Algebra & its applications (2019)

Convener(s)

 
Name: Dr. Aparna Jain Dr. Jeetendra Aggarwal

Prof. Geetha Venkataraman
Mailing Address:

Associate Professor,
Department of Mathematics,
Shivaji College, University of Delhi,
New Delhi -110027

Assistant Professor,
Department of Mathematics,
Shivaji College, University of Delhi,
New Delhi -110027

Academic Coordinator
Ambedkar University Delhi
Delhi – 110006
Email:  jainaparna at yahoo.com  jitenaggarwal at gmail.com geetha at aud.ac.in

 TEWs are meant only for the local teachers and therefore no travel and other hospitalities will be provided to the outstation participants

Dates: 

Monday, May 6, 2019 - 09:00 to Saturday, May 11, 2019 - 18:30

Venue: 

Venue Address: 

 

Shivaji College (University of Delhi), Ring Road, Raja Garden, New Delhi – 110027.

 

 

Venue State: 

Venue City: 

PIN: 

110027

Chrono Order: 

310

Syllabus: 

The Teacher’s Enrichment Workshop (TEW) is an outreach activity of the National Centre for Mathematics (NCM), which sponsors instructional schools and workshops at several levels in various places across the country. It is meant for college teachers to revisit, update and enrich their mathematical knowledge. An important component of the workshop is the discussion hour during which the teachers will have opportunities to get their doubts cleared and work out exercises, both routine and advanced.

This workshop on Algebra and its applications is primarily for Mathematics Teachers from colleges / universities in the region of Delhi NCR. The sessions will be aimed to discuss the fundamental concepts in Group theory, Ring theory, Linear Algebra, Algebraic Coding theory and their interesting applications. It may be noted that accommodation will NOT be provided to participants.

Speakers and Tutors

S. No.

Name

Affiliation

1

Prof. Geetha Venkataraman

Ambedkar University Delhi

2

Prof. Shanta Laishram

ISI, Delhi

3

Prof. Amit Kulshreshtha

IISER, Mohali

4.

Prof. Anuradha Sharma

IIIT, Delhi

 Syllabus

Name of the Speaker with affiliation

No. of Lectures

Title

Detailed Syllabus

Prof. Geetha Venkataraman (GV), Ambedkar University Delhi

6

Groups and Symmetry

Intuitive introduction and mathematical definition of Symmetry, Finite planar figures, Strip or Frieze Patterns, Classifying Frieze patterns, Wallpaper Patterns, Symmetry in art, architecture and around us, Symmetry Groups of finite Planar Objects, Group Actions, Orbit-Stabilizer Theorem, Platonic Solids (duality, verifying Euler’s formula), Symmetry Groups of Platonic Solids, Colouring Problems, Cauchy’s Theorem, Sylow’s Theorems, Class Equation, Cayley’s Theorem, Index Theorem etc.

Prof. Shanta Laishram (SL),

ISI Delhi

7

Ring Theory with applications to Number Theory

Rings and Fundamentals, Homomorphisms and Ideals, Quotient Rings, UFD, PID, Applications to Number Theory

Prof. Amit Kulshreshtha (AK),

IISER Mohali

4

Linear algebra and its applications

Sums of squares over fields, Fibonacci series and other similar iterative processes, Google’s ranking algorithm (PageRank), Multivariable calculus, Linear algebraic groups.

Prof. Anuradha Sharma (AS),

IIIT Delhi

7

Applications of Algebra to Coding Theory

Block codes, Hamming distance of a block code,  Sphere Packing bound, Singleton bound, Linear codes over finite fields, Dual codes, Hamming weight enumerator,  MacWilliams identity, Equivalence of Linear codes, Encoding and Decoding of linear codes, Cyclic codes, Generator polynomials, Generating idempotents, Decoding of cyclic codes, Burst-error-correcting codes

 References:

  1. Groups & Symmetry
    (a) M. A. Armstrong, Groups and Symmetry, Springer-Verlag, 1988.
    (b) Michael Artin, Algebra, (2nd Edition), Pearson, 2015.
    (c) Norman L. Biggs, Discrete Mathematics, (2nd Edition), OUP, 2003.
    (d) David S. Dummit and Richard M. Foote, Abstract Algebra, (3rd Edition), John Wiley and Sons, 2004.
    (e) Joseph A. Gallian, Contemporary Abstract Algebra, (8th Edition), Cengage Learning, 2013.

  2. Ring Theory with applications to Number Theory
    (a) Robert Ash, Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates, Dover Publications, 2007. (Chapter 2).
    (b) V. V. Prasolov, Polynomials, Springer-Verlag, 2004. (Chapter 2, Section 2.1).

