Seminar on Nov 27 - Pradip Kumar

Darboux chart on projective limit of weak symplectic Banach manifolds

Pradip Kumar

Harish-Chandra Research Institute, Allahabad

Time: 2 to 3 pm, Wednesday, November 27, 2013
Venue: CR 207

Abstract: In this talk, I will explain the meaning of Darboux chart on finite dimensional symplectic manifold. I will extend the definition of Darboux chart to infinite dimensional manifolds. I will prove an existence theorem for Darboux charts on weak symplectic PLB manifolds.

Seminar on October 29 - Tirthankar Bhattacharyya

Spectral and Complete Spectral Sets

Prof. Tirthankar Bhattacharyya

Indian Institute of Science, Bangalore

Time: 12 to 1 pm, Tuesday, October 29, 2013
Venue: CR 201

Abstract: A compact set \(K\) in \({\Bbb C}^n\) is a spectral set for a commuting tuple \(T=(T_1,\dots,T_n)\) of bounded Hilbert space operators if the joint spectrum of \(T\) is contained in \(K\) and if the von Neumann-type inequality \[ ||r(T_1,\dots,T_n)|| \le \sup\{ |r(z)| : z\in K\} \] holds for all rational functions \(r\) in \(Rat(K)\). If the corresponding inequality holds even for every \(m\times m\) matrix \(r=(r_{ij})\) with entries in \(Rat(K)\) then \(K\) is called a complete spectral set for \(T\). By a result of Arveson, \(K\) is a complete spectral set for \(T\) if and only if \(T\) possesses a normal boundary dilation over \(K\). For nice domains in \(\Bbb C\), such as the unit disc or annulus, the conditions of being spectral and completely spectral are equivalent. In the lecture we start with the classical theory and try to present some more recent positive and negative results on one and several variable spectral sets.

Seminar on October 10 - Sutanu Roy

Title: Associative twisted tensor product of C*-algebras

Speaker: Sutanu Roy, University of Goettingen

Date: October 10


Time & Venue: 12-1 pm, CR 204 (2nd Floor, B Wing)


Abstract: In this talk, we shall carry forward the notion of quasitriangular quantum groups, introduced by Drinfeld, in Hopf algebraic to C*-algebraic framework. Then we show that the coaction category of C*-algebras over a quasitriangular quantum group is monoidal.

New Maths Books in the Library

Lots of new books have just arrived at the SNU library, and especially ones related to algebra!

	Title	Author	Publisher
1	An Introduction to Abstract Algebra	Robinson, Derek J S	Hindustan Book Agency
2	Basic Abstract Algebra	Bhattacharya,P  Bet al	Cambridge University Press
3	Basic Algebra	Cohn, P M	Springer India
4	Algebra, Vols I to IV	Luthar and Passi	Narosa
5	Basic Quadratic Forms	Gerstein, Larry J	American Mathematical Society
6	Class Field Theory	Artin, Emil	W.A. Benjamin
7	Commutative Algebra with a View toward Algebraic Geometry	Eisenbud, David	Springer
8	Exercises in Modules and Rings	Lam, T Y	Springer
9	Exercises in Classical Ring Theory	Lam, T Y	Springer
10	Introduction to Ring Theory	Cohn, P M	Springer
11	The Classical Groups	Weyl, Hermann	Hindustan Book Agency
12	Undergraduate Algebra	Lang, Serge	Springer
13	Abstract Algebra	Dummit, David S	Wiley
14	An Introduction to Mathematical Cryptography	Hoffstein, Jeffrey	Springer
15	Finite Fields and Applications	Mullen, Gary L	American Mathematical Society
16	Further Algebra and Applications	Cohn, P M	Springer
17	Combinatorial Techniques	Sane,Sharad S	Hindustan Book Agency
18	A Classical Introduction to Modern Number Theory	Ireland,Kenneth F	Springer India
19	A Course in Number Theory and Cryptography	Koblitz, Neal	Springer India
20	Elementary Number theory	Jones, Gareth A	Springer
21	Introduction to Analytic Number Theory	Apostol	Narosa
22	Elementary  Number Theory	Krishnan, V K	Universities Press
23	An Introduction to Laplace Transforms and Fourier Series	Dyke, P P G	Springer
24	A Course in Calculus and Real analysis	Ghorpade, Sudhir	Springer
25	A Course in Multivariable Calculus and Analysis	Ghorpade, Sudhir	Springer
26	Complex Made Simple	Ullrich, David C,	American Mathematical Society
27	Complex Numbers from A to …Z	Andreescu and Andrica	Birkhauser
28	Differential Equations	Ross, Shepley L	Wiley India
29	Introduction to Calculus and Classical Analysis	Hijab, O	Springer
30	Real Mathematical Analysis	Pugh, C C	Springer
31	Introduction to Measure and Integration	Rana, I K	Narosa
32	System Dynamics	Palm, William J	Tata McGraw Hill
33	Introduction to the Mathematics of Finance	Williams, R J	American Mathematical Society
34	Geometry for College Students	Isaacs, I Martin	Brooks/Cole
35	Morse Theory	Milnor, John W	Hindustan Book Agency
36	Graph Theory	Diestel, Reinhard	Springer
37	Connected at Infinity	Bhatia, Rajendra	Hindustan Book Agency
38	Connected at Infinity II	Bhatia, Rajendra	Hindustan Book Agency
39	Mathematics and its History	Stillwell, John	Springer
40	An Introduction to Numerical Analysis	Atkinson, Kendall E	Wiley India
41	Numerical Methods for Scientific and Engineering Computation	Jain, Iyengar and Jain	New Age International
42	Linear Programming	Hadley	Narosa
43	Operations Research	Taha, Hamdy A	Pearson
44	Differential Equations with Mathematica	Abell and Braselton	Morgan Kauffmann
45	Mathematical Modelling with Case Studies	Barnes and Fulford	CRC Press

