TEW  Linear Algebra, Real Analysis and Topology (2023)
Speakers and Syllabus
Speaker  Affiliation  Topic(s)  Number of lecture hours  Number of tutorial hours 
Dr. Arindama Singh  IIT Madras  Linear Algebra:Vector spaces and subspaces, Linear independence, Basis and dimension, Row, Column spaces, Linear transformations and their matrix representations, Algebra of linear transformations, Change of basis, Eigenvalues and eigenvectors, Similarity transformations, Diagonalizable operators, Jordan canonical form, Inner product spaces, Gram Schmidt orthogonalization process, Normal, Selfadjoint and unitary operators, Spectral theorem for normal operators, Singular Value decomposition.  9  2 (conduct) +2 (assist) 
Dr. S. Ponnusamy  IIT Madras  Real Analysis :Countable and Uncountable sets, LUB axiom, Archimedean property, Sequence and Series, Convergence, Limsup, Liminf, BolzanoWeierstrass theorem, HeineBorel theorem, Continuity, Uniform continuity, Differentiability, Mean value theorem, Riemann integral and properties, Pointwise and Uniform convergence of sequence and series of functions, Existence continuous but nowhere differentiable functions.  9  2 (conduct) +2 (assist) 
Dr. G. P. Youvaraj  RIASM,Chennai  Topology :Basic concepts from Metric Spaces, Topological spaces, bases, subbases, subspace topology, order topology, product topology, quotient topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma, Tietz’s Extension Theorem, Tychonoff Theorem.  9  2 (conduct) +2 (assist) 
References:
1. George F. Simmons, “Introduction to Topology and Modern Analysis”, Krieger Publishing Company, Reprint, 2003.
2. James R. Munkres “Topology”, Pearson Education India, 2nd Edition, 2015.
3. Kenneth M Hoffman and Ray Kunze, “Linear Algebra”, Prentice Hall of India, 2nd Edition, 2015.
4. Robert G. Bartle and Donald R. Sherbert, “Introduction to Real Analysis”, Wiley, 4th Edition, 2011.
5. Strang G., “Linear Algebra and its applications”, Cengage Learning, 15th Reprint, 2014.
6. Walter Rudin, “Principles of Mathematical Analysis”, McGraw Hill Education, 3rd Edition, 2017.
7. William F. Trench, “Introduction to real analysis”, Pearson, 2002.
Time Table
Time 
09.30 Lecture 

11.15 Lecture 

14.00 Lecture 

15.45 

Mon Nov 27^{th} 
AS 

SP 
L 
GPY 

AS & SP 
S 
Tue Nov 28^{th} 
SP 
T 
GPY 
U 
AS 
T 
SP& GPY 
N 
Wed Nov 29^{th} 
GPY 
E 
AS 
N 
SP 
E 
GPY & AS 
A 
Thu Nov 30^{th} 
GPY 
A 
AS 
C 
SP 
A 
AS & SP 
C 
Fri Dec 1^{st} 
AS 

SP 
H 
GPY 

SP & GPY 
K 
Sat Dec 2^{nd} 
SP 

GPY 

AS 

GPY & AS 
S 
AS  Arindama Singh  9 lecture hours + 4 tutorial hours
SP  S.Ponnusamy 9 lecture hours + 4 tutorial hours
GPY  G. P. Youvaraj 9 lecture hours + 4 tutorial hours
Note: Tutorials will be conducted by one speaker and will be assisted by another speaker.