Refresher Course for College Teachers in Kerala State:2016-17
PROGRAMME - V
Venue: KSOM, Kozhikode
09-12 March, 2017
Topics of discussion:Differential Equations
Resourse Persons:
Prof. K Sandeep, TIFR-CAM Bangalore
Dr. A. K. Nandakumaran, Professor, Indian Institute of Science, Bangalore
Topics covered:
1- Existence and Uniqueness of solution for ODE
2- Smooth dependence on the data
3- Stability of linear systems
4- First order partial differential equations- Method of characteristics
Visit the link at http://nptel.ac.in/courses/111108081/
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2016-17
PROGRAMME - IV
Venue: KSOM, Kozhikode
09-12 February, 2017
Topics of discussion:Algebraic Number Theory
Resourse Persons:
Prof. Sanoli Gun, IMSc Chennai
Prof. Purushotham Rath, CMI Chennai
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2016-17
PROGRAMME - III
Venue: KSOM, Kozhikode
19-22 January, 2017
Topics of discussion:Semisimple Algebras and Group Representations
Resourse Persons:
Prof. K N Raghavan, IMSc Chennai
Prof. Vijay Kodiyalam, IMSc Chennai
Course Content
The resource persons for the program recommend the notes, exercises, and lectures
in the following links:
Notes and exercises:
---> http://www.imsc.res.in/~knr/past/afs-II_iisertvm_2015/Notes/knr_2.pdf
Videos of lectures:
---> https://www.youtube.com/playlist?list=PLhkiT_RYTEU0CcvzU49C5AYmX7mLHUvOb
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
KSOM Workshop for B.Sc. students in Idukki district, Kerala
28th, 29th, 30th November, 1st and 2nd December 2016
KSOM conducted a Workshop at Pavanatma College, Idukki district, Kerala during 28 November - 02 December 2016. The program was meant for BSc Mathematics students studying in colleges in Idukki, Kerala.
Resource Persons:
Prof. Sanoli Gun, IMSc Chennai
Prof. Purushotham Rath, CMI Chennai
Prof. B Ramakrishnan, HRI Allahabad
Special Lectures by:
Prof. Gautam Menon.IMSc Chennai
Prof. Murugan V, RKM Vevekananda College, Chennai
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics Tel: 0495 2809001 Email: murugumanick@ksom.res.in |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics Tel: 0495 2809004 Email: vijay@ksom.res.in |
Local Co-ordinators | ||
---|---|---|
Mr. Sijo P. George Assistant Professor Pavanatma College, Idukki Email: sijopgorg@gmail.com Mob: 9746105166 |
Mr. Bobin George Pavanatma College, Idukki Email: bobinkgeorge@gmail.com Mob: 9747905115 |
Mr. Tijo James Assistant Professor Dept. of Mathematics Pavanatma College, Idukki Email: tijojames@gmail.com Mob: 9946884650 |
Refresher Course for College Teachers in Kerala State:2016-17
PROGRAMME - II
Venue: KSOM, Kozhikode
03-06 November, 2016
Topics of discussion:Groups and their representations
Resourse Persons:
Prof. A J Parameswaran, TIFR Mumba
Prof. V Balaji, CMI Chennai
Course Content
Semisimple representations.Closed and "algebraic" subgroups of GL(n,C).
Nilpotent and semisimple elements: simultaneous upper triangulability of ommuting
matrices (Jordan decomposition). Nilpotent and unipotent groups, Torus, Classification of connected abelian groups, Solvable groups, Lie-Kolchin Theorem.
Reductive groups: If a connected algebraic group has a faithful irreducible representation then it is a reductive group. Classification of finite subgroups of GL(n,C): Theorem of Jordan.
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2016-17
PROGRAMME - I
Venue: KSOM, Kozhikode
20-23 October, 2016
Topics of discussion:Linear Algebra in Control Theory - An Introduction
Resourse Persons:
Prof. Subramanian Moosath, IIST Thiruvananthapuram
Dr. Priyadarshnam, IIST Thiruvananthapuram
Course Content
Linear algebra, Linear systems, and Control concepts
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2015-16
PROGRAMME - V
Venue: KSOM, Kozhikode
18-21 February, 2016
Topics of discussion:Complex Analysis
Resourse Persons:
Prof. Parameswaran Shankaran IMSc, Chennai
Prof. L Venkataraman Rtd Prof, Vivekananda College, Chennai
Course Content
Prof. Parameswaran Sankaran: Weierstrass theorem on infinite product representation, Hadamard's theorem, Mittag-Leffler
theorem, Gamma and Zeta functions (basic properties). Weierstrass function.
