Past exam of the mathematics course of the University of Cambridge / 2007 / ii

Table of contents
- Paper 1 ii
  - 1F Paper 1
    - Solution 1F
  - 2F Paper 1
    - i 2F
      - Solution i
    - ii 2F
      - Solution ii
    - iii 2F
      - Solution iii
  - 3G Paper 1
    - Solution 3G
  - 4G Paper 1
    - Solution 4G
  - 5I Paper 1
    - Solution 5I
  - 6B Paper 1
    - Solution 6B
  - 7E Paper 1
    - Solution 7E
  - 8B Paper 1
    - Solution 8B
  - 9C Paper 1
    - Solution 9C
  - 10A Paper 1
    - Solution 10A
  - 11G Paper 1
    - Solution 11G
  - 12G Paper 1
    - Solution 12G
  - 13I Paper 1
    - Solution 13I
  - 14B Paper 1
    - i 14B
      - Solution i
    - ii 14B
      - Solution ii
    - iii 14B
      - Solution iii
  - 15A Paper 1
    - Solution 15A
  - 16G Paper 1
    - Solution 16G
  - 17H Paper 1
    - Solution 17H
  - 18F Paper 1
    - Solution 18F
  - 19H Paper 1
    - Solution 19H
  - 20H Paper 1
    - a 20H
      - Solution a
    - b 20H
      - Solution b
    - c 20H
      - Solution c
  - 21H Paper 1
    - i 21H
      - Solution i
    - ii 21H
      - Solution ii
  - 22G Paper 1
    - Solution 22G
  - 23F Paper 1
    - Solution 23F
  - 24H Paper 1
    - i 24H
      - Solution i
    - ii 24H
      - Solution ii
    - iii 24H
      - Solution iii
  - 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
    - c 26J
      - Solution c
    - d 26J
      - Solution d
    - e 26J
      - Solution e
  - 27I Paper 1
    - Solution 27I
  - 28J Paper 1
    - i 28J
      - Solution i
    - ii 28J
      - Solution ii
    - iii 28J
      - Solution iii
  - 29A Paper 1
    - i 29A
      - Solution i
    - ii 29A
      - Solution ii
    - iii 29A
      - Solution iii
    - iv 29A
      - Solution iv
  - 30B Paper 1
    - Solution 30B
  - 31E Paper 1
    - i 31E
      - Solution i
    - ii 31E
      - Solution ii
    - iii 31E
      - Solution iii
  - 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
- Paper 2 ii
  - 1F Paper 2
    - Solution 1F
  - 2F Paper 2
    - Solution 2F
  - 3G Paper 2
    - Solution 3G
  - 4G Paper 2
    - Solution 4G
  - 5I Paper 2
    - Solution 5I
  - 6B Paper 2
    - Solution 6B
  - 7E Paper 2
    - Solution 7E
  - 8B Paper 2
    - Solution 8B
  - 9C Paper 2
    - Solution 9C
  - 10A Paper 2
    - Solution 10A
  - 11G Paper 2
    - Solution 11G
  - 12F Paper 2
    - i 12F
      - Solution i
    - ii 12F
      - Solution ii
    - iii 12F
      - Solution iii
  - 13B Paper 2
    - Solution 13B
  - 14B Paper 2
    - Solution 14B
  - 15C Paper 2
    - a 15C
      - Solution a
    - b 15C
      - Solution b
    - c 15C
      - Solution c
  - 16G Paper 2
    - Solution 16G
  - 17H Paper 2
    - Solution 17H
  - 18F Paper 2
    - Solution 18F
  - 19H Paper 2
    - Solution 19H
  - 20H Paper 2
    - a 20H
      - Solution a
    - b 20H
      - Solution b
    - c 20H
      - Solution c
  - 21H Paper 2
    - Solution 21H
  - 22G Paper 2
    - Solution 22G
  - 23F Paper 2
    - Solution 23F
  - 24H Paper 2
    - i 24H
      - Solution i
    - ii 24H
      - Solution ii
    - iii 24H
      - Solution iii
  - 25J Paper 2
    - a 25J
      - Solution a
    - b 25J
      - Solution b
    - c 25J
      - Solution c
    - d 25J
      - Solution d
    - e 25J
      - Solution e
  - 26J Paper 2
    - a 26J
      - Solution a
    - b 26J
      - Solution b
    - c 26J
      - Solution c
    - d 26J
      - Solution d
    - e 26J
      - Solution e
    - f 26J
      - Solution f
  - 27I Paper 2
    - i 27I
      - Solution i
    - ii 27I
      - Solution ii
  - 28J Paper 2
    - Solution 28J
  - 29I Paper 2
    - Solution 29I
  - 30A Paper 2
    - ii 30A
      - Solution ii
  - 31E Paper 2
    - Solution 31E
  - 32D Paper 2
    - Solution 32D
  - 33A Paper 2
    - Solution 33A
  - 34D Paper 2
    - Solution 34D
  - 35A Paper 2
    - Solution 35A
  - 36B Paper 2
    - i 36B
      - Solution i
    - ii 36B
      - Solution ii
    - iii 36B
      - Solution iii
  - 37C Paper 2
    - Solution 37C
  - 38C Paper 2
    - a 38C
      - Solution a
    - b 38C
      - Solution b
- Paper 3 ii
  - 1F Paper 3
