Real Analysis, Multivariable Calculus and Linear Algebra (2022)

 

Convener(s)
 
Name: Prof. Manjunath Krishnapur Susobhan Mazumdar
Mailing Address: Department of Mathematics
IISC Bangalore 		Department of Mathematics
St. Joseph’s College, (Autonomous), Bangalore
Email: manju at iisc.ac.in susobhan.sjc at gmail.com

 

In each of the courses, we will cover the basics of the subject and try to explain the most fundamental concepts well. It is expected that the audience has already seen the material in some form or the other, but by experience we know that many teachers might not have fully explored the meaning behind the concepts. Even some basic concepts like Cauchy sequences or linear transformations sometimes remains unclear. The main goal is to convey the underlying meaning behind these abstract-looking notions. In addition, we intend to have many tutorials/problem sessions to supplement the lectures. The goal of the workshop will be to bring the teachers to a level where they can solve problems at the level of JAM exam or the NBHM exam or NET exam and thus benefit the students as well. This program will have a considerable positive effect on students in many colleges/universities.

Dates: 

Monday, January 17, 2022 - 19:00 to Saturday, February 5, 2022 - 19:00

Venue: 

Venue Address: 

St. Joseph’s College, (Autonomous), Bangalore
PB 27094, 36 Lalbagh Road
Bangalore - 560 027

 

 

Venue State: 

Venue City: 

PIN: 

560027

Chrono Order: 

367

Syllabus: 

 

Syllabus to be covered in terms of modules of 6 lectures each :

 

Name of the Speaker No. of Lectures Detailed Syllabus
Prof. Koushik Ramachandran
Department of Mathematics
TIFR-CAM, Bangalore		 4 Real analysis(RA): Real numbers. Sequences and series of real numbers (Cauchy sequences, Heine-Borel, Bolzano-Weierstrass). Continuity and uniform continuity. Integration. Differentiation.
Prof. Divakaran D
Department of Mathematics
Azim Premji University , Bangalore		 4
Prof. R. Venkatesh,
Department of Mathematics IISC Bangalore		 4 Linear algebra(LA):Finite dimensional vector spaces over real or complex fields. Dual space, linear transformations. Determinant, characteristic polynomial, Eigenvalues and eigenvectors. Spectral theorem for self-adjoint linear operators. If possible, some `real-world' uses of matrices will be discussed. Multivariable calculus(MC): The derivative in higher dimensions. Gradient, divergence, curl, etc. Greens' theorem and Stoke's theorem (without the use of forms, more intuitive approach). Inverse function theorem.
Prof. Manjunath Krishnapur
Professor, Department of Mathematics IISC Bangalore		 4
Prof. A. K. Nandakumaran
Department of Mathematics IISC Bangalore		 4  Multivariable calculus(MC): The derivative in higher dimensions. Gradient, divergence, curl, etc. Greens' theorem and Stoke's theorem (without the use of forms, more intuitive approach). Inverse function theorem.
Prof.  Purvi Gupta
Department of Mathematics
IISC Bangalore		 4

 

References:
Linear algebra:

  • Gilbert Strang, Linear Algebra and Its Applications
  • Sheldon Axler, Linear algebra done right
  • David C Lay, Linear Algebra and its applications
  • Otto Bretscher, Linear Algebra with Applications

 

Real analysis:

  • Robert G Bartle and Donald R Sherbert, Introduction to Real Analysis
  • Sterling K Berberian, A first course in Real Analysis
  • Elementary Analysis, Kenneth A Ross
  • Sudhir R Ghorpade, Balmohan V Limaye, A course in Calculus and Real Analysis
  • Apostol, T. M., Mathematical Analysis
  • Tao, Analysis-I (TRIM series)
  • Ajit Kumar, S Kumaresan, A basic course in Real Analysis

Multivariable calculus:

  • Tao, Analysis-II (TRIM series)
  • Charles Chapman Pugh, Real Mathematical Analysis
  • Sudhir R Ghorpade, Balmohan V Limaye, A course in Multivariable , Calculus and Analysis
  • Peter D Lax and Maria Shea Terrell, Multivariable Calculus with Applications
  • Apostol, T. M., Mathematical Analysis
  • Spivak, M., Calculus on Manifolds

 

Names of the tutor(s) / course associate with their affiliation and status:

  1. Linear Algebra: Dr. Kousik Dhara, Post-Doctoral Fellow, Weizmann Institute of Science, Bangalore and
    Dr. Arundhati Krishnan, Post Doctoral Fellow, University of Waterloo
  2. Real Analysis: Dr. Raisa D’souza, Assistant Professor, St. Joseph’s College, (Autonomous), Bangalore and
    Dr. Tulsi Srinivasan, Assistant Professor, Azim Premji University, Bangalore
  3. Multivariable Calculus: Aakanksha Jain, Research Scholar, Indian Institute of Science, Pritam Ganguly,
    Research Scholar, Indian Institute of Science

