ISL Galois Theory (2014)
Venue: | S.G.G.S. Institute of Engineering and Technology Nanded, Maharashtra |
Dates: | 1^{st} to 13^{th} Dec, 2014 |
Convener(s) | Speakers, Syllabus and Time table | Applicants/Participants |
Name | Sudhir R. Ghorpade | Arunkumar R. Patil |
Mailing Address | Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076 |
S.G.G.S. Institute of Engineering and Technology, Vishnupuri, Nanded 431 606 |
Resource Persons:
Five resource persons from reputed institutions of India delivered lectures in the school. These resource persons were as follows:
1. Prof. Sudhir R Ghorpade, IIT Mumbai.
2. Prof. Arunkumar R. Patil, SGGS IE and T, Nanded
3. Prof. Indranath Sengupta, IIT Gandhinagar.
4. Prof. Jugal K. Verma, IIT Mumbai.
5. Prof. Balwant Singh, CEBS, Mumbai.
These speakers together delivered 24 lectures of one-and-half hour duration spread over two weeks. In addition, four lectures on Unity in Mathematics were arranged. These lectures were given by following two eminent speakers:
1. Prof. V. Srinivas, School of Mathematics, TIFR, Mumbai had delivered a talk on Connection of Galois Theory with fundamental groups on December 11, 2014.
2. Prof. T. N. Venkataramana, School of Mathematics, TIFR, Mumbai had delivered a talk on connection of Galois Theory with monodromy groups on December 12, 2014.
Tutorials:
Two hours tutorials were conducted on every day. Along with instructors following three persons assisted as a tutor to conduct tutorial sessions:
1. Mrinmoy Datta, Reserach Scholar, IIT Bombay, Mumbai
2. Joydip Saha, RKM Vivekananda University, Belur Math, Howrah, Kolkatta
3. Gaurab Tripathi, Research Scholar, Jadhavpur University
Week 1 | ||||||
Time |
December 1 |
December 2 Tuesday |
December 3 Wednesday |
December 4 |
December 5 Friday |
December 6 Satuday |
9:30 - 11:00 | SRG | SRG | SRG | IS | SRG | IS |
11:00 - 11:30 | Tea/coffee | |||||
11:30 - 1:00 | ARP | ARP | SRG | IS | IS | IS |
Lunch | ||||||
2:30 - 4:30 | Tutorial (SRG + Tutors) |
Tutorial (SRG + Tutors) |
Tutorial (ARP+ Tutors) |
Tutorial (IS + Tutors) |
Tutorial (IS + Tutors) |
Tutorial (IS + Tutors) |
4:30 - 5:00 | Tea/ coffee/ Snacks |
Week 2 | ||||||
Time |
December 8 |
December 9 Tuesday |
December 10 Wednesday |
December 11 |
December 12 Friday |
December 13 Satuday |
9:00 - 10:30 | JKV | JKV | BS | JKV | UiMT - VS | BS |
10:30 - 11:00 | Tea/coffee | |||||
11:00 - 12:30 | IS | SRG | JKV | UiMT - VS | UiMT - VS | Tutorial (BS + Tutors) |
Lunch | ||||||
2:00 - 3:30 | JKV | JKV | BS | UiMT - VS | BS | |
3:30 - 4:00 | Tea/ coffee/ Snacks | |||||
4:00 - 6:00 | Tutorial (IS + Tutors) |
Tutorial (JKV + Tutors) |
Tutorial (JKV + Tutors) |
Tutorial (BS + Tutors) |
Tutorial (JKV + Tutors) |
Speakers | Unity in Mathematics Talks | Tutors |
SRG - Sudhir R. Ghorpade IIT Bombay |
VS - V. Srinivas TIFR, Mumbai |
Mrinmoy Datta |
ARP - Arunkumar R. Patil SGGS, Nanded |
TNV - T. N. Venkataramana TIFR, Mumbai |
Joydip Saha |
IS - Indranath Sengupta IIT Gandhinagar |
Gaurab Tripathi | |
JKV - Jugal K. Verma IIT Bombay |
||
BS - Balwant Singh CEBS, Mumbai |
Topics covered
SRG Sudhi R Ghorpade (in Weeks 1 and 2)
- Evolution of the theory of equations and a historical overview of Galois theory
- Permutations, Cycles and transpositions, Symmetric Functions
- Fundamental Theorem for Symmetric Polynomials, Newton’s identities
- Polynomials and their roots, Fundamental Theorem of Algebra, Irreducibility criteria for polynomials over Q
- Resultants and Discriminants
- Norm, Trace and Discriminant
ARP Arunkumar R. Patil
- Group actions, Cauchy’s theorem
- Sylow’s theorems and Structure Theorem for finite abelian groups
IS Indranath Sengupta (in Weeks 1 and 2)
- Simple groups: simplicity of A_{n} and PSL(2, p)
- Solvable groups, Composition series and Jordan-Holder Theorem
- Field extensions; basic properties
- Splitting fields and normal extensions
- Separable extensions, Primitive element theorem
- Construction by ruler and compass, classical Greek problems (in Week 2)
JKV J.K.Verma (in Week 2)
- Galois groups and Galois extensions
- Fundamental Theorem of Galois Theory
- Applications to: Regular polygons, Fundamental theorem of algebra, Cubic equations
- Calculating Galois groups of cubics and quartics
- Solvable extensions and Galois’ criteria for solvability
BS Balwant Singh (in Week 2)
- Finite fields
- Construction of algebraic closure of a field, Examples
- Roots of unity, cyclotomic extensions
- Cyclic extensions, Hilbert’s Theorem 90, Artin-Schreier extensions
Unity in Mathematics Talks
- VS V. Srinivas : Connection with fundamental groups
- TNV T. N. Venkataramana : Connection with monodromy groups
Message to the Participants of ISL on Galois Theory, Nanded
Galois theory is one of the most beautiful topics in mathematics. We have planned an exciting programme for you and we hope you will enjoy it and benefit from it. However, in order to get the most out of this course, we recommend that you follow the guidelines given below.