    - Solution 1F
  - 2F Paper 3
    - Solution 2F
  - 3G Paper 3
    - Solution 3G
  - 4G Paper 3
    - Solution 4G
  - 5I Paper 3
    - Solution 5I
  - 6B Paper 3
    - Solution 6B
  - 7E Paper 3
    - Solution 7E
  - 8B Paper 3
    - i 8B
      - Solution i
    - ii 8B
      - Solution ii
    - iii 8B
      - Solution iii
  - 9C Paper 3
    - Solution 9C
  - 10A Paper 3
    - Solution 10A
  - 11F Paper 3
    - Solution 11F
  - 12F Paper 3
    - i 12F
      - Solution i
    - ii 12F
      - Solution ii
  - 13B Paper 3
    - i 13B
      - Solution i
    - ii 13B
      - Solution ii
    - iii 13B
      - Solution iii
    - iv 13B
      - Solution iv
  - 14E Paper 3
    - i 14E
      - Solution i
    - ii 14E
      - Solution ii
    - iii 14E
      - Solution iii
  - 15A Paper 3
    - Solution 15A
  - 16G Paper 3
    - Solution 16G
  - 17H Paper 3
    - Solution 17H
  - 18F Paper 3
    - i 18F
      - Solution i
    - ii 18F
      - Solution ii
  - 19H Paper 3
    - Solution 19H
  - 20H Paper 3
    - Solution 20H
  - 21G Paper 3
    - Solution 21G
  - 22F Paper 3
    - i 22F
      - Solution i
    - ii 22F
      - Solution ii
  - 23H Paper 3
    - i 23H
      - Solution i
    - ii 23H
      - Solution ii
    - iii 23H
      - Solution iii
  - 24J Paper 3
    - a 24J
      - Solution a
    - b 24J
      - Solution b
    - c 24J
      - Solution c
  - 25J Paper 3
    - a 25J
      - Solution a
    - b 25J
      - Solution b
    - c 25J
      - Solution c
    - d 25J
      - Solution d
    - e 25J
      - Solution e
  - 26I Paper 3
    - i 26I
      - Solution i
    - ii 26I
      - Solution ii
  - 27J Paper 3
    - i 27J
      - Solution i
    - ii 27J
      - Solution ii
    - iii 27J
      - Solution iii
    - iv 27J
      - Solution iv
  - 28I Paper 3
    - Solution 28I
  - 29A Paper 3
    - Solution 29A
  - 30B Paper 3
    - Solution 30B
  - 31E Paper 3
    - Solution 31E
  - 32D Paper 3
    - Solution 32D
  - 33A Paper 3
    - Solution 33A
  - 34D Paper 3
    - Solution 34D
  - 35E Paper 3
    - Solution 35E
  - 36B Paper 3
    - i 36B
      - Solution i
    - ii 36B
      - Solution ii
  - 37C Paper 3
    - Solution 37C
  - 38C Paper 3
    - a 38C
      - Solution a
    - b 38C
      - Solution b
- Paper 4 ii
  - 1F Paper 4
    - Solution 1F
  - 2F Paper 4
    - Solution 2F
  - 3G Paper 4
    - Solution 3G
  - 4G Paper 4
    - Solution 4G
  - 5I Paper 4
    - Solution 5I
  - 6B Paper 4
    - Solution 6B
  - 7E Paper 4
    - i 7E
      - Solution i
    - ii 7E
      - Solution ii
    - iii 7E
      - Solution iii
  - 8B Paper 4
    - i 8B
      - Solution i
    - ii 8B
      - Solution ii
  - 9C Paper 4
    - a 9C
      - Solution a
    - b 9C
      - Solution b
  - 10A Paper 4
    - Solution 10A
  - 11F Paper 4
    - i 11F
      - Solution i
    - ii 11F
      - Solution ii
  - 12G Paper 4
    - Solution 12G
  - 13I Paper 4
    - Solution 13I
  - 14E Paper 4
    - i 14E
      - Solution i
    - ii 14E
      - Solution ii
  - 15C Paper 4
    - Solution 15C
  - 16G Paper 4
    - Solution 16G
  - 17H Paper 4
    - Solution 17H
  - 18F Paper 4
    - Solution 18F
  - 19H Paper 4
    - Solution 19H
  - 20H Paper 4
    - Solution 20H
  - 21H Paper 4
    - Solution 21H
  - 22G Paper 4
    - Solution 22G
  - 23F Paper 4
    - Solution 23F
  - 24H Paper 4
    - i 24H
      - Solution i
    - ii 24H
      - Solution ii
  - 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
    - c 26J
      - Solution c
    - d 26J
      - Solution d
    - e 26J
      - Solution e
  - 27I Paper 4
    - Solution 27I
  - 28J Paper 4
    - Solution 28J
  - 29I Paper 4
    - Solution 29I
  - 30A Paper 4
    - Solution 30A
  - 31B Paper 4
    - Solution 31B
  - 32D Paper 4
    - Solution 32D
  - 33A Paper 4
    - Solution 33A
  - 34D Paper 4
    - Solution 34D
  - 35E Paper 4
    - Solution 35E
  - 36A Paper 4
    - Solution 36A
  - 37B Paper 4
    - i 37B
      - Solution i
    - ii 37B
      - Solution ii
    - iii 37B
      - Solution iii
    - iv 37B
      - Solution iv
  - 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/2007/PaperII_1.pdf

