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Found total 224 results. Displaying results from 141 to 160.

 
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141
Plane Geometries

Give a pedestrian approach to the classical Euclidean, elliptical and hyperbolic geometries with a minimal (incomplete) set of axioms. Included in our book ``A Course in Geometry?.

Keywords :

B.Sc
MTTS Level :
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(Downloaded 612 times last on 15 March 2026, 10:55 am
142
An Example of a Prime Ideal

Gives a simple example of a prime ideal in the polynomial ring of two variables, namely the example of a parabola.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 710 times last on 15 March 2026, 08:03 am
143
A topological Proof of the Infinitutde of Primes

Topological proof of the infinitude of primes

Keywords :

included in the topology notes.
MTTS Level :
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(Downloaded 780 times last on 15 March 2026, 10:46 pm
144
Topics in Measure Theory

This hand-out deals with the notion of product measures, proved Fubini and Tonelli theorems, gives proofs of Radon-Nikodym theorem and a simple proof of a lemma needed in the study of complex measures.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1452 times last on 16 March 2026, 01:18 am
145
Proper Maps

Gives all the basic results of proper maps within contexts. An important concept in modern topology but rarely found in textbooks on topology.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 2148 times last on 15 March 2026, 06:08 pm
146
Maps into the Punctured Plane

It takes an analytic approach to the problem of determining the fundamental group of the circle by looking at homotopy classes of maps into $C^*$, the punctured plane.

Keywords :

M.Sc./Ph.D
MTTS Level :
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(Downloaded 1030 times last on 15 March 2026, 11:08 pm
147
Examples of Cosets and Quotient Groups

Lists examples of quotient groups for practice. Details may be found in ``Outline of Group Theory?

Keywords :

B.Sc
MTTS Level :
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(Downloaded 1342 times last on 15 March 2026, 11:52 am
148
How to work with quotient rings?

It teaches you how to work with quotient rings.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 3694 times last on 16 March 2026, 04:07 am
149
Quotient Topology

Will make you comfortable with the notion of quotient spaces with lots of examples with rigorous proofs.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 6573 times last on 16 March 2026, 11:00 am
150
Raleigh Quotients and Spectral Theorems

Uses the method of Raleigh quotients to deduce the spectral theorem for symmetric maps and an orthogonal maps.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 603 times last on 15 March 2026, 10:38 am
151
Rank Theorem

Rank theorem (of differential calculus) is proved here.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1571 times last on 16 March 2026, 07:03 am
152
Summary of Real Analysis — Batch B (2007–08)

Daily sheet of a course in real analysis up to continuity. This is perhaps what we do in Level O of MTTS camps.

Keywords :

B.Sc
MTTS Level :
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(Downloaded 2864 times last on 15 March 2026, 06:27 am
153
Summary of Real Analysis — Semester 1 (2008)

Actual summary of the course as it unfolded, a subset of real_analysis_2008.pdf.

Keywords :

2nd Year B.Sc onwards up to First year M.Sc
MTTS Level :
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(Downloaded 1315 times last on 15 March 2026, 07:43 am
154
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.

Keywords :


MTTS Level :
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(Downloaded 2537 times last on 15 March 2026, 10:57 am
155
Summary of Real Analysis 2 – Semester 2 (2009-10)

Integration in $R^n$ a terse treatment with a complete proof of the change of variable formula in $R^n$.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 814 times last on 16 March 2026, 10:50 am
156
Summary of Real Analysis 2 – Semester 2 (2009-10)

Calculus of several variables up to Taylor's theorem and maxima-minima

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1770 times last on 16 March 2026, 01:36 am
157
Reduction modulo p

Irreducibility of polynomials using reduction modulo a prime (to be done yet!)

Keywords : Polynomials, Irreducibility criteria, Reduction modulo a prime

MSc
MTTS Level : 2
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(Downloaded 662 times last on 15 March 2026, 07:47 am
158
Riesz-Fredholm-Schauder Theory

Gives a direct proof of Fredhohlm alternative theorem without using spectral theorem for compact operators.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 775 times last on 15 March 2026, 06:50 pm
159
Riesz-Markov Representation Theorem

It proves Riesz representation theorem for positive linear functionals on the space of continuous functions with compact support on a locally compact space. While it closely follows the treatment found in Rudin's Real and complex analysis, it makes use of the fact that students at this level would be familiar with Lebesgue measure theory and hence provides a simpler argument.

Keywords :

M.Sc./Ph.D.
MTTS Level :
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(Downloaded 2385 times last on 16 March 2026, 05:45 am
160
Continuity of the Roots of a Polynomial

It gives three proofs of the continuity of roots of polynomials as dependents on the coeeficients. Needs to write a perspective (pun intended!) of the third proof!

Keywords :

M.Sc./Ph.D
MTTS Level :
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(Downloaded 1361 times last on 15 March 2026, 10:33 pm