PRE-REQUISITES: Participants are expected to be familiar with Linear Algebra and rudiments of Abstract Algebra (at least some basic working knowledge of groups, rings, fields and vector spaces). You may like to review this before coming to Nanded. There are several books available on Linear Algebra as well as Abstract Algebra, and also a vast amount of resources on the Internet. We recommend in particular, M. Artin’s Algebra. A low-priced Indian edition is readily available in many bookshops and on the Internet; see, for example:
http://www.flipkart.com/algebra-2-e-english-2nd/p/itmdx5gwcgrgbjxh?pid=9788120343290
Artin’s book covers both linear algebra and abstract algebra, and it will suffice to be familiar with Chapters 1-4 and 10 from this book. Another possibility is to look A First Course in Abstract Algebra, by J. B. Fraleigh, also available in Indian reprint at bookstores or Flipkart.
More enterprising persons among you may also be able to get a free soft copy of these books on the Internet by doing a Google search with keywords such as author, title, pdf.
Those who prefer watching and listening to lectures rather than read books may see at least the first few lectures of a nice video course on algebra at Harvard by Prof. Benedict Gross:
http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra
For the “Unity in Mathematics” talks, it will be desirable to have some exposure to basics of topology and complex analysis. Standard references here are Topology, by J. R. Munkres and Complex Analysis, by L. Ahlfors.
DURING THE INSTRUCTIONAL SCHOOL: There will be at least 3 hours of lectures and 2 hours of ttutorials almost every day. A lot of topics will get covered in a rather short time. It is important that you keep pace with it and not miss any lectures or tutorials. Also you are expected to put in at least 3 hours of self-study each day to go over the material covered on that day and to solve problems. Do not hesitate to ask questions during or after the lectures, and please be sure to take an active part in the tutorials. Do not plan any other extraneous activity or visit during the days of the school. You may, however, wish to take a day off on Sunday, 7th December 2014 and plan a touristic visit on your own to the city of Nanded or nearby places such as Ellora caves near Aurangabad. Outstation participants will be paid a daily allowance on this day instead of free breakfast, lunch and dinner. We wish you a pleasant and fruitful stay in Nanded.
- Sudhir Ghorpade and Arunkumar Patil
Actual Participants |
Sr. | SID | Full Name | Gender |
Affiliation |
State | Position | Univ/ Inst. Ms.C MA |
Year of Passing M.Sc./ M.A | Ph.D. Deg. Date |
1 | 6726 | Mr. Nitin Shridhar Darkunde | Male | SCHOOL OF MATHEMATICAL SCIENCES, S.R.T.M.UNIVERSITY, NANDED. Nanded |
Maharashtra | Assistant Professor | UNIVERSITY OF PUNE, PUNE | 2008 | |
2 | 6900 | Mr Uday Subhash Divyaveer | Male | Swami Ramanand Teerth Marathwada University | Maharashtra | Assistant Professor |
IIT-B |
2009 | |
3 | 6862 | Dr. Surendranath Reddy | Male | Swami Ramanand Teerth Marathwada University | Maharashtra | Assistnat Professor | University of Hyderabad | 2006 | 11 Jul 2012 |
4 | 6810 | Mr Mahesh Sahebrao Wavare | Male | RAJARSHI SHAHU MAHAVIDYALAYA, LATUR | Maharashtra | Assistant Professor and Head | PUNE UNIVERSITY, PUNE | 2002 | |
5 | 6901 | Mr. Sharad Bhagwanrao Kadam | Male | Anandibai Raorane Arts, Commerce & Science College, Vaibhavwadi | Maharashtra | Assistant Professor | School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded | 2012 | |
6 | 7084 | Mr. Dipak Sandu Jadhav | Male | Smt. Chandibai Himathmal Mansukhani College | Maharashtra | Assistant Professor | University of Mumbai | 2008 | |
7 | 6779 | Dr. Rupali Jain | Female | SRTM University | Maharashtra | Assistant Professor | Dr. BAMU, Aurangabad | 2005 | 21 Feb 2014 |
8 | 7387 | Mr. Subhash Krishnan | Male | K. J. Somaiya College of Science and Commerce | Maharashtra | Associate Professor | Mumbai University | 1990 | |
