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Found total 224 results. Displaying results from 21 to 40.

 
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21
Noncontractibility of the Circle

Non-contractibility of the circle and Brouwer Fixed point theorem in $R^2$. Proofs are analytic in nature, as we classify the functions into punctured plane.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1307 times last on 02 April 2025, 03:41 am
22
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.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1868 times last on 31 March 2025, 07:40 pm
23
Compact Metric Spaces

Give equivalent conditions for a metric space to be compact

Keywords :

Final year BSc, 1st year MSc
MTTS Level :
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(Downloaded 1552 times last on 31 March 2025, 07:49 am
24
Compact Spaces

Proves Heine-Borel theorems in $R$, $R^n$ and Tykonoff's theorem.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 979 times last on 01 April 2025, 10:16 am
25
Properties Equivalent to the LUB Property of Ordered Fields

Properties equivalent to LUB property. Almost similar to the article ?complete1.pdf? but contains an example of complete non-Archimedean field.

Keywords :

Final year B.Sc,, M.Sc.
MTTS Level :
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(Downloaded 2306 times last on 26 March 2025, 06:10 pm
26
Properties Equivalent to the LUB Property of Ordered Fields

Properties equivalent to LUB property. Almost similar to the article ?complete.pdf?, but contains more details but excludes an example of complete non-Archimedean field.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1663 times last on 01 April 2025, 05:48 pm
27
A Diagnostic Quiz in Complex Analysis

A diagnostic quiz in complex analysis.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1557 times last on 31 March 2025, 11:08 pm
28
Complex Analysis: Handout-1 (Basic Calculus on C)

A handout dealing with limits, differentiation of functions from $R$ to $C$, from 4C$ to $C$ and integartion of $C$-valued continuous funtions on $[a,b]$.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1376 times last on 30 March 2025, 08:07 am
29
Complex Analysis: Handout-2 (Results on Power Series)

Results on power series

Keywords :


MTTS Level :
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(Downloaded 2065 times last on 27 March 2025, 08:07 am
30
Complex Analysis: Handout-3 (Cauchy-Riemann Equations)

Cauchy-Riemann equations

Keywords :

it also brings out the `geometric' meaning of C-R equations. A must read for students who like geometry.
MTTS Level :
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(Downloaded 1458 times last on 29 March 2025, 06:18 pm
31
Complex Analysis: Handout-7 (Path Integrals)

Path integrals

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1028 times last on 26 March 2025, 08:34 pm
32
Complex Analysis: Handout-7 (Properties of Holomorphic Functions

Properties of holomorphic functions. No proofs.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1071 times last on 31 March 2025, 01:39 pm
33
Complex Analysis: Handout-8 (Weierstrass Theorem)

Weierstrass theorem on uniform convergence (on compact subsets) of holomorphic functions.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1120 times last on 31 March 2025, 04:17 pm
34
Connected and Path-connected Spaces

A quick introduction to connected and path-connected spaces. More details may be found in my book on metric spaces.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 3940 times last on 01 April 2025, 10:01 pm
35
Construction of real numbers

Construction of real numbers

Keywords :

B.Sc./M.Sc
MTTS Level :
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(Downloaded 1186 times last on 28 March 2025, 11:47 am
36
Banach Contraction Principle

Proofs of Banach's contraction mapping theorem and its applications to ODE and integral equations.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 826 times last on 31 March 2025, 01:17 pm
37
Correspondence Theorem for Groups

Proves the stated result with a nontrivial application (which is missing in standard textbooks).

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1457 times last on 02 April 2025, 05:00 am
38
Covering Spaces

Basic notions of covering spaces with emphasis on topological manifolds.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 779 times last on 27 March 2025, 11:16 pm
39
Existence of Continuous Logarithms

Proves the existence of continuous logarithms on star-shaped domains in $R^n$ with values in $C^*$. As an application, gives a proof of no-retraction theorem.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 752 times last on 27 March 2025, 01:12 am
40
A Continuous but Nowhere Differentiable Function

Establishes the existence of a continuous nowhere differentiable function in a seriesof graded exercises. Rest assured it is easy!

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1185 times last on 30 March 2025, 04:40 am