2023 Autumn semester:
Apoorva Khare
- Course description: Mathematics 219 is a Core Course for
the
Integrated Maths Ph.D. and Undergraduate Math Major programs in
IISc
Mathematics. For more details (including a list of topics), click
on
the link with text 'Mathematics 219' above.
- Meetings: Tue Thu 10 – 11:30 am, in
Lecture Hall LH-5 (Maths Dept.).
- Please join the Microsoft Team "MA219
– Linear Algebra – Fall 2023", from a valid IISc email
account. If this does not work for some reason, then please email me
(khare@iisc) from your IISc email account.
- Pre-requisites: For undergraduates: UM
102.
- Handout/syllabus: Click on this link.
Homework assignments
Homework 1
(finalized; due by 5:30 pm
on Thursday August 17, 2023, in TA office hours, or earlier in
class)
Homework 2
(due by 5:30 pm on Thursday August 31, 2023, in TA office hours,
or earlier in class)
Homework 3
(due by 5:30 pm on Thursday September 7, 2023, in TA office hours,
or earlier in class)
Homework 4
(due by 5:30 pm on Thursday September 14, 2023, in TA office hours,
or earlier in class)
Homework 5
(due by 5:30 pm on Thursday October 5, 2023, in TA office hours,
or earlier in class)
Homework 6
(finalized; due by 12:30 pm on Friday October 27, 2023, in TA
office hours, or earlier in class)
Homework 7
(due by 5:30 pm on Thursday November 2, 2023, in TA office hours,
or earlier in class)
Homework 8
(no further updates – this was already
final! And is due by 5:30 pm on Monday November 20, 2023, in TA
office, or earlier)
Homework 9
(finalized; due by 5:30 pm on Monday November 27, 2023, in TA
office, or earlier in class)
Mathematics
341: Matrix Analysis and Positivity
2023 Autumn semester:
Apoorva Khare
- Course description: This course explores matrix positivity and
operations that preserve it. These involve fundamental questions that have been
extensively studied over the past century, and are still being studied in the
mathematics literature, including with additional motivation from modern
applications to high-dimensional covariance estimation. The course will bring
together techniques from different areas: analysis, linear algebra,
combinatorics, and symmetric functions.
- Meetings: Tue Thu 2 – 3:30 pm, Mathematics
Lecture Hall LH-1
- Pre-requisites: A course in linear algebra, and a course in calculus/real
analysis.
- Handout/syllabus: See this link; the topics to be
discussed are on the course
page.
- Course notes: Click on this link for the course notes.
- Homework assignments
Homework 1
(due by Thursday September 7 in class, or previously in office
hours)
Homework 2
(due by Thursday September 21 in class, or previously in office
hours)
2022 Autumn semester:
Apoorva Khare
- Course description: Mathematics 219 is a Core Course for
the
Integrated Maths Ph.D. and Undergraduate Math Major programs in
IISc
Mathematics. For more details (including a list of topics), click
on
the link with text 'Mathematics 219' above.
- Meetings: Tue Thu 10 – 11:30 am, in
Lecture Hall LH-1 (Maths Dept.).
- Please join the Microsoft Team "MA219 -
IISc Math - Fall 2022", from a valid IISc email account. If this
does not work for some reason, then please email me (khare@iisc) from
your IISc email account.
(Note: Eighteen UG-2020 members have already been added.)
- Pre-requisites: For undergraduates: UM
102.
- Handout/syllabus: Click on this link.
Mathematics
315: Lie Algebras and their Representations
2022 Autumn semester:
Apoorva Khare and R. Venkatesh
- Course description: Mathematics 315 is an Elective Course
on (semisimple) Lie algebras and their representations.
- Meetings: Tue Thu 3:30 – 5 pm, in
Lecture Hall LH-4 (Maths Dept.).
- Please join the Microsoft Team "MA315 - IISc Math -
Fall 2022", from a valid IISc email account. If this does not
work for some reason, then please email me (khare@iisc) from your
IISc email account.
2021 Autumn semester:
Apoorva Khare
- Course description: Mathematics 219 is a Core Course for
the
Integrated Maths Ph.D. and Undergraduate Math Major programs in
IISc
Mathematics. For more details (including a list of topics), click
on
the link with text 'Mathematics 219' above.
- Meetings: Tue Thu 8:30 – 10 am, on
Microsoft Teams. See this
link, for which you first need to be logged into either VPN
(remote access) or in your IISc Microsoft Outlook account in a
separate tab in the same browser.
- To join the Microsoft Team and mailing list, check the
link in the preceding point for which Team to join – from a
valid IISc email account. If this does not work for some reason, then
please email me (khare@iisc) from your IISc email account.
(Note: UG-2019 members will be automatically added.)
- Pre-requisites: For undergraduates: UM
102.
- Handout/syllabus: Click on this link.
2020 Autumn semester:
Apoorva Khare
- Course description: Mathematics 219 is a Core Course for
the
Integrated Maths Ph.D. and Undergraduate Math Major programs in
IISc
Mathematics. For more details (including a list of topics), click
on
the link with text 'Mathematics 219' above.
- Meetings: Tue Thu 10 – 11:30 am,
Microsoft Teams. See this
link, for which you first need to be logged into either VPN
(remote access) or in your IISc Microsoft Outlook account in a
separate tab in the same browser.
