Past exam of the mathematics course of the University of Cambridge / 2010 / ii / Paper 4

www.maths.cam.ac.uk/undergrad/pastpapers/files/2010/PaperII_4.pdf

Table of contents
- 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

1G (Number Theory)

Solution

2F (Topics in Analysis)

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

11G (Number Theory)

Solution

12F (Geometry of Group Actions)

Solution

13J (Statistical Modelling)

Solution

14D (Dynamical Systems)

Solution

15D (Classical Dynamics)

Solution

16G (Logic and Set Theory)

Solution

17F (Graph Theory)

Solution

18H (Galois Theory)

i

Solution

ii

Solution

19F (Representation Theory)

Solution

20G (Number Fields)

Solution

21H (Algebraic Topology)

Solution

22H (Linear Analysis)

Solution

23G (Algebraic Geometry)

i

Solution

ii

Solution

iii

Solution

iv

Solution

24H (Differential Geometry)

i

Solution

ii

Solution

iii

Solution

25I (Probability and Measure)

Solution

26I (Applied Probability)

a

iii

Solution

b

Solution

c

Solution

27J (Principles of Statistics)

Solution

28J (Optimization and Control)

i

Solution

ii

Solution

iii

Solution

29I (Stochastic Financial Models)

Solution

30E (Partial Differential Equations)

Solution

31C (Asymptotic Methods)

a

Solution

b

Solution

c

Solution

32C (Principles of Quantum Mechanics)

Solution

33B (Applications of Quantum Mechanics)

Solution

34C (Statistical Physics)

i

Solution

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