 

Time Table: 

  Tentativetime-table:

  WEEK1 WEEK 2 WEEK 3
Day Date 6:00–7:00 PM 7:10–8:10 PM Date 6:00–7:00 PM 7:10–8:10 PM Date 6:00–7:00 PM 7:10–8:10 PM
Mon 17/01 LA1(MK) RA1(KR) 24/01 LA5(VN) RA5(DD) 31/01 LA7(VN) MC3(ND)
Tues 18/01 LA2(MK) RA2(KR) 25/01 LA6(VN) RA6(DD) 01/02 LA8(VN) MC4(ND)
Wed 19/01 Tutorial LA I
(KD+AR)		 Tutorial RA I
(RD+TL)		 26/01 Tutorial RA III
(RD+TL)		 Tutorial LA III
(KD+AR)		 02/02 Tutorial LA IV
(KD+AR)		 Tutorial MC II
(AJ+PG)
Thu 20/01 LA3(MK) RA3(KR) 27/01 RA7(DD) MC1(ND) 03/02 MC5(PV) MC6(PV)
Fri 21/01 LA4(MK) RA4(KR) 28/01 RA8(DD) MC2(ND) 04/02 MC7(PV) MC8(PV)
Sat 22/01 Tutorial LA II
(KD+AR4)		 Tutorial RA II
(RD+TL)		 29/01 Tutorial RA IV
(RD+TL)		 Tutorial MC I
(AJ+PG)		 05/02 Tutorial MC III
(AJ+PG)		 Tutorial MC IV
(AJ+PG)

 

Lecturers
ND: A. K. Nandakumaran
VN: R Venkatesh
MK: Manjunath Krishnapur
KR: Koushik Ramachandran
DD: Divakaran D
TBA: To be announced

Tutors
AR: Arundhati Krishnan,
KD: Koushik Dhara,
TL: Tulsi Srinivasan,
RD: Raisa D’souza,
AJ: Aakanksha Jain
PG: Pritam Ganguly

 

 

 

Selected Applicants: 

 

