Notes that are currently being written may be found linked here
| I | Name | Sname | C | c | |
|---|---|---|---|---|---|
| I | Bl nd | Som Phene | I | Bl nd.pdf | c |
| I | Counting | Som Phene . Prakhar Patel | Blind, Number, Entropy, Subadditivity, Shearer Lemma | 04042021I.pdf | c |
| MA 403 | Real Analysis | Sanjoy Pushti . IITB | Completeness Axiom, Ordered Field, Metric Space, Bolzano-Weierstrass, Heine-Borel, Continuity, Uniform Continuity | 29062019.pdf | c |
| 1.2 | Probability Theory | Tasho Kaletha. Som Phene | Kolmogorov Axiom | 01092020.pdf | c |
| QFTSU21 | I Integral | Som Phene | Ordinary Differential Equation, Conservation | c |
Partial Differential Equations and Homogenization
- Modern Theory of Partial Differential Equations (PDEs) based on MA 534 IITB, by Prof. Mayukh Mukherjee. Course content and review.
- Hypoellipticity of Elliptic Operators. Reference: Prof. Richard Melrose’s notes on Differential Analysis.
- Unified approach to homogenization and time dispersive media based on lectures by Prof. Kirill Cherednichenko at IITB.
- Hille-Yosida, Holder Regularity of Laplacian, Radon Transform for Wave Equation, Perron’s Method based on course projects by Vaibhav Kumar, Soumyajit Saha, Ankur Pandey and Soham Chatterjee in MA 534, IITB.
- Numerical Methods for Partial Differential Equations (PDEs) based on MA 540, IITB by Prof. Harsha Hutridurga.
- Yamabe Problem based on Prof. Saikat Mazumdar’s talk at IITB.
- Harmonic Maps in Analysis of Nonlinear Geometric PDEs- Stratification and Regularity theory based on Prof. Aaron Naber’s lectures at IITB.
- 2nd Order PDEs and associated Markov Processes based on Prof. Rajeeva Karandikar’s Sukhatme Memorial lecture at IITB.
Ordinary Differential Equations and Dynamical Systems
- Ordinary Differential Equations, Linear Systems of ODEs and Nonlinear Systems based on MA 417, IITB by Prof. Gopal Krishna Srinivasan. References: Coddington and Levinson, Brauer and Nohel, Lefschetz. Genesis, nature and scope of ODEs, Existence and Uniqueness including Gronwall Lemma and it’s applications, Dependence on initial conditions and parameters, Kneser’s theorem. Linear Systems, Floquet Theory for periodic Linear vector fields, Monodromy Matrix, Characteristic Polynomial, Jordan Normal forms, Holomorphic Functions of Matrices, Lagrange Sylvester Interpolation
- Dynamical Systems based on MA 525, IITB by Prof. Muthusamy Vanninathan. References: Perko, Hirsch and Smale. Cauchy Lipschitz theorem, Osgood Uniqueness theorem, Dependence on initial parameters and conditions, Linear Systems, phase portraits of planar systems, Stable Manifold Theorem, Hartman Grobman Theorem, Poincare Bendixson Theorem.
- Index Theory.
Steklov Eigenvalues
- Extremal eigenvalue problems in connection to minimal surfaces based on Prof. Richard Schoen’s talk.
- Hersch’s Theorem for first Steklov Eigenvalue convergence.
- Harmonic Maps and egienvalues
Differential Topology and Geometry
- Differential Topology
- Differential Geometry based on MA 556, IITB by Prof. Saurav Bhaumik.
- Differential Geometry for Control Theory based on SC 624, IITB by Prof Debashish Chatterjee and TA Rayyan and help from Mishal Assif.
- Smooth Atlas, Left Invariant Vector Fields
- Symplectic Geometry and Classical Mechanics based on Prof. Tobias J Osborne’s lectures at Institut für Theoretische Physik Leibniz Universität Hannover.
- Differential forms and De Rham Cohomology based on Prof. Gopal Krishna Srinivasan’s SCV Seminar series at IITB.
- Tensor Algebra based on Youtube series by Eigenchris.
- Analytical and Geometric Dynamics based on Prof. Srikant.
Several Complex Variables
- Hatrog’s Extension Phenomenon: Domain of Holomorphicity characterized by vanishing of Dolbeault Cohomology (analogue of De Rham Cohomology in several complex variables) based on Prof. Gopal Krishna Srinivasan’s SCV Seminar series at IITB.