Ref: Complex Analysis by Ahlfors (Chapter 5)
Prof. L Venkataraman : Cauchy theory (basically complex integration and its applications). Cauchy-Goursat Theorem, Cauchy Integration Formulas, Singularities, Residue Theorem, Evaluation of Ontegrals using Residues, Argument Principle, Maximum Modulus Principle.
1. Conformal Mappings
2. Analytic Continuation
3. Riemann Mapping Theorem
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
KSOM Workshop for B.Sc. students in Wayanad district, Kerala
09-13 December, 2015
KSOM conducted a Workshop at Wayanad during 09-13 December, 2015. The program was meant for BSc Mathematics students studying in colleges in Wayanad.
Resource Persons
Dr. S Kumaresan (Department of Mathematics,, Hyderabad University)
Dr. V. Muruganandam (Department of Mathematics, NISER, Bhuvaneswar)
Dr. M. Manickam (KSoM)
Dr. A. K. Vijayarajan (KSoM)
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics Tel: 0495 2809001 Email: murugumanick@ksom.res.in |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics Tel: 0495 2809004 Email: vijay@ksom.res.in |
Local Co-ordinators | ||
---|---|---|
Dr. Pamy Sebastian Head, Dept. of Mathematics Mary Matha Arts & Science College, Mananthavady, Wayanad Email: pamyseb@gmail.com Mob: +919446970984 |
Mr. Latheesh Kumar A R Sulthan Bathery, Wayanad Email: latheesby@gmail.com Mob: +919947049112 |
Mr. Santhosh Kumar C G Assistant Professor Dept. of Mathematics W M O Arts & Science College, Muttil, Wayanad Email: skumarcg@gmail.com Mob: +919447780543 |
Refresher Course for College Teachers in Kerala State:2015-16
PROGRAMME - IV
Venue: KSOM, Kozhikode
12-15 November, 2015
Topics of discussion:Topologies, Filters and Uniformities
Resourse Persons:
Prof. K. N. Raghavan, IMSc Chennai
Course Content
Basic reference: Bourbaki, General Topology, Part I, Chapters I and II
Other references:
J L Kelley, General Topology
Gilman & Jerison, Rings of Continuous Functions
Abstract:
Following Bourbaki (Chapter I), we will study filters and their limits. Filters, like nets, generalize sequences. They enable us to restore intuition to the notion of continuity: a map between general topological spaces is continuous if and only if, for every filter in the domain that converges to a point, the direct image filter converges to the image of that point. Moreover, Hausdorfness may be defined as the property that every filter has at most one limit point, (quasi-)compactness as the property that every filter admits at least one cluster point.
Following Gilman & Jerison, we will illustrate the use of filters in the study of rings of continuous functions (such as C[0,1]).
Following Bourbaki again (Chapter II), we will study uniformities. Cauchy sequences and uniform continuity are not topological notions (they are not preserved under homeomorphisms; their usual definitions presume a metric) but they are closely related to topological notions. Uniform spaces generalize metric spaces. Like a metric, a uniformity too induces a topology. Uniform continuity, Cauchy filters, and completions may be defined in the context of uniform spaces.
Some notes following Bourbaki may be found at http://www.imsc.res.in/~knr/past/top15 (these notes are being currently added to).