1F (Number Theory)

Solution

2F (Topics in Analysis)

i

Solution

ii

Solution

iii

Solution

3G (Geometry of Group Actions)

Solution

4G (Coding and Cryptography)

Solution

5I (Statistical Modelling)

Solution

6B (Mathematical Biology)

Solution

7E (Dynamical Systems)

Solution

8B (Further Complex Methods)

Solution

9C (Classical Dynamics)

Solution

10A (Cosmology)

Solution

11G (Coding and Cryptography)

Solution

12G (Geometry of Group Actions)

Solution

13I (Statistical Modelling)

Solution

14B (Further Complex Methods)

i

Solution

ii

Solution

iii

Solution

15A (Cosmology)

Solution

16G (Set Theory and Logic)

Solution

17H (Graph Theory)

Solution

18F (Galois Theory)

Solution

19H (Representation Theory)

Solution

20H (Number Fields)

a

Solution

b

Solution

c

Solution

21H (Algebraic Topology)

i

Solution

ii

Solution

22G (Linear Analysis)

Solution

23F (Riemann Surfaces)

Solution

24H (Differential Geometry)

i

Solution

ii

Solution

iii

Solution

25J (Probability and Measure)

a

Solution

b

Solution

c

Solution

d

Solution

26J (Applied Probability)

a

Solution

b

Solution

c

Solution

d

Solution

e

Solution

27I (Principles of Statistics)

Solution

28J (Stochastic Financial Models)

i

Solution

ii

Solution

iii

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