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Download MTTS Expository Articles

The articles are prepared by Prof. S Kumaresan, the MTTS Programme Director and usually gets distributed to the MTTS/ Mini MTTS/ PTMT participants.

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Sl No Title Description Targeted Audience MTTS Level Downloads
1 Summary of Real Analysis Batch B (200708) Daily sheet of a course in real analysis up to continuity. This is perhaps what we do in Level O of MTTS camps.
B.Sc O,1 1348 downloads so far.
Last downloaded on: 14-08-2018 11:46 AM
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2 Outline of Group Theory A complete course (with a lot of examples and exercises with just enough hints) in the theory groups leading up to Sylow's theorems.
B.Sc 1 1121 downloads so far.
Last downloaded on: 14-08-2018 07:12 AM
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3 A Review of Differential Calculus The article reviews several variable calculus with emphasis on concepts, theorems and their geometric contents. It gives a lot of examples which will wean the reader away from Jacobian computations!
M.Sc. 2 716 downloads so far.
Last downloaded on: 13-08-2018 05:19 PM
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4 Structure of Linear Maps Gives a motivated and clutter free proofs of many theorems about the structure of linear maps. Proves Jordan canonical form, spectral theorems for self-adjoint,normal, unitary and orthogonal maps, singular value decompositions, triangular forms.
Final year B.Sc, M.Sc 1,2 693 downloads so far.
Last downloaded on: 14-08-2018 10:02 AM
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5 Complex Analysis: Handout-2 (Results on Power Series) Results on power series
610 downloads so far.
Last downloaded on: 13-08-2018 05:19 PM
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6 Outline of a Course in Field Theory A more thorough treatment of Galois theory with good set of exercises. Plan to write it up as a small book.
M.Sc. 2 606 downloads so far.
Last downloaded on: 13-08-2018 05:19 PM
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7 Completeness of R Gives perhaps the simplest proof of Cauchy completeness of $\R$. Does not use anything other than the definitions of convergence and Cauchy sequences and LUB property of $\R$. This needs wider publicity. Included in out book on Real analsyis.
2nd year B.Sc O,1 589 downloads so far.
Last downloaded on: 13-08-2018 05:19 PM
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8 Functional Analysis (2011) Summary of Lectures An outline of a course in functional analysis given at University of Hyderabad. Contains a lot of concrete examples, spaces of functions and good exercises. Prepares the students for future use of functional analysis in other parts of mathematics. Goes up to the spectral theom for compact self-adjoint operators, Riesz-Schauder theory of compact operators, their applications to integral equations.
M.Sc. 2 588 downloads so far.
Last downloaded on: 13-08-2018 05:19 PM
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9 An Outline of Real Analysis An outline of real analysis ; one of the trio (2008, 2010, 2012). Our book ?A Basic course in Real Analysis? is based on these.
581 downloads so far.
Last downloaded on: 14-08-2018 09:10 AM
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10 Exercises on Inverse images Has a good set of exercises which are meaningful in mathematics to make the studenst deal with the concept confidently. This is a problem area all over.
O O 569 downloads so far.
Last downloaded on: 14-08-2018 01:53 AM
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