Expository articles


 

Search for an article

Part of title, description, or keywords. Minimum 4 characters required.

 Reset search and show all articles

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

 
SL
Article Name
Broad subject area
Abstract & Keywords
Targetted Audience
Number of downloads
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 :
Download now
(Downloaded 1783 times last on 15 March 2026, 11:16 pm
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 :
Download now
(Downloaded 3246 times last on 15 March 2026, 12:30 pm
23
Compact Metric Spaces

Give equivalent conditions for a metric space to be compact

Keywords :

Final year BSc, 1st year MSc
MTTS Level :
Download now
(Downloaded 1770 times last on 15 March 2026, 08:48 pm
24
Compact Spaces

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

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 1331 times last on 15 March 2026, 09:24 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 :
Download now
(Downloaded 2491 times last on 15 March 2026, 03:16 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 :
Download now
(Downloaded 2103 times last on 15 March 2026, 09:58 am
27
A Diagnostic Quiz in Complex Analysis

A diagnostic quiz in complex analysis.

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 1755 times last on 15 March 2026, 09:55 am
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 :
Download now
(Downloaded 1615 times last on 15 March 2026, 01:21 pm
29
Complex Analysis: Handout-2 (Results on Power Series)

Results on power series

Keywords :


MTTS Level :
Download now
(Downloaded 2359 times last on 15 March 2026, 09:25 pm
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 :
Download now
(Downloaded 1672 times last on 15 March 2026, 02:23 pm
31
Complex Analysis: Handout-7 (Path Integrals)

Path integrals

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
Download now
(Downloaded 1260 times last on 14 March 2026, 01:07 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 :
Download now
(Downloaded 1454 times last on 15 March 2026, 04:06 am
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 :
Download now
(Downloaded 1606 times last on 14 March 2026, 01:04 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 :
Download now
(Downloaded 6415 times last on 15 March 2026, 01:14 am
35
Construction of real numbers

Construction of real numbers

Keywords :

B.Sc./M.Sc
MTTS Level :
Download now
(Downloaded 1768 times last on 16 March 2026, 12:48 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 :
Download now
(Downloaded 1159 times last on 15 March 2026, 08:43 am
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 :
Download now
(Downloaded 2116 times last on 15 March 2026, 11:16 pm
38
Covering Spaces

Basic notions of covering spaces with emphasis on topological manifolds.

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 1097 times last on 15 March 2026, 10:03 am
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 :
Download now
(Downloaded 933 times last on 15 March 2026, 11:28 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 :
Download now
(Downloaded 1547 times last on 15 March 2026, 10:26 am