Seminar on September 25 - Abhishek Ranjan

Title:              Arbitrage Structure and Finite Date Model with Financial Restriction
Speaker:       Dr Abhishek Ranjan

Department of Applied Mathematics
Université Paris 1 Panthéon Sorbonne, France

Time:               2 pm, Wednesday, September 25, 2013.

Venue:             TBA

Abstract:         We consider a (T+1)-date model of a financial exchange economy with finitely many agents having non-ordered preferences and portfolio constraints. There is a market for physical commodities for every state today and in the future, and financial transfers across time and states are allowed by means of finitely many nominal or numeraire assets. We examine the properties of the financial structure F and the set of its (limited) arbitrage-free prices Q_F. The set of arbitrage-free prices is shown to be a convex cone under a sufficient condition that holds in particular for short lived assets. Furthermore, we provide examples of equivalent financial structures F and F’ such that Q_F is a convex cone, but Q_F’ is neither convex nor a cone. At the end, we provide several existence results of equilibrium in a financial exchange economy for which portfolios are either defined by linear constraints or a convex set extending the framework of unconstrained case by Cass (1984, 2006), Werner (1985), Duffie (1987), Gaenakopolos and Polemarchakis (1997), framework of linear equality constraints by Balasko et al. (1990) and framework of 2-date by Cornet and Gopalan (2007), Aouani and Cornet (2011, 2013).

About the Speaker:   Dr Ranjan completed his PhD from the Paris School of Economics and Université Paris 1 Panthéon Sorbonne in 2012. His research interests are in Applied Mathematics, General Equilibrium Models, Financial Economics, and Decision Under Uncertainty.

Seminar on September 24 - Vijay Patankar

Congruences between Modular Forms and p-Adic Families of Modular Forms

(from Ramanujan to Hida)

Speaker:       Dr Vijay Patankar

                         International Institute of Information Technology, Bangalore

Time:               3 pm, Tuesday, September 24, 2013.

Venue:            TBA

Abstract:  In this expository talk, we will give an introduction to congruences between modular forms as first observed by Ramanujan and how that has led to p-adic families of modular forms. 

Among many other things, Ramanujan studied certain natural arithmetic functions such as the Partition function and the Sum of Divisors function.  In 1916, Ramanujan in his paper On certain arithmetical functions, observed certain congruences between distinct arithmetic functions and hence between the generating functions associated to them (which are in fact modular forms). In 1967, Serre interpreted these congruences in terms of Galois representations and conjectured the existence of Galois representations associated to modular forms (proved by Deligne 1968). In 1972, Serre constructed a p-adic family of Eisenstein forms. In 1986, Hida constructed p-adic families of cusp-forms and the associated p-adic families of Galois representations.

All these developments were essential tools for Andrew Wiles' proof of Fermat's Last Theorem. 