  3. Linear Algebra and its applications
    (a) Gilbert Strang, Linear Algebra and Its Applications, (4th Edition), Thompson Learning, 2006.
    (b) Sheldon Axler, Linear Algebra Done Right, (3rd Edition), Springer-Verlag, 2015.

  4. Applications of Algebra to Coding Theory
    (a) S. Ling and C. Xing, Coding Theory, Cambridge University Press, 2004
    (b) MacWilliams and Sloane, The Theory of error-correcting codes, North-Holland publishing company, 1983.
    (c) W. Cary Huffman and Vera Pless, Fundamental of error-correcting codes, Cambridge University Press, 2003.
    (d) Raymond Hill, A first course in Coding Theory, Oxford University Press, 1990.

Time Table: 

 Time-table (with names of speakers and tutors):

Day

Date

Lecture
1
(9.30
to
10.30)

Tea

Lecture
2
(11.00
to
12.00)

Lecture
3
(12.00
to
1.00)

Lunch

(1.00
to
2.20)

Lecture 4
(2.30
to
3.30)

Tea

Discussion

(4.00
to
5.00)

Snacks

(5.05
to
5:20)

 

 

 

 

 

 

 

 

 

 

 

Mon

06.05.2019

GV

 

GV

AK

 

AK

 

AK

 

Tue

07.05.2019

GV

 

GV

AK

 

AK

 

AK

 

Wed

08.05.2019

AS

 

AS

SL

 

SL

 

SL

 

Thu

09.05.2019

AS

 

SL

AS

 

SL

 

SL+AS

 

Fri

10.05.2019

SL

 

SL

AS

 

AS

 

AS

 

Sat

11.05.2019

SL

 

AS

GV

 

GV

 

GV

Valedictory

Selected Applicants: 

 

Instructions for participants:
 
