Past exam of the mathematics course of the University of Cambridge / 2006 / ii

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

Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2006/PaperII_1.pdf

1H (Number Theory)

Solution

2G (Topics in Analysis)

Solution

3F (Geometry and Groups)

Solution

4G (Coding and Cryptography)

Solution

5I (Statistical Modelling)

6B (Mathematical Biology)

Solution

7E (Dynamical Systems)

Solution

8E (Further Complex Methods)

Solution

9C (Classical Dynamics)

Solution

10D (Cosmology)

a

Solution

b

Solution

11G (Topics in Analysis)

i

Solution

ii

Solution

12F (Geometry and Groups)

Solution

13I (Statistical Modelling)

Solution

14E (Dynamical Systems)

a

Solution

b

Solution

15C (Classical Dynamics)

a

Solution

b

Solution

c

Solution

16H (Logic and Set Theory)

Solution

17F (Graph Theory)

Solution

18H (Galois Theory)

Solution

19F (Representation Theory)

a

Solution

b

i

Solution

ii

Solution

iii

Solution

20G (Number Fields)

Solution

21H (Algebraic Topology)

Solution

22G (Linear Analysis)

Solution

23F (Riemann Surfaces)

Solution

24H (Differential Geometry)

a

Solution

b

Solution

c

Solution

25J (Probability and Measure)

a

Solution

b

Solution

c

Solution

d

Solution

26J (Applied Probability)

a

Solution

b

Solution

27J (Principles of Statistics)

a

Solution

b

c

Solution

28I (Stochastic Financial Models)

a

Solution

b

Solution

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