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, Self-adjoint 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, Bolzano-Weierstrass theorem, Heine-Borel 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 27th |
AS |
|
SP |
L |
GPY |
|
AS & SP |
S |
|
Tue Nov 28th |
SP |
T |
GPY |
U |
AS |
T |
SP& GPY |
N |
|
Wed Nov 29th |
GPY |
E |
AS |
N |
SP |
E |
GPY & AS |
A |
|
Thu Nov 30th |
GPY |
A |
AS |
C |
SP |
A |
AS & SP |
C |
|
Fri Dec 1st |
AS |
|
SP |
H |
GPY |
|
SP & GPY |
K |
|
Sat Dec 2nd |
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.