- To join the Team, please email me (khare@iisc)
from your IISc email account. (Note: UG-2018 members are
added.)
- Pre-requisites: For undergraduates: UM
102.
- Handout/syllabus: Click on this link.
Mathematics
341: Matrix Analysis and Positivity
2019 Autumn semester:
Apoorva Khare
- Course description: This course explores matrix positivity and
operations that preserve it. These involve fundamental questions that have been
extensively studied over the past century, and are still being studied in the
mathematics literature, including with additional motivation from modern
applications to high-dimensional covariance estimation. The course will bring
together techniques from different areas: analysis, linear algebra,
combinatorics, and symmetric functions.
- Meetings: Tue Thu 3:30 – 5 pm, Mathematics
Lecture Hall LH-3
- Pre-requisites: A course in linear algebra, and a course in calculus/real
analysis.
- Handout/syllabus: See this link (most/all of the topics should get
discussed, though not in the order in the link).
- Course notes: Click on this link for the course notes.
- Homework assignments
Homework 1
(due by Friday August 23, in TA's office hours or earlier in class)
Homework 2
(due by Friday September 6, in TA's office hours or earlier in class)
Homework 3
(due by 5pm on Monday September 16, in Instructor's office hours)
2019 Autumn semester:
Apoorva Khare
- Course description: Mathematics 212 is a Core Course for the
Integrated Maths Ph.D. and Undergraduate Math Major programs in IISc
Mathematics. For more details (including a list of topics), click on
the link with text 'Mathematics 212' above.
- Meetings: Tue Thu 11:30 am – 1 pm, Mathematics
Lecture Hall LH-3
- Pre-requisites: For undergraduates: UM 203.
- Handout/syllabus: Click on this link.
- Homework assignments
Homework 1
(due by Friday August 16, in TA's office hours or earlier in class)
Homework 2
(due by Friday August 23, in TA's office hours or earlier in class)
Homework 3
(due by Friday August 30, in TA's office hours or earlier in class)
Homework 4
(due by Friday September 6, in TA's office hours or earlier in class)
Homework 5
(due by 5pm on Monday September 16, in Instructor's office hours)
Homework 6
(due by Friday October 4, in TA's office hours or earlier in class)
Homework 7
(due by Friday October 11, in TA's office hours or earlier in class)
Homework 8
(due by Friday November 8, in TA's office hours or earlier in class)
Homework 9
(due by Friday November 15, in TA's office hours or earlier in class)
Homework 10
(due by Monday November 25, in TA's office hours; now updated)
2019 Spring semester:
Apoorva Khare
- Course description: Click on the link with text 'Mathematics UM102' above.
- Course handout: Click on this
link.
- Notes on uniqueness of determinant: Click on this
link.
- Homework assignments
Homework 1
(due by Wednesday January 9, in class)
Homework 2
(due by Wednesday January 16, in class)
Homework 3
(Quiz 1 on Monday January 28, in class)
Homework 4
(Quiz 2 on Monday February 4, in class)
Homework 5
(Quiz 3 on Monday February 11, in class)
Homework 6
(Not for a Quiz nor for HW submission, but relevant to mid-sem
syllabus)
Homework 7
(Quiz 4 on Monday March 18, in class)
Homework 8
(Quiz 5 on Monday March 25, in class)
Homework 9
(Quiz 6 on Monday April 1 – not a joke! – in class)
Homework 10
(Quiz 7 on Monday April 8, in class)
Homework 11
(Quiz 8 on Monday April 15, in class)
Homework 12
(Not for a Quiz nor for HW submission, but relevant to Final
syllabus)
2018 Autumn semester:
R. Venkatesh and Apoorva Khare
Mathematics 341: Matrix Analysis and Positivity
2018 Spring semester:
Apoorva Khare
- Course description: This course explores matrix positivity and
operations that preserve it. These involve fundamental questions that have been
extensively studied over the past century, and are still being studied in the
mathematics literature, including with additional motivation from modern
applications to high-dimensional covariance estimation. The course will bring
together techniques from different areas: analysis, linear algebra,
combinatorics, and symmetric functions.
- Meetings: Wed Fri 11am – 12:30pm, Mathematics Lecture Hall LH-3
- Midterm: Friday February 23, in class.
- Pre-requisites: A course in linear algebra, and a course in calculus/real
analysis.
- List of topics: See this link (all but one or two sub-topics were discussed, though not in the order in the link).
- Course notes: Click on this link for the course notes.
2017 Autumn semester:
Apoorva Khare
- Mathematics 221 is a Core Course in real analysis, for the Integrated
Ph.D. program in IISc Mathematics.
This semester, we will closely follow Rudin's Principles of
Mathematical Analysis.
- Course handout: Click on this
link.
- Homework assignments
Homework 1
(due by Friday August 25, in TA's office hours or earlier in class)
Homework 2
(due by Friday September 8, in TA's office hours or earlier in class)
Homework 3
(due by Friday September 29, in TA's office hours or earlier in class)
Homework 4
(due by Tuesday October 24, in class)
Homework 5
(due by Tuesday November 7, in class)
Homework 6
(due by Friday November 17, in TA's office hours or earlier in class)
Homework 7
(due by Wednesday December 6, in Instructor's office hours by 4pm, or earlier in class)