Past exam of the mathematics course of the University of Cambridge / 2011 / ii / Paper 4

www.maths.cam.ac.uk/undergrad/pastpapers/files/2011/PaperII_4.pdf

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

1I (Number Theory)

i

Solution

ii

Solution

2F (Topics in Analysis)

a

Solution

b

i

Solution

ii

Solution

3G (Geometry and Groups)

Solution

4G (Coding and Cryptography)

Solution

5J (Statistical Modelling)

Solution

6B (Mathematical Biology)

Solution

7C (Dynamical Systems)

i

Solution

ii

Solution

8E (Further Complex Methods)

Solution

9C (Classical Dynamics)

i

Solution

ii

Solution

10E (Cosmology)

Solution

11I (Number Theory)

i

Solution

ii

Solution

12G (Geometry and Groups)

Solution

13J (Statistical Modelling)

Solution

14C (Dynamical Systems)

i

Solution

ii

Solution

15C (Classical Dynamics)

Solution

16H (Logic and Set Theory)

Solution

17F (Graph Theory)

i

Solution

ii

Solution

18H (Galois Theory)

i

Solution

ii

Solution

iii

Solution

iv

Solution

19I (Representation Theory)

i

Solution

ii

Solution

iii

Solution

20F (Number Fields)

i

Solution

ii

Solution

iii

Solution

21H (Algebraic Topology)

Solution

22G (Linear Analysis)

Solution

23H (Algebraic Geometry)

Solution

24I (Differential Geometry)

Solution

25K (Probability and Measure)

i

Solution

ii

Solution

iii

Solution

26J (Applied Probability)

i

Solution

ii

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