  1. Please carry a valid identity card. 
  2. Travelling allowance and accommodation are not provided to the participants in Teacher's Enrichment Workshops. Outstation participants are requested to make their own arrangements.
  3. Selected participants are expected to attend all sessions of the workshop. Certificates of participation will be issued only to the participants with full attendance.
  4. Participants are required to bring their own notebooks, textbooks and pens etc.
    Full Name Gender Affiliation Position in College/ University Univ. / Inst. M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Deg. Date
1 23792 Dr. Gunjan Khurana Female Indraprastha College for Women Asst.Prof Delhi 2007 02/11/2018
2 23846 Ms. Apeksha Verma Female Miranda House Asst.Prof University of Allahabad 2008  
3 23865 Ms. Priyanka Tomer Female SGSITS, Indore SGSITS And Hod& Associate Professor Chaudhary Charan Singh University Campus Meerut Uttar Pradesh 2013  
4 23893 Dr Dimple Singh Thakran Female Amity University Asst.Prof M.D. Rohtak 2001 14/07/2013
5 23960 Dr. Jagbir Singh Male Department of Mathematics Asst.Prof Maharshi Dayanand University, Rohtak 2005 19/09/2014
6 24082 Mr. Gaurav Tyagi Male Mahamana Malviya Degree College , Khekra , Baghpat(U P)250101 Asst.Prof C C S University , Meerut 2009  
7 24194 Dr. Manish Garg Male The LNMIIT, Jaipur ( Deemed-to-be- University) Asst.Prof Chaudhary Charan Singh University Uttar Pardesh 2007 27/07/2012
8 24203 Dr. Deepti Kaur Female Maitreyi College, University of Delhi Asst.Prof Hansraj College, University of Delhi 2009 15/05/2018
9 24286 Ms. Teena Kohli Female Janki Devi Memorial College Asst.Prof Hansraj College, University of Delhi 2008  
10 24343 Mr Ashesh Kumar Jharwal Male Shivaji College,University of Delhi Asst.Prof Ramjas College, Univ. of Delhi 2006  
11 24406 Mr Dilip Kumar Male Maharaja Agrasen College Asst.Prof IIT Kanpur M.Sc. Mathematics 2016  
12 24417 Ms. Seema Gupta Female Bhagini Nivedita College Asst.Prof Devi Ahilya University 2006  
13 24421 Ms. Kavita Devi Female Zakir Husain Delhi College, University of Delhi Asst. Panjab University 2004 12/11/2011
14 24519 Mr. Chandra Prakash Male RAMJAS College Asst.Prof BHU 2008  
15 24538 Ms. Chanpreet Kaur Female Janki Devi Memorial College Asst.Prof DU 2010  
16 24659 Mrs. Sweeti Yadav Female Ram Lal Anand College, University of Delhi Asst.Prof University of Delhi 2011  
17 24700 Mr. Sandeep Kumar Male Ramjas College, University of Delhi Asst.Prof C.C.S. University Meerut 2007  
18 25057 Mr. Suresh Kumar Yadav Male Ramjas College Asst.Prof C C S University Meerut 2006  
19 25223 Ms. Manisha Manisha Female Government College for Women Asst.Prof IIT Kanpur 2015  
20 25349 Mr. Vinod Kumar Male Govt. College for Women Asst.Prof Indian Institute of Technology Roorkee 2011  
21 25683 Mr. Rajender Kumar Male Deshbandhu College Asst.Prof CCS University, Meerut, UP 2007  
22 25917 Dr. Priyambada Tripathi Female University of Delhi Asst.Prof Banaras Hindu University 2008 30/12/2015
23 25952 Dr. Sushil Yadav Male Maharaja Agrasen College, University of Delhi Asst.Prof Delhi University 1996 30/09/2015
24 25974 Mrs Sonia . Female Janki Devi Memorial College, DU Asst.Prof IP College for Women, DU 2010  
25 26029 Dr. Bhavneet Kaur Female Lady Shri Ram College for Women Asst.Prof University of Delhi 2004 19/11/2016
26 26031 Dr. Shilpi Verma Female Shivaji College Asst.Prof IITR, Roorkee 2000 02/08/2013
27 26129 Dr. Megha Agarwal Female Ramanujan College Asst.Prof IIT Delhi    
28 26210 Dr. Vandana Rajpal Female Shivaji College Asst.Prof IITD 2009 09/11/2014
29 26257 Dr. Sarika Goyal Female Bennett University Greater Noida Asst.Prof Delhi University 2009 31/10/2015
30 26285 Dr. Nisha Gupta Female Lakshmibai college, university of Delhi Asst.Prof Hansraj College, university of Delhi, Delhi 2003 30/11/2009
31 26346 Dr Neetu Rani Female Shivaji College, University of Delhi, Delhi Asst.Prof Kurukshetra University 1997 18/01/2009
32 26349 Mrs. Jaspreet Kaur Female St. Stephens college Asst.Prof Delhi university 2004 18/11/2017
33 26475 Mr. Jitendra Singh Male Shivaji College Asst.Prof Indian Institute of Technology, Delhi 2007  
34 26508 Ms Bhawna Bansal Gupta Female Miranda House, University of Delhi Asst.Prof Miranda House, University of Delhi 2007  
35 26550 Dr. Surbhi Madan Female Shivaji College Asst.Prof Kirori Mal College, University of Delhi 1998 24/03/2012
36 26575 Mr Umesh Chand Male MS college saharanpur Asst.Prof CCS university Meerut 2008  
37 26620 Mr. Nitesh Kumar Male Shivaji College Asst.Prof IIT GANDHINAGAR 2016  
38 26639 Dr. Ruchi Arora Female SGTB khalsa college Asst.Prof University of delhi 2000 15/07/2010
39 26701 Dr. Aparna Vyas Female Manav Rachna University Asso.Prof M.Sc., University of Allahabad, UP 2006 12/07/2010
40 26703 Mr. Mukesh Kumar Male Shivaji College, University Of Delhi Asst.Prof University Of Delhi 2015  
41 26711 Dr. Dinesh Kumar Male Deen Dayal Upadhyaya College, University Of Delhi Asst.Prof Hindu College, University of Delhi 2009 09/08/2016
42 26712 Ms. Krishma Babbar Female Lady Shri Ram College for Women, University of Delhi Guest Lecturer St. Stephen’s College, University of Delhi 2014  
43 26770 Dr Arti Sharma Female Janki Devi Memorial College Asst.Prof Jammu University 2009 19/11/2018
44 26704 Ms. Monika Yadav Female Indraprastha Institute of Information Technology Delhi PhD Indian Institute of Technology Delhi 2018  
45 26694 Mr. Sandeep Sharma Male Indraprastha Institute of Information Technology Delhi PhD Central University of Haryana 2016  
46 26713 Ms. Akansha Arora Female Indraprastha Institute of Information Technology, Delhi PhD Student Indraprastha College For Women, Delhi University (M.Sc. Mathematics) 2016  
47 24609 Mr Harshit Mathur Male Department of Mathematics, University of Delhi PhD Scholar Hindu College, University of Delhi 2013  
   Waiting List          
1 26767 Ms. Prachi Gupta Female Department of Mathematics, University of Delhi Ph.D. University of Delhi 2015  
2 26644 Dr. Dinesh Tripathi Male Manav Rachna University Asst.Prof Deen Dayal Upadhyay Gorakhpur University 2007 01/01/2017
3 24096 Mr. Vishal Gupta Male delhi university Asst.Prof IIT Guwahati 2010  
4 23943 Dr Aisha Jabeen Female Jamia Millia Islamia Guest Faculty Aligarh Muslim University 2011 21/02/2018

 

 

How to Reach: 

Click here

 

School Short Name: 

aia

Last Date Application: 

Friday, March 15, 2019

School Type: 

TEW