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2015-16
PROGRAMME - III
Venue: KSOM, Kozhikode
18-21 October, 2015
Topics of discussion: Differential Geometry
Resourse Persons:
Prof. S Kumaresan, University of Hyderabad
Prof. G Santhanam, IIT, Kanpur
Course Content
1. Review of Multivariable Calculus (3 lectures)
2. Curves: Definition, vector field, Frenet – n- frame, existence of curves with prescribed curvatures, curvature and torsion of a space curve, Frenet-Serret formula. (3 L)
3. Surfaces: Definition, vector field, quadratic form, first fundamental form, second fundamental form, curvature of curves on a surface, Principal curvature, Gaussian and mean curvatures. (6 L)
References:
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2015-16
PROGRAMME - II
Venue: KSOM, Kozhikode
10-13 September, 2015
Topics of discussion: Matrix Analysis & Applications
Resourse Persons:
Prof. A. Chandrashekaran, Central University of Tamilnadu
Prof. Sachindranath Jayaraman, IISER, Thiruvananthapuram
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2015-16
PROGRAMME - I
Venue: KSOM, Kozhikode
23-26 August, 2015
Topics of discussion: Topology
Resourse Persons:
Prof. A J Parameswaran, TIFR Mumbai
Prof. A J Jayanthan, Goa University
Differentiable maps, Tangent space, Implicit function theorem, Critical Points, Structure Theorem for nondegenerate critical points, Topological and Differentiable manifolds, Differentiability of functions on a manifold, Sard’s theorem, Partitions of unity, para compactness., Whitney’s Embedding Theorem, Morse functions and their Existence, CW complexes, Change of Topology as one passes a non degenerate critical point.
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Initiation into Mathematics 2015 - mini MTTS Programme
Venue: KSOM, Kozhikode
04-09 May, 2015
A one week long Mini Mathematics Training and Talent Search programme organized during May 4-9, 2015 at Kerala School of Mathematics, Kozhikode, Kerala with the funding of National Board of Higher Mathematics, Govt. of India.
The program was targeted to students in the second year/fourth semester B.Sc/Integrated M.Sc programmes having Mathematics as one of the compulsory papers. The topics which discussed in the program were Number Theory, Foundations of Set Theory, Real Analysis, Group Theory, and Linear Algebra. The program was conducted on the solid academic support of the prestigious Mathematics Training and Talent Search (MTTS) programme and it took up and implemented the meticulous teaching methodology of MTTS.
Resource Persons
Dr. P.S. Srinivasan : Foundations of Mathematics / Real Analysis
Dr. Subramanyan Moosath : Linear Algebra
Dr. Vishnu Namboothiri K : Group theory
Local Coordinator | Academic Coordinator |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. Vishnu Namboothiri K Department of Mathematics, BJM Govt. College Chavara, Kerala |
OUTREACH PROGRAMME: Refresher Course for M.Sc. students in Kerala State
Venue: KSOM, Kozhikode
17-26 April, 2015
KSOM conducted a refresher course during April 2015 for final year M.Sc. Mathematics students in Kerala. The course covered some basic topics of Algebra, Analysis, and Number Theory.
Resource Persons
Prof. M Manickam, KSOM : Algebra
Dr. A K Vijayarajan, KSOM : Linear Algebra
Prof. B Ramakrishnan, HRI Allahabad : Number Theory
Prof. Joseph Mathew, Formerly KSOM : Analysis
Prof. A J Parameswaran, TIFR Mumbai : Topology ----------Lecture Notes
Co-ordinator |
---|
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2014-15
PROGRAMME - VI
Venue: KSOM, Kozhikode
19-22 February, 2015
Topics of discussion: Measure Theory
Resourse Persons:
Prof. B. V. Rao, CMI, Chennai
Dr. A. K. Vijayarajan, KSOM
Prof. Joseph Mathew, KSOM
Prof. B V Rao & Prof. Joseph Mathew
1 Quick review of basic measure theory including Monotone Class theorem, Caratheodory extension; MCT, DCT, Fatou;
2 Radon-Nikodym theorem; Lebesgue decomposition; various notions of convergence;
3. Product spaces and Fubini;
4. L_p spaces; Specializing to p=2 simple introduction to Fourier series.
Dr. A K Vijayarajan
Spectral Measures
Course Materials
Prof. B V Rao
Prof. Joseph Mathew
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2014-15
PROGRAMME - V
Venue: KSOM, Kozhikode
08-11 January, 2015
Topics of discussion: Algebra
Resourse Persons:
Prof. U. K. Anandavardhanan, IIT Bombay
Prof. A V Jayanthan, IIT Madras
Prof. U. K. Anandavardhanan : Representation Theory
Generalities on linear representations, characters, Schur's lemma, orthogonality relations, induced representations, Mackey's criterion.
