography)

Solution

5J (Statistical Modelling)

Solution

6A (Mathematical Biology)

Solution

7D (Dynamical Systems)

Solution

8E (Further Complex Methods)

Solution

9D (Classical Dynamics)

Solution

10D (Cosmology)

Solution

11F (Geometry of Group Actions)

Solution

12H (Coding and Cryptography)

Solution

13J (Statistical Modelling)

Solution

14E (Further Complex Methods)

i

Solution

ii

Solution

iii

Solution

iv

Solution

15D (Cosmology)

Solution

16G (Logic and Set Theory)

Solution

17F (Graph Theory)

a

Solution

b

i

Solution

ii

Solution

iii

Solution

iv

Solution

18H (Galois Theory)

i

Solution

ii

Solution

iii

Solution

19F (Representation Theory)

i

Solution

ii

Solution

20G (Number Fields)

Solution

21H (Algebraic Topology)

Solution

22H (Linear Analysis)

Solution

23G (Riemann Surfaces)

Solution

24G (Algebraic Geometry)

i

Solution

ii

Solution

iii

Solution

25H (Differential Geometry)

i

Solution

ii

Solution

iii

Solution

26I (Probability and Measure)

Solution

27I (Applied Probability)

a

Solution

b

Solution

c

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