About the Speaker: Dr Patankar obtained his PhD from the University of Toronto in 2005. He has held positions at the Cold Spring Harbor Laboratory (New York), Microsoft Research India (Bangalore), Bhaskaracharya Pratishthana (Pune) and Indian Statistical Institute (Chennai). His research interests are in Number Theory, Algebraic Complexity Theory and Cryptography.

MAT101 Calculus I - Assignment 1 - Solutions

M101 Student Data

Students enrolled in M101 Calculus I for the Monsoon 2013 semester should fill this form to get enrolled on the course account in Blackboard and to get regular updates etc. If the form is not visible below, then login to your SNU account in another tab/window, and then refresh this page.

MAT 101 - Calculus I - Assignment 2

Please start on the Exercises from Sections 1.6 to 2.4 right away. Your first midterm on Sep 14 will be up to Sec 2.4.

Assignment 2

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Part A

The following exercises from Stewart's Essential Calculus are to be solved for presentation and discussion in the tutorials:

• [Section 1.6] 1, 3, 13, 26, 41, 47
• [Section 2.1] 3, 7, 10, 16, 26, 31, 47
• [Section 2.2] 1, 3, 6, 9, 21, 33, 43
• [Section 2.3] 10, 18, 21, 22, 33, 57, 63
• [Section 2.4] 6 to 10, 25, 27, 43, 48, 54
• [Section 2.5] 4, 23, 47, 55, 65, 66
• [Section 2.6] 8, 16, 19, 32
• [Section 2.7] 2, 9, 13, 24
• [Section 2.8] 7, 21
• [Section 3.1] 13, 23, 24
• [Section 3.2] 22, 32, 35, 66
• [Section 3.3] 7, 29, 39, 58
• [Section 3.4] 9, 20

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Part B

Submit written solutions to the following to your tutor by September 23:

• [Section 1.6] 19, 23, 49
• [Section 2.1] 28, 48
• [Section 2.2] 4, 23, 39
• [Section 2.3] 23, 40, 67
• [Section 2.4] 16, 30, 51
• [Section 2.5] 49, 57, 69
• [Section 2.6] 11, 17, 44
• [Section 2.7] 11, 28, 38
• [Section 2.8] 13, 24
• [Section 3.1] 25, 31
• [Section 3.2] 23, 38, 78
• [Section 3.3] 23, 62, 68
• [Section 3.4] 17

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Extra Credit

Submit the following to Prof Habib by September 16: Consider the cubic function \(f(x)=x^3+ax^2+bx+c\). Calculate \(\lim\limits_{x\to\pm\infty}\frac{f(x)}{x^3}\)and use this to show that there is a real number \(c\) such that \(f(c)=0\).

Edit on Sep 16: Last date of submission of Extra Credit problem is changed to Friday, Sep  20. Submission must be to Prof Habib. Also note that there are two uses of \(c\) in the problem which is an oversight. Change the second \(c\) to \(d\).

MAT101 Calculus I - Assignment 1

Department of Mathematics, Shiv Nadar University
Monsoon Semester 2013-14
MAT 101 Calculus I

Assignment 1

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Part A

The following exercises from Stewart's Essential Calculus are to be solved for presentation & discussion in the tutorials:

• [Section 1.1] 1, 3, 4, 17, 23, 25, 28, 35, 43, 51, 57, 59, 61
• [Section 1.2] 2, 4, 5, 8, 13, 17, 23, 26, 35, 52, 53
• [Section 1.3] 3, 7, 11, 23, 29
• [Section 1.4] 10, 13, 21, 22, 30, 43, 46
• [Section 1.5] 3, 10, 13, 15, 26, 35, 37

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Part B

Submit written solutions of the following to your Tutor by September 2:

• [Section 1.1] 5, 6, 18, 44, 62
• [Section 1.2] 18, 49, 58, 62
• [Section 1.3] 9, 27, 43
• [Section 1.4] 7, 23, 31
• [Section 1.5] 16, 31, 40

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Extra Credit

• [Section 1.5] 47

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IAYM Selections

The "Inviting All Young Minds" summer internship programme is being organized at SNU from June 10 to 29. The following SNU students have been selected for it:

Laavanya Gupta	BS Mathematics
Manika	BTech CSE
Akshay Prasad	BTech ECE
Nipun Abbi	BTech ME
Dikshant Chitkara	BTech ECE
Shivangana Gupta	BTech EEE
Nidhi Dubey	BTech EEE
Balakumaran S E	BTech ME
Ankita Srivastav	BTech CSE
Rahul Madan	BTech CSE
Aditya Goel	BTech ME
Shubhankar Mathur	BTech CSE
Akanksha Tiwari	BTech EEE
Shubham Jain	BTech EEE

In addition there may be 2 or 3 seats available for students from outside SNU. The eligibility criterion is that you should have completed Class XII and should have taken Mathematics in +2. You can apply by filling in the online application form before 5pm on Tuesday, June 4.