Prof. A. V. Jayanthan : Commutative Algebra
Modules over Commutative rings, ascending and descending chain conditions, Noetherian rings and modules, Hilbert basis theorem.
References:
1. Abstract Algebra by Dummit and Foote
2. Algebra by Artin.
3. Algebra by Lang.
4. Introduction to Commutative Algebra by Atiyah and Macdonald.5. Linear Representations of Finite Groups by Serre.
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2014-15
PROGRAMME - IV
Venue: KSOM, Kozhikode
06-09 November, 2014
Topics of discussion: Real & Complex Analysis
Resourse Persons:
Dr. K. Sandeep, TIFR-CAM, Bangalore
Dr. Venky Krishnan, TIFR-CAM, Bangalore
Dr. K Sandeep
R^n calculus, continuity, various notions of differentiability, inverse function and implicit function theorems, extension of these notions to Banach spaces, finally some applications.
Dr. Venky Krishnan
From Cauchy Riemann equations to some advanced topics of Analytic continuation.
Course Materials
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2014-15
PROGRAMME - III
Venue: KSOM, Kozhikode
09-12 October, 2014
Topics of discussion: Number Theory & Cryptography
Resourse Persons:
Prof. Surya Ramana, HRI Allahabad
Mr. Kasi Viswanadham, HRI Allahabad
Mr. Jay G Mehta, HRI Allahabad
D. Surya Ramana
Arithmetical functions
Proof of prime number theorem
G. Kasi Viswanadham
Some topics in Elementary Number Theory - Time estimates, divisibility and Euclidean algorithm, congruences, applications to factoring
Finite Fields and Quadratic Residues - finite fields, Quadratic residues and reciprocity
Jay Mehta
Classical Cryptography - some simple cryptosystems, different types of Ciphers, Cryptanalysis of Ciphers
Public Key cryptography - idea of public key cryptography, RSA and
discrete log
Reference books
Introduction to analytic and probabilistic number theory- G. Tenenbaum
Introduction to analytic number theory -T. Apostol
Number theory and Cryptography- N. Koblitz
Cryptography Theory and Practice- Douglas R. Stinson
Course Materials
Cryptography Theory and Practice
Introduction to Cryptography
Course in Number Theory And Cryptography
Prime Number Theory
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2014-15
PROGRAMME - II
Venue: KSOM, Kozhikode
11-14 September, 2014
Topics of discussion: Topology
Resourse Persons:
Prof. A.J. Parameswaran, TIFR Bombay
Prof. Parameswaran Sankaran, IMSc Chennai
Homological Algebra: Complexes and homology, Exact sequences, Long exact sequence assciated to a short exact sequence of complexes.
Topology: Simplicial complexes, CW Complexes.
Homology Thoeries: Simplicial Homology, Cellular Homology, Singular Homology.
Main Theorems (Only statements with examples): Excision Theorem, Homology sequence of a pair/tripple, Functoriality. Invariance of domain.
Further if time permits: Brouwer fixed point theorem, Lefschetz fixed point theorem and Borsuk-Ulam theorem.
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Refresher Course for College Teachers in Kerala State:2014-15
PROGRAMME - I
Venue: KSOM, Kozhikode
14th, 16th & 17th August, 2014
Topics of discussion: Advanced Functional Analysis
Resourse Persons:
Prof. E. K. Narayanan, IISC, Bangalore
Prof. P. K. Sanjay, NIT, Calicut
Diagonalization of matrices
Singular value decomposition
Self adjoint operators
C* algebras
Gefland theory
Gelfand-Naimark theorem
Spectral theorem
Spectral measures
Compact operators etc.
The two series of lectures will complement each other; First one, demystifying the finite dimensional spectral theorem (diagonalization of self adjoint matrices) following a paper of Adam Koranyi by doing the singular decomposition first (see A. Koranyi: Around the finite dimensional spectral theorem, Amer. Math. Monthly 108 (2001) no.2 120-125) and the second, introducing the participants to the infinite dimensional version.
