TEW - Algebra & Multivariate Calculus (2020)

Speakers and Syllabus

 Name of the Speaker with affiliation, who will cover each module of 6 lectures. No. of Lectures Detailed Syllabus Prof. C.S. Dalawat,Harish Chandra ResearchInstitute, Prayagraj 8 Preliminaries , What Is Linear Algebra?Vector Spaces , Fields Linear Subspaces and Linear Hulls Linear Independence and Dimension, Infinite-Dimensional vector spaces and Zorn’s Lemma,Quotient Spaces Linear Maps, Rank and Nullity theorem. Matrices, Row and Column Operations , Linear Equations Matrices and Linear Maps, Determinants Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem. Diagonalisation. Some applications. Dr. Sanjay Kumar Singh,Indian Institute of ScienceEducation and Research(IISER) Bhopal. 8 Laws of composition, monoids, groups,homomorphisms, Isometry, Symmetry Group, Rings, fields, modules, ring homomorphism,module homomorphism, Submodules, quotient modules, direct sums, direct products Ideals, Prime Ideal, Maximal Ideal, PID, UFD. Fields, Polynomial rings, Structure of finite fields,Minimal polynomials Codes, Linear Codes, Hamming weight, Minimum distance, Generator matrix and parity-check matrix. Bounds in coding theory Construction of linear codes, Reed-Muller codes,cyclic codes, Goppa codes, Some basic problems and applications. Dr. Siddhartha Sarkar,Indian Institute of ScienceEducation and Research(IISER) Bhopal 8 Limit, continuity, Differentiable maps, Basic Properties; Smooth functions, Diffeomorphisms , Examples; Directional derivatives, Partial Derivatives and the Chain Rule; Equality of mixed partial derivatives; Jacobian Matrix, Mean Value Theorem. Taylor’s theorem up to second order and applications to maxima-minima. Gradient, Divergence, Curl Multiple integrals, Repeated integrals, Fubini's theorem, The Jacobian theorem, Line, surface and volume integrals, Green's Theorem, Gauss's divergence Theorem, Stoke's Theorem.

References:

1. Online Notes: http://www.mathe2.uni-bayreuth.de/stoll/lecture-notes/LinearAlgebraI.pdf
2. T.S. Blyth, Module Theory: An Approach To Linear Algebra
3. Tom Apostol, Mathematical Analysis.
4. Walter Rudin, Principles of Mathematical Analysis.
5. San Ling and Chaping Xing, Coding Theory A First Course.

Names of the Tutors / Course Associates with their affiliation and status:

1. Dr. Punam Gupta, (Assistant Professor)
Dr. Harisingh Gour Vishwavidyalaya.
2. Dr. Triloki Nath, (Assistant Professor)
Dr. Harisingh Gour Vishwavidyalaya.
3. Dr. R.K. Pandey, (Assistant Professor)
Dr. Harisingh Gour Vishwavidyalaya.

Time Table

 Day Date Lecture 110.00–11.30 Tea11.30–12.00 Lecture 212.00–1.00 Lunch1.00–2.00 Lecture 32.00-3.30 Tea3.30-3.45 Discussion/Tutorial3.45-4.45 Tea &Snacks5.00 PM (name of theSpeaker) (name of theSpeaker) (name of theSpeaker) Name of theTutor Mon 25 May CSD SKS SS PG & TN Tue 26 May CSD SKS SS PG & TN Wed 27 May CSD SS SKS RKP & TN Thu 28 May CSD SS SKS RKP & TN Fri 29 May SS CSD SKS PG & RKP Sat 30 May SS CSD SKS PG & RKP

CSD: Prof. C.S. Dalawat,, SKS: Dr. Sanjay Kumar Singh, SS: Dr. Siddhartha Sarkar,PG: Dr. Punam Gupta, TN: Dr. Triloki Nath, RKP: Dr. R.K. Pandey

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