The IAYM 2013 program features student projects applying mathematics and computation skills to problems in financial modeling and cryptography. Selected students get a Rs 5000 stipend and accommodation and food in the SNU hostels.

Admissions to Minor in Mathematics

The following students have been admitted to the Minor in Mathematics. Welcome to the department! We'll shortly sit down with you and work out your program for the next academic year.

	Name	Major
1	Veeramachaneni Bharath	Civil
2	Akshit Singhal	CSE
3	Ansh Gandhi	CSE
4	Anurag Joshi	CSE
5	Jyoti Joshi	CSE
6	Manika	CSE
7	Sacchit Sreenivasan	CSE
8	Varun Mishra	CSE
9	Akshay Prasad	ECE
10	Gokul Devunuri	ECE
11	Pranav Sridhar	ECE
12	Sahana V	ECE
13	Shikha Elizabeth Joseph	ECE
14	Siva Suganya B	EE
15	Akhilesh Vij	Mech
16	G Sai Charan	Mech
17	Shahrukh Athar	Physics
18	Akshat Saxena	Economics
19	Aneesha Parvathaneni	Economics
20	Kaustubh Sanjay Kambekar	Economics

Minor in Mathematics Form

Applications for the Maths Minor are closed. Results will be out shortly!

Minor in Mathematics Announcement

Undergraduate students of Shiv Nadar University who are not majoring in Mathematics have the option to take a Minor in Mathematics. A Minor in Mathematics can serve two distinct functions (apart from enjoying the beauty of the subject!):

• Acquiring the academic background for higher studies in Mathematics.
• Acquiring modelling and computational skills for applications of Mathematics in other disciplines or in industry.

Academic Requirements:

You have to acquire a minimum of 27 credits from the University Wide Elective (UWE) courses offered by the Department of Mathematics. These credits must satisfy the following minimum requirements:

1. Three courses from Group A for a total of 12 credits: MAT 101 (Calculus I), MAT 240 (Algebra I), MAT 260 (Linear Algebra), MAT 280 (Numerical Analysis I), MAT 284 (Probability & Statistics).
2. One course from Group B (3 credits): MAT 199, 299, 399, 499 (Projects).
3. Remainder from any other UWE courses offered by the Department of Mathematics.
4. The above is subject to the further requirement that a course should not count towards both Major and Minor requirements.
5. The credit requirement may be lowered to 23 credits for majors which already have a significant component of compulsory Mathematics courses.

The Undergraduate Advisor for Mathematics will help you work out an appropriate choice of courses depending on your interests and background.

How to Apply:

1. For the 2013 session, there are 20 seats available for a Minor in Mathematics.
2. You are eligible to apply for the Minor if you have already earned or are currently enrolled in at least 3 credits from courses offered by the Department of Mathematics, and if your GPA from these courses is at least 6.
3. Eligible applicants will be interviewed, and admission to the Minor will be determined by the results of that interview. The probable interview dates are April 29 and 30.
4. You can apply by filling out the online form before 5pm on April 26. (Click to go to the online form.)
5. For further details please contact the UG Advisor for Mathematics, Amber Habib. You can meet him during his office hours or send an email to amber.habib@snu.edu.in to make an enquiry or seek an appointment.
6. Please note that you must take admission for the Minor as described here. It is not enough to merely take adequate credits on your own. 

Other Information:

1. Once admitted to the Minor in Mathematics, you will select courses for the Minor in consultation with the UG Advisor for Mathematics.
2. You must sign up for the Minor before the end of your 6th semester. However, it is advisable to do so earlier so that there is sufficient time to plan your courses. The best time is during your 3rd or 4th semesters.
3. If you fail to complete the Minor during your first 4 years, you may have to spend an extra semester to complete it. If you do so, any scholarship or fee waiver you were granted for your regular course of study will lapse and you will have to pay the full fees for the extra period.
4. You may of course enroll for UWE courses offered by the Department without being admitted to the Minor. However, students enrolled for the Minor will have priority while registering for these courses. The Department will also do its best to schedule courses so that Minor students will be able to complete their requirements.