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

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

Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2005/PaperII_1.pdf

1H (Number Theory)

Solution

2F (Topics in Analysis)

Solution

3G (Geometry of Group Actions)

Solution

4J (Coding and Cryptography)

Solution

5I (Statistical Modelling)

Solution

6E (Mathematical Biology)

a

Solution

b

Solution

7B (Dynamical Systems)

Solution

8A (Further Complex Methods)

Solution

9C (Classical Dynamics)

Solution

10D (Cosmology)

a

Solution

b

Solution

c

Solution

11F (Topics in Analysis)

Solution

12G (Geometry of Group Actions)

Solution

13I (Statistical Modelling)

Solution

14B (Dynamical Systems)

Solution

15C (Classical Dynamics)

i

Solution

ii

Solution

16F (Logic and Set Theory)

Solution

17F (Graph Theory)

Solution

18G (Galois Theory)

Solution

19G (Representation Theory)

i

Solution

ii

Solution

iii

Solution

20G (Number Fields)

Solution

21H (Algebraic Topology)

i

Solution

ii

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

27I (Principles of Statistics)

Solution

28J (Stochastic Financial Models)

Solution

29C (Partial Differential Equations)

Solution

30A (Asymptotic Methods)

Solution

31D (Integrable Systems)

a

Solution

b

Solution

c

Solution

32D (Principles of Quantum Mechanics)

Solution

33B (Applications of Quantum Mechanics)

Solution

34B (Electrodynamics)

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