Weekly outline

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  This section contains general information about the course.

  • News/Announcements forum
  • LaTeX tutorial URL
  • Essays Folder
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  31 July - 6 August

  Week 1
  

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  Modeling
  "A theory is an idealized approximation to the reality."

  • Representational Measurement Theory URL
  • Philosophy of Mathematics URL
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  7 August - 13 August

  Week 2

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  Sets and Relations
  

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  • Assignment 1 File
  • Submission Format for assignment Page
  • Submit Assignment-1 Assignment (2.2)
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  • The Cathedral and the Bazaar by Eric Steven Raymond URL
  • The Tragedy of the Commons by Garrett Hardin URL
  • The Nature of the Firm by R. H. COASE URL
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    Books to look through:
    

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    1. Theory of Justice by John Rawls
    2. Social Choice and Individual Values by Kenneth Arrow

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    Theme : Geometry, Space and Time

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  • Critique of Pure reason(1781) - Immanuel Kant URL
  • The common sense of exact sciences(1886) - Clifford URL
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  14 August - 20 August

  Week 3

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  Structures and Evolution of Number Systems
  

  • Submit Assignment 2 Assignment (2.2)
  • Cannot see the wood for the trees.

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  • Bourbaki, who was(is) he(she)? URL
  • Every Integral Domain can be embedded in a field of fractions. URL
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  21 August - 27 August

  Week 4

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  • The Science of Scientific writing URL
  • I don't know Donald Knuth! URL
  • Aha, comics! Fun... URL
  • Tycho Brahe URL
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    Are you aware of ABACUS? Look out for Chinese remainder theorem. Do you see the role of primes in system of congruences?

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  • 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?
    

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  • Explore : "Integral domain can be embedded in a field of fractions." in context of the Z-transform.

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  28 August - 3 September

  Week 5

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  • Symmetry URL
  • Symmetry is something we do with an object and still some relationships between parts of object do not change.

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  • History of modern mathematics - D E Smith URL
  • Some of the group theory books in library Page
  • Arthur Cayley Page
  • Group Explorer URL
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    Two interesting software packages for ALGEBRA
    
  • GAP URL
  • AXIOM URL
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  • Isomorphism URL
  • "It is like, different concrete objects having the same inner souls."
    

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  • Joseph Fourier URL
  • Books on Fourier in DAIICT library Page
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  4 September - 10 September

  Week 6

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  • Vector Space URL
  • Paul R Halmos Page
  • Wallpaper groups Page
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  11 September - 17 September

  Week 7

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  • Assignment 3 File
  • Submit Assignment 3 Assignment (2.2)
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    Social Contract
    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
    

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  • "Friends, Romans, Countrymen.." -Mark Anthony Page
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  18 September - 24 September

  Week 8

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  • Assignment 4 File
  • Submit Assignment 4 Assignment (2.2)
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    Theories are there because of limitations, primarily to overcome limitations.
    

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  • Impossibility Theory Page
  • John D Barrow URL
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  25 September - 1 October

  Week 9
  

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  • Bertrand Russell URL
  • Self Reference Page
  • Hillary Putnam URL
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    "You could not have predicted the invention of a wheel."

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    Stone's Representation Theorem : (Existential)
    Every boolean algebra is isomorphic to the algebra of subsets of some set.
    

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  2 October - 8 October

  Week 10

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  • A representation of a group G is a homomorphism from G to GL(V)...
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    For a finite group G, there is a finite number of 'atomic' smallest possible matrix representations from which all other matrix representations are 'built'.
    

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  • Slide Ruler URL
  • Can one hear the shape of a drum? URL
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  9 October - 15 October

  Week 11

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  • 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.
    

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    • 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
    

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  16 October - 22 October

  Week 12

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  EXAM WEEK
  
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  23 October - 29 October

  Week 13

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  • Assignment 5 File
  • Submit Assignment 5 Assignment (2.2)
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    Leo Tolstoy
  • Gibbs Phenomena URL
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  30 October - 5 November

  Week 14

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  SEMESTER BREAK
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  6 November - 12 November

  Week 15

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  • On Being the Right Size - Haldane URL