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
OUTREACH PROGRAMME
Refresher Course for B.Sc. Mathematics Students in Kerala State
Venue: KSOM, Kozhikode
22 - 30 April, 2014
KSOM conducted refresher course during April 2014 for B.Sc. Mathematics IV Semester students studying in Kerala state. The course covered some basic topics of Algebra, Analysis, Linear Algebra and Number Theory.
The course with relaxed schedule and interactive sessions discussed abstract topics in Number Theory, Analysis, Algebra and Linear Algebra. The sessions were handled by Joseph Mathew, A. K. Vijayarajan, V Srivatsa, P Jisna, P Shankar(KSOM) and Kirankumar V B.
Topics covered:
Analysis:
Real number system, Rational numbers, Irrational numbers, Completeness axiom
Sequences, Cauchy sequences, Convergence
Series, Convergence
Topology of the real line
Algebra:
Groups-subgroups-Cyclic groups-Group homomorphisms and Isomorphisms-Normal subgroups
Introduction to Rings and Fields
Linear Algebra:
Vector spaces, Sums and Direct Sums
Linear Independence, Bases and Dimension
Linear maps, Matrices
Number Theory:
Divisibility
Congruences and some basic theorems
Quadratic reciprocity law
Some arithmetic functions
Primitive roots
Co-ordinators | |
---|---|
Dr. A K Vijayarajan Associate Professor e-mail: vijay@ksom.res.in Phone: 0495 2809004 Fax: 0495 2809010 |
Prof. Joseph Mathew Visiting Professor e-mail: jmathew@ksom.res.in Phone: 0495 2809005 Fax: 0495 2809010 |
Discussion Meeting on ANALYTIC & ALGEBRAIC GEOMETRY
Venue: KSOM, Kozhikode
24 - 28 March, 2014
A. J. Parameswaran & Indranil Biswas
TIFR
Speakers | Participants |
---|---|
Nitin Nitsure Jens Kristian Egsgaard Arijith Dey |
Nitin Nitsure Usha Bhosle Amit Hogadi Chanchal Kumar. Sukhendu Mehrotra D.S. Nagaraj S. S. Kannan. Arijit Dey V. Balaji Sergey Arkhipov Jean-Baptiste Meilhan Jens Kristian Egsgaard Florian Schätz. Daniel Tubbenhauer Joergen Ellegaard Andersen Henning Haahr Andersen Niels Leth Gammelgaard Søren Fuglede Jørgensen Jens Jakob Kratmann Nissen Arash Momeni Kenneth Rasmussen Simon Stoltze Anders D. Jakobsen Troels B. Andersen Dennis H. Pedersen Paolo Masulli |
Orientation/Refresher Course for College Teachers in Kerala State-2013-14
PROGRAMME - VI
Venue: KSOM, Kozhikode
07-10 March, 2014
Topics of discussion: Measure Theory
Resourse Persons:
Dr. K. Sandeep,
TIFR Centre for Applicable Mathematics, Bangalore
Dr. Joseph Mathew, KSOM
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Orientation/Refresher Course for College Teachers in Kerala State-2013-14
PROGRAMME - V
Venue: KSOM, Kozhikode
27 February - 02 March, 2014
Topics of discussion: Topology
Resourse Persons:
Prof. A J Parameswaran, TIFR Mumbai
Algebraic Topology: (A J Parameswaran & Sagnik )
1: $\pi_1$: definition, Homotopy, Exapmles.
2: VanKampen Theorem; Computation of the Fundamental groups of various spaces.
3: Covering Spaces: Path lifting, Homotopy lifting, Codition for arbitrary map lifting....
4: Invariance of Domain, Separation Theorem, Jordan curve Theorem ...
5: Universal covering (Existence - statement only) Relation between $\pi_1$ and fibres of covering maps.
Prof. Parameswaran Sankaran, IMSc, Chennai
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Orientation/Refresher Course for College Teachers in Kerala State-2013-14
PROGRAMME - IV
Venue: KSOM, Kozhikode
10-13 January, 2014
Topics of discussion: Functional Analysis
Resourse Persons:
Prof. Dr. T. Sengadir, Central University, Tamilnadu
Topic: Distribution Theory, Sobolev Spaces, Semigroup Theory , Basic PDE, Nonlinear Analysis, Fourier Transforms
Dr. D. Surya Ramana, HRI, Allahabad
Topic: The basic theorems of functional analysis - Hahn Banach, Completeness and Banach Spaces, Operators, Baire Category Theorem, Uniform Boundedness, Closed Graph Open Mapping together with some well-known applications.