Serial SID Full Name Gender Affiliation Position in College/ University Year of Passing M.Sc./M.A Ph.D. Degree Date
1 33439 Prof. Yoshuva Genesis Male Bishop Heber College Assistant Professor 2017  
2 33440 Prof. Muthuvel Muthuvel Male Bishop Heber college, Trichy Assistant Professor 2014  
3 33641 Mr. Darshan A Male Sri. H. D. Devegowda Government First Grade College Assistant Professor 2014  
4 33695 Dr, Vidya K N Female St. Philomena's College Assistant Professor 2014 16/04/2019
5 33827 Dr Syed Ali Male Thiruvalluvar University
Vellore.632115.		 Assistant Professor 2005 25/12/2010
6 34805 Mr. Vishalsingh Sarjeetsingh Chauhan Male DIEMS, Aurangabad Asst Prof 2008  
7 37032 Mr Mukesh Dhanuka Male Larambha College, Larambha Lecturer 2015  
8 37052 Mr. Ranjit Gangadhar Ghumde Male Shri Ramdeobaba College of Engineering and Management, Nagpur Assistant Professore 2007 07/02/2017
9 37068 Dr. Avinoy Paul Male Cachar College Assistant Professor 2004 01/07/2014
10 37317 Dr. Sonia - Female Chandigarh University Assistant Professor 2004 19/09/2019
11 37358 Dr. Munish Kansal Male Thapar Institute of Engineering and Technology Assistant Professor 2009 01/03/2017
12 37428 Mr Rock Ramesh Male St.Joseph's College (Autonomous) Assistant Professor 2006  
13 37447 Dr. Rajender Kumar Male Deshbandhu College Assist. Prof. 2007  
14 37464 Mr. Suresh Shivarudrappa Hiremath Male R A Podar College of Commerce and Economics Autonomous Matunga Mumbai Assistant Professor 2006 16/11/2016
15 37467 Mr. Bhimanand Pandurang Gajbhare Male vaidyanath Collège Parli-Vaijnath, Dist. Beed Assistant Professor 2005  
16 37475 Mr. Debdut Sengupta Sengupta Male SALESIAN COLLEGE Asst. Prof. 2014  
17 37518 Ms. Shital Dilip Solanki Female Ajeenkya DY Patil University, Pune Assistant Professor, PhD Student 2010 31/01/2020
18 37521 Dr Madhusudhan S Male Alva's Institute of Engineering and Technology Associate Professor 2007 18/11/2021
19 37523 Mrs. Karabi Saikia Female Dhakuakhana College Asst. Prof. 2004  
20 37527 Dr. Gautam Kalita Male Indian Institute of Information Technology Guwahati Assistant Professor 2010 28/02/2014
21 37570 Dr. Nathiya Narayanaraju Female Vellore Institute of Technology Chennai Assistant Professor 2008 03/06/2016
22 37601 Mr Yadaiah Venkata Male PU PG centre - Kollapur Assistant professor on contract 2001  
23 37629 Mr. Firdous Ahmad Mala Male GDC Sopore Assistant Professor 2007  
24 37637 Mr. Mudassir Ahmad Bhat Male Govt. Degree College Boys Anantnag Assistant Professor 2009  
25 37671 Mr. Anapagaddi Sudhir Kumar Male RGUKT Assistant Professor 2013  
26 37706 Mr Sameer Ahmad Gupkari Gupkari Male JKIMS Assistant Professor 2005  
27 37714 Dr. Anil Sharma Male Chandigarh University Assistant Professor 2013 09/04/2018
28 37752 Mr Prafull Chandra Das Male Pathani Samanta Degree College, Khandapada, Nayagarh Lecturer 2009  
29 37755 Dr. Rajanish Kumar Rai Male Jaypee Institute of Information Technology, Noida. Assistant Professor 2014 19/02/2020
30 37796 Dr. Dinesh Tripathi Male Manav Rachna University Asso. Prof. 2007 01/01/2017
31 37797 Dr. Rahul Shukla Male Ramjas College, University of Delhi Assistant Professor 2013 11/09/2021
32 37805 Dr Gaurav Kumar Male GDC Paloura Assistant Professor 2011 29/12/2017
33 37808 Dr. Revathy M Female KPR College of Arts Science and Research Assistant Professor II & Head 2011 14/03/2020
34 37810 Ms. Poornima S Female KPR College of Arts Science and Research Assistant Professor 2016  
35 37812 Mr. Karthik And Madhavan Male KPR COLLEGE OF ARTS SCIENCE AND RESEARCH ASSISTANT PROFESSOR 2014  
36 37815 Mr. Sureshkumar Ramasamy Male KPR COLLEGE OF ARTS SCIENCE AND RESEARCH ASSISTANT PROFESSOR 2015  
37 37835 Ms Rakhi Pote Pote Female Kendriya Vidyalaya-2 Camp, Belagavi Teacher 2012  
38 37839 Dr. Aijaz Ahmad Najar Male Govt. Degree College Kulgam Assistant Professor 2009 31/03/2016
39 37849 Dr. Kanagaraj K Male Srinivasa Ramanujan Centre Assistant Professor 2011 20/10/2020
40 37852 Mr S Rajagopal Rajagopal Male VIT Chennai Research Scholar with Assistant Professor Junior 2010  
41 37855 Mr. Vijayanarayanan U Male NPR COLLEGE OF ENGINEERING AND TECHNOLOGY Assistant Professor 2014  
42 37863 Dr Nitakshi Goyal Female Akal Degree College, Mastuana Assistant Professor 2012 14/02/2020
43 37874 Mr. Bhuwan Joshi Joshi Male Graphic Era Deemed to be University Asst. Prof. 2011 19/12/2019
