Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 4

www.maths.cam.ac.uk/undergrad/pastpapers/files/2005/PaperII_4.pdf

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

1H (Number Theory)

i

Solution

ii

Solution

2F (Topics in Analysis)

i

Solution

ii

Solution

3G (Geometry of Group Actions)

Solution

4J (Coding and Cryptography)

Solution

5I (Statistical Modelling)

Solution

6E (Mathematical Biology)

a

i

Solution

ii

Solution

b

iii

Solution

c

Solution

7B (Dynamical Systems)

Solution

8A (Further Complex Methods)

Solution

9C (Classical Dynamics)

i

Solution

ii

Solution

10D (Cosmology)

a

Solution

b

Solution

c

Solution

11H (Number Theory)

a

Solution

b

Solution

12G (Geometry of Group Actions)

Solution

13I (Statistical Modelling)

i

Solution

ii

Solution

iii

Solution

14A (Further Complex Methods)

Solution

15D (Cosmology)

Solution

16F (Logic and Set Theory)

Solution

17F (Graph Theory)

Solution

18G (Galois Theory)

i

Solution

ii

Solution

19G (Representation Theory)

i

Solution

ii

Solution

20G (Number Fields)

Solution

21H (Algebraic Topology)

Solution

22F (Linear Analysis)

Solution

23H (Riemann Surfaces)

Solution

24H (Differential Geometry)

i

Solution

ii

Solution

iii

Solution

25J (Probability and Measure)

Solution

26I (Applied Probability)

a

Solution

b

Solution

c

Solution

27I (Principles of Statistics)

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