Dr. A K Vijayarajan, Kerala School of Mathematics, Kozhikode
Topic: Topologies of B(H)
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Orientation/Refresher Course for College Teachers in Kerala State-2013-14
PROGRAMME - III
Venue: KSOM, Kozhikode
22-25 November, 2013
Topics of discussion: Complex Analysis
Time Schedule | |||||||||
Date | 9:00-10:15 | 10:15- 10:30 | 10:30-11:45 | 11:45-12:00 | 12:00-1:15 | 1:15-2:30 | 2:30-3:30 | 3:30-3:45 | 3:45-4:45 |
22-Nov-13 | AJP | Hot Break | EKN | Cool Break | AJP | Lunch Break | Tutorial EKN | Hot Break | Tutorial AJP |
23-Nov-13 | EKN | AJP | EKN | Tutorial AJP | Tutorial EKN | ||||
24-Nov-13 | AJP | EKN | AJP | Tutorial EKN | Tutorial AJP | ||||
25-Nov-13 | EKN | AJP | EKN | Tutorial AJP | Tutorial EKN | ||||
Resource Persons:
Prof. A J Prameswaran, TIFR Mumbai
Topic: Quick review of topological preliminaries, simply connectedness, homotopy etc. Definition of log and n^th roots, lifting of maps, covering maps. Covering spaces of C*, C** and D*. Applications: Characterization of nowhere vanishing functions, Picard Theorems, Fundamental Theorem of Algebra.
Prof. E K Narayanan, IISc, Bangalore
Topic: Quick review of holomorphic (analytic) functions, Cauchy-Riemann equations, Cauchy's theorem, power series. Properties of holomorphic functions, zeros, maximum modulus principle, Liouville's theorem, isolated singularities, arguments principle, open mapping theorem. If time permits some major theorems like, Montel's theorem, Riemann mapping theorem and Pciard's theorem (Ahlfors's proof).
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Orientation/Refresher Course for College Teachers in Kerala State-2013-14
PROGRAMME - II
Venue: KSOM, Kozhikode
08-11 November, 2013
Topics of discussion: Real Analysis
Time Schedule | |||||||||
Date | 9:00-10:15 | 10:15- 10:30 | 10:30-11:45 | 11.45-12:00 | 12:00-1:15 | 1:15-2:30 | 2:30-3:45 | 3:45-4:00 | 4:00-5:00 |
08-Nov-13 | EKN | Hot Break | SS | Cool Break | EKN | Lunch Break | EKN | Hot Break | Tutorial SS |
09-Nov-13 | SS | EKN | SS | EKN | Tutorial JM | ||||
10-Nov-13 | JM | SS | EKN | EKN | Tutorial EKN | ||||
11-Nov-13 | EKN | SS | SS | JM | Discussion/ Feedback | ||||
Resource Persons:
EKN: E K Narayanan, IISc, Bangalore
Topic: Borel \sigma-algebra, outer measure, measurable sets, construction of Lebesgue measure on \mathbb R, measurable functions, introduction to Lebesgue integration and limit theorems.
SS: S. Somasundaram, Manonmaniam Sundaranar University,Tirunelveli
Topic: Nets and Ordinal Topology
JM: Joseph Mathew, Kerala School of Mathematics
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Orientation/Refresher Course for College Teachers in Kerala State-2013-14
PROGRAMME - I
Venue: KSOM, Kozhikode
11-14 October, 2013
Topics of discussion: Galois Theory, Field Extension and Commutative Algebra
Time Schedule | |||||||
Date | 9:30-11:00 | 11:00-11:30 | 11:30-1:00 | 1:00-2:30 | 2:30-3:30 | 3:30-4:00 | 4:00-5:00 |
11-Oct-13 | PS | Tea Break | PS | Lunch Break | PS | Tea Break | PS |
12-Oct-13 | PS | PS | PS | PS | |||
13-Oct-13 | RT | RT | RT | RT | |||
14-Oct-13 | RT | RT | RT | RT | |||
Resource Persons:
PS : Parameswaran Sankaran, IMSC, Chennai : Galois Theory
RT: R Thnagadurai, HRI, Allahabad : Commutative Algebra
Co-ordinators | |
---|---|
Prof. M Manickam Director Kerala School of Mathematics |
Dr. A K Vijayarajan Associate Professor Kerala School of Mathematics |
Outreach Programme -
Refresher Course for B.Sc. Mathematics Students in Kerala State
Venue: KSOM, Kozhikode
14-22 September, 2013
KSOM conducted refresher course during September 2013 for B.Sc. Mathematics Final year students in Kerala state. The course covered some basic topics of Algebra and Analysis.
