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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
11 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. 2 336 downloads so far.
Last downloaded on: 18-11-2017 07:37 AM
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12 Group Actions Gives the definition, some interesting examples and exercises. Good way to master group actions, as students learn only the left/right and conjugacy actions in a typical algebra course.
B.Sc./M.Sc 1,2 298 downloads so far.
Last downloaded on: 16-11-2017 11:13 PM
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13 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 1,2 291 downloads so far.
Last downloaded on: 20-11-2017 11:55 AM
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14 Limit Inferior and Limit Superior A thorough treatment of limsup and liminf. This topic is a source of concern for many students.
B.Sc 1,2 275 downloads so far.
Last downloaded on: 16-11-2017 11:14 PM
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15 Cardinality and Countability A quick review of cardinality, countability and uncountability via problems. Readers are asked to refer to Munkres for details. Hints are given to some where our proofs are different from those in Munkres. Some explicit bijections are given so as to train a student in the art of setting up such functions.
1st/2nd year B.Sc O,1 266 downloads so far.
Last downloaded on: 16-11-2017 11:15 PM
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16 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 255 downloads so far.
Last downloaded on: 16-11-2017 11:15 PM
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17 Problems in Algebraic Topology Assignments in a first course in algebraic topology. A good set of exercises to face your pre-Ph.D.exams.
2nd year M.Sc. 241 downloads so far.
Last downloaded on: 16-11-2017 11:16 PM
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18 Complex Analysis: Handout-3 (Cauchy-Riemann Equations) Cauchy-Riemann equations
it also brings out the `geometric' meaning of C-R equations. A must read for students who like geometry. Final 241 downloads so far.
Last downloaded on: 16-11-2017 11:16 PM
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19 Simple and Direct Proofs of Some Results in the Theory of Compact Spaces Simple and direct proofs of some results in the theory of compact spaces.
Final year B.Sc, M.Sc 1,2 234 downloads so far.
Last downloaded on: 16-11-2017 11:17 PM
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20 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. 232 downloads so far.
Last downloaded on: 16-11-2017 11:17 PM
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