9 | 7274 | Mr. Amol Khandagale | Male | Department of Mathematics, Dr. Babasaeb Ambedkar Marathwada University, Aurangabad | Maharashtra | Asst Prof. | M. Sc. | 2006 | |
10 | 7214 | Ms. Jita Parida | Female | Priyadarshini Indira Mahavidyalaya , Sambalpur University | Orissa | Lecturer | Sambalpur University | 2004 | |
11 | 6938 | Mr. Bhairunath Shivaji Satpute | Male | Vaidyanath College,Parli-V. | Maharashtra | Assiatant Professor | Shivaji Univesity | 2002 | |
12 | 6758 | Miss Syed Zarqua Mohammedi | Female | S.G.G.S IE&T | Maharashtra | lecturer | S.R.T.M.University | 2011 | |
13 | 7391 | Mr Prashant Gurulingayya Swami | Male | SJCET, Palghar | Maharashtra | Assistant Professor | S.R.T.M.University NANDED | 2010 | |
14 | 7248 | Ms. Sudeshna Roy | Female | IIT BOMBAY | Maharashtra | PhD | JADAVPUR UNIVERSITY | 2013 | |
15 | 7550 | Mr. Samriddho Roy | Male | IIT Bombay | Maharashtra | PhD | Jadavpur University | 2013 | |
16 | 7422 | Mr. Arindam Jana | Male | IIT BOMBAY | Maharashtra | Phd | RAMAKRISHNA MISSION VIDYAMANDIRA | 2012 | |
17 | 7423 | Mr. Avijit Panja | Male | IIT BOMBAY | Maharashtra | Phd | RAMAKRISHNA MISSION VIDYAMANDIRA | 2012 | |
18 | 7094 | Mr. Sachin Pandurang Basude | Male | School of Mathematical Sciences | Maharashtra | Ph.D student | Swami Ramanand Teerth Marathwada University | 2011 | |
19 | 7251 | Mr. Gobinda Rakshit | Male | IIT Bombay | Maharashtra | Research Scholar | IIT Kanpur | 2011 | |
20 | 6738 | Ms. Tripti Dahiya | Female | The maharaja sayaji rao university of Baroda | Gujarat | Msc student | the maharaja sayaji rao university of Baroda | Appeared/ Awaiting Result | |
21 | 7215 | Dr. Pasham Narasimha Swamy | Male | GITAM University | Andhra Pradesh | Assistant Professor | Osmania University | 2002 | |
22 | 7546 | Mr Umanath S | Male | JAMAL MOHAMED COLLEGE | Tamil Nadu | M.Sc STUDENT | JAMAL MOHAMED COLLEGE | Appeared/ Awaiting Result | |
23 | 6819 | Ms. Jyoti Singh Siwach | Female | THE MAHARAJA SAYAJIRAO UNIVERSITY OF BARODA, VADODARA | Gujarat | MSc STUDENT | UNIVERSITY | Appeared/ Awaiting Result | |
24 | 6756 | Mr. Amit Sharma | Male | PRATAP INSTITUE OF TECHNOLOGY AND SCIENCE | Rajasthan | Assistant Professor | Maharshi Dayanand University, Rohtak | 2006 | |
25 | 7326 | Ms. Sharmishtha Sunil Deshmukh | Female | G.R. Patil College | Maharashtra | Assistant Professor. | S.R.T.M.U. Nanded | 2012 | |
26 | 7239 | Mr Rajesh Digambarrao Sonkamble | Male | EKLVAYA RESIDENTIAL SCHOOL | Maharashtra | Post Graduate Teacher | SRTMU NANDED | 2006 | |
27 | Raju A. Muneshwar | Assistant Professor | Science College,Nanded. | 1997 |
How to reach
The Instructional School for Lecturers on Galois Theory will be held at the SGGS Institute of Engineering and Technology, Nanded. Nanded is a large city in the Marathwada region of Maharashtra and is well connected to most places in India by train. For example, there are direct trains from Amritsar, Delhi, Mumbai, Nagpur, Pune, Bangalore, Hyderabad, and Aurangabad. When making a train booking, beware that the official name of the Nanded Railway station in the IRCTC website is H SAHIB NANDED (being an abbreviation for Hazur Sahib Nanded) and the codename is NED. Currently, there are no direct flights to Nanded. But it is possibly to fly to Aurangabad or Hyderabad and reach Nanded by road in about 5 hours.In Nanded, the SGGS Institute of Engineering and Technologyis popularly known as SGGS Engineering College. It is located at Vishnupuri and is about 10 kms away from the Nanded railway Station (=Hazur Sahib Nanded Station). This station has two sides named `Gokul Nagar Side' and `Main Side'. The Main side is just beside Platform no. 1. Get off at the Main side (do not go to Gokul Nagar side), and you will see an AutoRickshaw stand. One can ask auto rickshaw driver to take you to SGGS Engineering College Vishnupuri. It will cost you Rs. 100 (maximum) for an individual ride. A shared auto rickshaw ride costs Rs. 25/- per person.Auto rickshaw's are available easily everywhere in Nanded.