44 37876 Mr. Dinesh Kumar Male Deshbandhu College, University of Delhi, Delhi Assistant Professor 2013  
45 37879 Mr. Thyagarajan M Male Agurchand Manmull Jain College Asst. Prof. 2005  
46 37880 Mr Murugan M Male Agurchand Manmull Jain college Assistant professor 2012  
47 37883 Ms. Divya Chopra Female Jawahar Navodaya Vidyalaya chikkajogihalli Bellary PGT MATHS 2019  
48 37889 Mr Gnanam Mahesh Kalakaoi Male AGURCHAND MANMULL JAIN COLLEGE Asst. Prof 2013  
49 37890 Dr. Pankaj Kumar Male Deshbandhu College, University of Delhi Assistant Professor 2012 11/09/2021
50 37901 Dr. Sarswati Shah Shah Female The NorthCap University Asst. Prof. 2015 27/03/2021
51 37902 Dr. N. Annamalai Male Central University of Tamil Nadu Guest Faculty 2011 26/02/2019
52 37906 Dr. Jitendra Kumar Male Swami Vivekanand Subharti University Assistant Professor 2006 16/02/2016
53 37909 Mr. Sudhakar Baskar Male MVJ COLLEGE OF ENGINEERING ASSITANT PROFESSOR 2018  
54 37915 Mr. Manoj Kumar Nahlia Male G.H.S.GOVT. PG COLLEGE SUJANGARH Asst.Prof. 2015  
55 37916 Dr. Chinmay Kumar Giri Male National Institute of Science and Technology, Berhampur Asst. Prof. 2013 14/02/2018
56 37919 Mr. Ganesh Tulshiram Sanap Male K.P.G. ARTS, COMMERCE AND SCIENCE COLLEGE, IGATPURI, NASHIK, MAHARASHTRA Assistant Professor 2013  
57 37920 Prof. Dipak Sandu Jadhav Male Smt. Chandibai Himathmal Mansukhani College, Ulhasnagar - 03 Assistant Professor 2008  
58 37926 Dr. Molla Basir Ahamed Male Jadavpur University Assistant Professor 2012 18/07/2017
59 37940 Dr Dharmendra Kumar Male Sri Guru Tegh Bahadur Khalsa College University of Delhi Associate Professor 2004 14/09/2021
60 37973 Mr. Deepak Sambhaji Shelke Male Jaikranti college katraj Pune Assistant professor 2017  
61 37977 Ms. Chethana R V Female Narendra college puttur Asst. Professor 2016  
62 37979 Dr. Selvi Sellappan Female N.K.R. GOVERNMENT ARTS COLLEGE FOR WOMEN. ASSISTANT PROFESSOR 2001 29/04/2013
63 37986 Mr. Swapnil Sadanand Belekar Male St.Xavier's College Assistant Professor 2017  
64 37989 Mr. Vishal Gupta Male maitreyi college assistant professor 2010  
65 37998 Mr. Pranil Bhalchandra Waikar Male Jai Hind college (Autonomous), Mumbai Assistant professor 2015  
66 38003 Dr. R. Srimathi Female Idhaya College of Arts and Science for Women Assistant Professor 2013 07/07/2020
67 38006 Mr. Subhajit Paul Male Salesian College, Siliguri Campus Asst. Prof. 2010  
68 38008 Mrs Pratima Negi Female Zakir Husain Delhi College, University of Delhi Assistant Professor 2000  
69 38009 Ms. Pooja Punyani Female The Northcap University Asst. Professor 2012 14/03/2021
70 38012 Dr Sheere Farhat Ansari Female Integral University, Lucknow Assistant Professor 2011  
71 38013 Dr. Nayan Bhat K Bhat K Male St. Joseph's College (Autonomous), Bangalore Assistant Professor 2015 08/05/2021
72 38015 Dr. Suhas B N Male St. Joseph's College (Autonomous), Bangalore Assistant Professor 2010  
73 38016 Mr Jesse P Francis Male St. Joseph's College, Bangalore Assistant Professor 2014  
74 38023 Dr. Bamdeb Dey Male Assam Don Bosco University Assistant Professor 2001 01/06/2018
75 38025 Dr Gerard Rozario J Male St. Josephs College (Autonomous), Bangalore Assistant Professor 2005 28/08/2019
76 38029 Dr. Arshpreet Kaur Female MCM DAV College for Women Assistant Professor 2014 11/11/2020
77 38031 Ms. Champakumari M Female St. Joseph’s College Assistant Professor 2017  
78 38032 Mrs. Maria Anncy Female St. Joseph's college PhD 2011 08/08/2021
79 38033 Ms. Deepika S Female St. Joseph's College (Autonomous) Asst. Professor 2016  
80 38034 Dr. Vijay Kumar Shukla Male Shiv Harsh Kisan P.G. College, Basti Assistant Professor 2010 08/11/2019
81 38039 Mr. Vipul Snehi Male Lalit Narayan Mithila University Asst. Prof 2013  
82 38041 Dr. Deepa Mathew Female St. Joshephs College Bangalore Asst. Professor 2017 08/10/2021
83 38042 Dr R.A.Daisy Singh Singh Female St. Joseph's college, Autonomous. Assistant Professor 1998 08/02/2020
84 38047 Dr. Harsha Arora Female Govt. College For Women Hisar Haryana Asso. Prof.   11/11/2016
85 38056 Dr. Sarita Choudhury Female Science College (Autonomous) Hinjilicut Asst. Prof. 2012 08/02/2017
86 38057 Prof Hemant Kumar Nashine Male VIT Vellore Professor 1999 28/08/2010
87 38066 Ms. Nithiya . K. . . Female Vellore Institute of Technology TRA 2009  
88 38068 Dr. Sunanda Saha Saha Female VIT Velllore Assistant Professor 2010  

School Short Name: 

ramcla

School Type: 

TEW