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 Research
Institute, 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 Science
Education 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 Science
Education 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 1
10.00–11.30
Tea
11.30–12.00
Lecture 2
12.00–1.00
Lunch
1.00–2.00
Lecture 3
2.00-3.30
Tea
3.30-3.45
Discussion/
Tutorial
3.45-4.45
Tea &
Snacks
5.00 PM
    (name of the
Speaker)
  (name of the
Speaker)
  (name of the
Speaker)
  Name of the
Tutor
 
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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