Algebra
- Hopf Algebras, Monoids, Posets, Hyperplane Arrangements and Euler Characteristic.
- Lie Groups, Symmetry and Shimura Varieties based on the lecture series given by Prof. Dipendra Prasad at IITB and his suggested references. They provide an introduction to Lie groups, Homogeneous Spaces, Symmetric Spaces, Crash Course on Riemannian Geometry, Classification of semisimple Lie Groups, Theorems by Harish Chandra, Eichler Shimura Theory.
- Lie Groups and Lie ALgebras 1, Lie Groups and Lie Algebras 2 based on MA 5108, IITB by Prof. Sudarshan Gurjar. References for which are Hall and Chevalley.
- Notes on Group theory for Physicists based on PH 520, IITB by Prof. Ramadevi and other online resources for application of group theory in Quantum Mechanics, standard refernces for which are Hammermesh and Georgi.
- Noether’s Theorem in Classical Dynamics (Continuous Symmetries)
Analysis
- Functional Analysis based on MA 824, IITB Prof. Mayukh Mukherjee.
- Introductory Calculus
- Real Analysis will be uploaded soon.
Michael Atiyah’s Work (Highlight- the Atiyah Singer Index Theorem)
- Notes based on lectures by Prof. MS. Raghunathan at IITB.
- Atiyah Patodi Singer Index Theorem a Physicist’s derivation (including non-compact Manifolds, supersymmetry and Witten index) based on Dr. Arnab Rudra’s talk at IITB.
Numerical Analysis
- Topics in Numerical Analysis based on MA 856, IITB by Prof. A.K. Pani.
- Numerical Methods for Partial Differential Equations (PDEs) based on MA 540, IITB by Prof. Harsha Hutridurga.
Systems and Control
- Quantum Control based on SC 701, IITB by Prof. Navin Khaneja.
- Solid State Systems and Control Work out 1 based on SC 624, IITB by Prof. Navin Khaneja.
- Differential Geometry for Control Theory based on SC 624, IITB by Prof Debashish Chatterjee and TA Rayyan and help from Mishal Assif.
- Process Control and Instrumentation based on MM 401, IITB by Prof. N. K. Khosla.
- Physics and Control, Linear Systems, Quantum Control based on SC 701, IITB by Prof. Navin Khaneja.
- Optimization based on SC 607, IITB by Prof. Ankur Kulkarni.
- Analytical and Geometric Dynamics based on Prof. Srikant.
Operators on Hilbert Space for Quantum Theory
- Quantum Theory based on lectures by Prof. Frederic Schuller, Friedrich-Alexander-University of Erlangen-Nürnberg.
- Operators on Hilbert Spaces based on MA 506, IITB by Prof. Rekha Kulkarni.
Electromagnetic Theory
Nanoscience and Nanotechnology
- Graphene and Carbon Nanotube Tight Binding derivation of Bandstructure
- Non-Interacting Fermi Gas
- Quantum Dots
- Second Quantization, Optical Absorption in low dimensions
- Nanolasers
- Mie Scattering Frohlich Condition
- Maxwell’s Equations and Lasing
Computational Many Body Physics
- Course Content and Review Computational Many Body Physics PH 513, IITB by Prof. Soumya Bera.
- Time Evolving Block Decimation (TEBD) based on PH 513, IITB by Prof. Soumya Bera.
- Kitaev Model and Majorana Fermions based on my course project for the above.
- Spin Chains based on lecture series by Prof. Ribhu Kaul at IITB.
Phase Transformations
- Phase Transformations based on MM 325, IITB by Prof. N. Prabhu, tutorial problems, practice, exams, solutions, notes from Porter and Easterling all written. My mistakes and common mistakes document.
- X-Ray Diffraction
- Abstract Phase Transformations
Philosophy
- Observations on Language
- Nirvana and Anattavada in Buddhist Philosophy via Topology
- Introduction to Philosophy HS 301 IIT Bombay Notes, Course Review published in UG info Booklet
- Rant on being asked for motivation to apply for a job
- Environmental Studies and it’s philosophy. ( will be Uploadrd around June)
Miscellaneous
- Theory of Machines and Machine Design, my final answers.