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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 1537 downloads so far.
Last downloaded on: 19-12-2018 01:03 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 1302 downloads so far.
Last downloaded on: 19-12-2018 02:02 AM
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3 The Role of LUB Axiom in Real Analysis Brings out the role of LUB property (order completeness) of $\R$. Gives a unified view of many of the crucial results in a first course in real analysis
likely to be best for a review of basic real analysis. B.Sc. 948 downloads so far.
Last downloaded on: 19-12-2018 05:04 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 1,2 904 downloads so far.
Last downloaded on: 19-12-2018 05:15 PM
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5 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. 2 841 downloads so far.
Last downloaded on: 15-12-2018 07:05 PM
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6 Complex Analysis: Handout-2 (Results on Power Series) Results on power series
797 downloads so far.
Last downloaded on: 15-12-2018 09:16 PM
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7 Arithmetic-Geometric Mean Inequality Proof by Induction and Calculus A proof of the classic inequality on AM-GM using calculus and induction.
2nd /final year BSc O 765 downloads so far.
Last downloaded on: 19-12-2018 07:09 AM
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8 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. 2 739 downloads so far.
Last downloaded on: 18-12-2018 02:34 AM
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9 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. 2 705 downloads so far.
Last downloaded on: 15-12-2018 07:06 PM
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10 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,1 704 downloads so far.
Last downloaded on: 16-12-2018 05:32 AM
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