The Advanced Training in Mathematics Schools (ATM Schools) were launched by the National Board for Higher Mathematics (NBHM) in May 2004. The purpose of these schools is to provide training in core subjects in Mathematics to Ph.D. students, young researchers and teachers. The emphasis in these schools is on learning mathematics by doing it. IIT Bombay and TIFR have jointly established the National Centre for Mathematics (NCM) in 2011. The instructional schools and workshops which were earlier planned by an NBHM committee on ATM Schools are now being organized under the supervision of the Apex Committee of the NCM.
Dates: 27 Nov 2023 to 9 Dec 2023
For more details please click https://www.atmschools.org/school/2023/ist/ala
Syllabus:
| Sr. | Name of the speaker and Affiliation | Topic of lectures | Number of lectures |
| 1 | Dr. Samarpita Ray, INSPIRE Faculty fellow, ISI Bangalore. | Canonical Forms.Eigenvalues and eigenvectors of matrices and linear maps, Diagonalizability.Minimal and characteristic polynomials, Cayley-Hamilton theorem.Jordan and Rational canonical forms over complex numbers. | |
| 2 | Prof. Vinayak Sholapurkar S.P. College, Pune/ Bhaskaracharya Pratishthana, Pune. | Inner products and Orthogonality. Bilinear forms, Symmetric bilinear forms, hermitian forms.Orthogonality, Orthonormal basis, Gram-Schmidt process.Spectral theorem.Basic theory of inner products on real and complex vector spaces.Spectral theorem for hermitian and normal linear maps (finite dimensional case). | |
| 3 | Dr. Chandrasheel Bhagwat | Multilinear Algebra. Multilinear maps on vector spaces: basic theory and examples.Theory of determinant map as an alternating n-linear form on F^n.Tensor product of vector spaces, symmetric tensors, alternating tensors.Applications to differential forms on euclidean spaces and deRham cohomology. | |
| 4 | Prof. B. Sury ISI Bangalore | Quadratic forms and Linear groups. Quadratic forms: Classification, signature for real quadratic forms.Linear Groups defined preserving quadratic forms: Orthogonal and Unitary groups.Groups SO (3) and SU (2), conjugacy classes and geometry of sphere. |
References:
- M. Artin, Algebra, Pearson Publications.
- Hoffman and Kunze, Linear Algebra, Pearson publications.
Course Associates
i) Mr. Gahininath Sonawane, S. P. College, Pune.
ii) Dr. Rohit Joshi, IISER, Pune.
iii) Mr. Shubham Jaiswal, IISER, Pune.