The course with relaxed schedule and interactive sessions discussed abstract topics in Number Theory, Analysis, Algebra, Linear Algebra and Graph Theory. The sessions were handled by V. Krishna Kumar(NICER, Bhuvaneswar), P. K. Sanjay(NIT, Calicut), Ananthavardhanan (IIT, Bombay), Jijo Sukumaran (Govt. College, Kasargod), M. Manickam, Joseph Mathew, A. K. Vijayarajan and Guram Donadze (KSOM).
Time Schedule | |||||||
Date | 9:30-11:00 | 11:00-11:30 | 11:30-1:00 | 1:00-2:30 | 2:30-3:30 | 3:30-4:00 | 4:00-5:00 |
14-Sep-13 | MM | Tea Break | SPK | Lunch Break | JM | Tea Break | AKV |
15-Sep-13 | GD | AKV | SPK | GD | |||
16-Sep-13 | MM | GD | JM | AKV | |||
17-Sep-13 | MM | JM | No sessions | No sessions | |||
18-Sep-13 | MM | JM | VK | VK | |||
19-Sep-13 | JM | AKV | GD | VK | |||
20-Sep-13 | JM | VK | JS | GD | |||
21-Sep-13 | GD | AKV | JM | Res. Sch. | |||
22-Sep-13 | AKV | GD | Discussion | Discussion | |||
MM: M. Manickam - Algebra
JM: Joseph Mathew - Topics in Analysis
VK:V Krishna Kumar - Construction of Number system
SPK: Sanjay P K - Topics in Analysis
GD: Guram Donadze - Graph Theory
AKV: A. K. Vijayarajan - Linear Algebra
JS : Jijo Sukumaran - Linear Algebra
Res. Sch.: Research Scholar, KSOM - Tutorial
Co-ordinator
Dr. A K Vijayarajan
Associate Professor, KSOM
Short Term Discussion Meeting
31 December 2012 - 13 January 2013
Visitors
1. Bipin Balaram, Assistant Professor, Dept. of Mechanical Engineering, Amrita School of Engineering, Amrita Viswa Vidyapeetham, coimbatore.
2. Vinod V., Research Scholar, Dept. of Mechanical Engineering, NIT Calicut.
Venue: KSOM, Kozhikode
PLAN OF WORK
The basic objective of this work is to develop a robust numerical method for obtaining the periodic solutions of nonlinear ordinary differential equations and to device a strategy to quantitatively estimate the change in this solution when the system parameters are slowly varied. Historically, homotopy based methods like parametric continuation coupled with shooting algorithms has been used to perform this task. With the help of an arc-length reparameterisation technique at singular points in the parameter space, this can be used for practical bifurcation analysis too. But this scheme has two serious shortcomings.
First, it makes the assumption that the frequency of the solution is the same as that of the forcing
function and hence, runs into trouble when dealing with self-excited systems like Van der Pol
oscillators. This means that systems like coupled self-excited oscillators, which are of great
practical importance in areas like physics, engineering and biology and which show such intresting
behaviour as synchronisation and clustering, cannot be studied using this simple continuation
strategy. So, an effort will be made to develop a continuation strategy based on generalised
shooting method which treats the frequency of the periodic solution also as an unknown. This
means that the new scheme should converge to a point in the enhanced state space of dimension
2n+1; 2n being the dimension of the initial condition vector. Preliminary efforts show that the use of
homotopy methods will reduce this problem to an algebraic one with 2n equations in 2n+1
variables. This poses a challenge which we hope to address. This scheme shall be used to study the
synchronisation in (dissipatively and reactively) coupled Van der Pol oscillators in a ring by treating
the coupling constant as the continuing parameter with an emphasis on tracking down possible
bifurcation phenomenon.
