- This section contains general information about the course.
31 July - 6 AugustWeek 1
"A theory is an idealized approximation to the reality."
7 August - 13 AugustWeek 2
Sets and Relations
Books to look through:
1. Theory of Justice by John Rawls 2. Social Choice and Individual Values by Kenneth Arrow
Theme : Geometry, Space and Time
14 August - 20 AugustWeek 3
Structures and Evolution of Number Systems
- Cannot see the wood for the trees.
21 August - 27 AugustWeek 4
Are you aware of ABACUS? Look out for Chinese remainder theorem. Do you see the role of primes in system of congruences?
- Do you agree that, "There is no compulsive relationship between linearity and time invariance." ? What do we mean by domain and range operations while talking about functions? In connection with Digital Signal Processing, is delay a domain or a range operation? Can you qualify linearity as a behavior of the range?
- Explore : "Integral domain can be embedded in a field of fractions." in context of the Z-transform.
28 August - 3 SeptemberWeek 5
- Symmetry is something we do with an object and still some relationships between parts of object do not change.
Two interesting software packages for ALGEBRA
- "It is like, different concrete objects having the same inner souls."
4 September - 10 SeptemberWeek 6
11 September - 17 SeptemberWeek 7
The term social contract describes a broad class of philosophical theories whose subject is the implied agreements by which people form nations and maintain a social order. In laymen's terms this means that the people give up some rights to a government in order to receive social order. - Wikipedia
18 September - 24 SeptemberWeek 8
Theories are there because of limitations, primarily to overcome limitations.
25 September - 1 OctoberWeek 9
2 October - 8 OctoberWeek 10
- A representation of a group G is a homomorphism from G to GL(V)...
For a finite group G, there is a finite number of 'atomic' smallest possible matrix representations from which all other matrix representations are 'built'.
9 October - 15 OctoberWeek 11
- Theorem: Let G be a `finite' group. P:G->GL(V) be a representation, where V is a vector space then, If V1 is an invariant subspace of the group then we can always find V2 which is also an invariant subspace of the group, and V1+V2(direct sum) is the whole vector space.
• Joseph Fourier 1768-1830
Elena Prestine: Applied Harmonic Analysis : Models of the Real World
• F.G. Frobenius 1849-1917
Charles Curtis: Pioneers of Representation Theory
16 October - 22 OctoberWeek 12
23 October - 29 OctoberWeek 13
30 October - 5 NovemberWeek 14
6 November - 12 NovemberWeek 15