Second, existing continuation strategies are equipped to carry out the solution continuation in the
euclidean state space alone. But in many cases involving n coupled oscillators, the dynamics is
restricted to a manifold embedded in the 2n dimensional state space. For example, the dynamics of
a double pendulum can be studied on a 4 dimensional euclidean state space, but the modulo 2π
nature of dynamics means that it is restricted to a torus. There can be significant computational
gains if this continuation can be restricted to the manifold. Keeping this in mind, the possibility of
adapting the developed continuation scheme to work on the appropriate manifold will be explored.
This will involve the use of techniques from computational differential geometry.
Outreach Programme -
Refresher Course for B.Sc. Mathematics Students in Kerala State
Venue: KSOM, Kozhikode
23-29 December, 2012
This outreach programme was meant for B.Sc. Mathematics third year students, who were studying in Kerala state. The course covered some basic topics of Algebra, Analysis and Number Theory. Some first year students of M.Sc. Mathematics also participated.
Outreach Programme for Higher Secondary School Students
Venue: KSOM, Kozhikode
02 October, 2012
Second phase of outreach programme for Higher Secondary School Students in the nearby region was held at KSOM in continuation with the Outreach Programme for Higher secondary School Students conducted in May 2012. This programme connected students with mathematical role models and shared their knowledge of and passion for mathematics and its various subspecialities and related fields.
Speakers
1 | Dr. M Manickam | Director, KSOM |
2 | Prof. E. Krishnan | Formerly Professor, University College, TVM |
3 | Prof.U. K. Anandavardhanan | Professor, IITB |
4 | Prof. A K Vijayarajan | Associate Professor, KSOM |
5 | Prof. Joseph Mathew | Visiting Professor, KSOM |
Outreach Programme for Higher Secondary School Teachers
Venue: KSOM, Kozhikode
30 September- 01 October, 2012
A two days discussion meeting with MathematicsTeachers of Higher Secondary Schools in the nearby region was held at KSOM in continuation with the Outreach Programme for Higher secondary School Teachers conducted in May 2012.
Speakers
1 | Dr. M Manickam | Director, KSOM |
2 | Prof. E. Krishnan | Formerly Professor, University College, TVM |
3 | Prof.U. K. Anandavardhanan | Professor, IITB |
4 | Prof. A K Vijayarajan | Associate Professor, KSOM |
5 | Prof. Joseph Mathew | Visiting Professor, KSOM |
Outreach Programme for Higher Secondary School Students
Venue: KSOM, Kozhikode
5th May, 2012
In continuation with the discussion meeting with Higher Secondary School Mathematics Teachers held at KSOM on 7th April, 2007, an outreach programme for HSS students conducted at KSOM. KSCSTE Member Secretary Dr. K. K. Ramachandran inauguratede the programme.
Panorama Lecture
Venue : KSOM, Kozhikode
01 - 05 May, 2012
Prof. Ram Murty from Queens University, Canada delivered a series of "Panorama Lectures" on Ramanujan & L-functions from 01 to 04, May 2012.
Discussion meeting with Higher Secondary School Mathematics Teachers
Venue: KSOM, Kozhikode
7th April, 2012
Mathematics in Schools
Mathematics underpins so many aspects of our lives and provides the foundation for science, engineering, economics, finance and many other professional fields. For all these reasons, it is critical to help students early on to appreciate the beauty and power of mathematics and to begin to understand how it plays out in so many areas. Of course, teachers are already experts at encouraging and guiding students, but having the added support of a mathematical research institute provides obvious benefits not only for students but for the teachers and mathematicians as well.
Discussion Meeting
As a prelude to the outreach program for Higher Secondary School students, a one day discussion meeting held at KSOM with mathematics teachers of Higher Secondary Schools who are teaching for +1/+2 students in the near by region to discuss and find out the modalities of conducting the outreach program.
Prof. Michael A. Dritschel of University of Newcastle, UK visited KSOM
08 - 12 March, 2012
The visit was for a discussion meeting on `Operator Spaces and Operator Theory' with KSOM Faculty and researchers working in the area.