My Philosophy
For doing higher studies you should really be motivated beyond money
and positions at company. You need to put more effort to get into IISc
and passing out than getting up the ladder at the organization. This
degree may not help anyone for any promotions or incentives @
office. But the knowledge from this degree will definitely help
you cross many artifical barriers that you have put in life for not
working (too technically) to your satisfaction. Selecting research as a
career has few challenges. Visit www.phds.org and www.phdcomics.com for
more clarifications on research career.
How to go about
- You need to identify a professor of your interest area. Mine
being e-commerce. The engineering challenges/ research challenges are
always different. So be careful before approaching the professor. check
his website, student's website and the papers of him and his students.
better to have discussions with students before the discussing with
professor.
- Start interacting with him and express you interest of joining
iisc. no professor will sign immediately for erp unless and until they
see the committment of the student. so they expect to work with them
for an year or so. definitely not more than an year. and then they will
sign.
- Identify a research supervisor at organization. preferrably
ph.d.
- With your 1 year work with the professor you would identify a
research problem.
- This is the time you meet the application requirement at least.
for applying you need a reserach supervisor in the organization,
research supervisor from iisc and a reserach proposal. you have crossed
30% of the degree.
- You need to prepare in three technical areas. one in the area of
the research proposal, one mathematics area related to your research
and one computer science area. by default the computer science area
will become algorithms for many.
- Interview is similar to ph.d interview. there will be 6-7
professors sitting and will interview you. toughest part. they will ask
very very fundamental question. at the end of the interview if you go
through u will feel the interview as easy interview, if you dont go
through u will feel bad thinking u dont even know such basic things.
:).
For more information about IISc ERP please visit the link
IISc ERP
page.
Subject I Studied
I selected Linear Algebra and Datastructures and Algorithms as my topic
of interest for interview.
Linear Algebra
The following are the famous books under this subject.
Linear
Algebra and its Application by David C Lay. Low Price Edition costs
around Rs. 300.
Introduction to Linear Algebra by Gilbert Strang. Low Price Edition
costs around Rs. 300.
Linear Algebra by Kenneth M Hoffman, Ray Kunze. Low Price Edition costs
around Rs. 200.
Karthik and myself prepared together this subject. The way we studied
were we watched the videos of Gilbert Strang from
OCW
MIT 18.06 website and read the similar chapters from David C Lay.
More than computations, the concept of Linear Algebra need to
understood deeply. Lots of discussion will really aid.
Validate your understanding by working out all the exercises
(especially true or false and objective questions) in Lay, exercises
and examination from OCW MIT site. Work out the Practice Exams and
Review sheets from the
http://www.laylinalgebra.com/free_site/rev_mat.html.
You can always mail David C Lay and Gilbert Strang in case you have any
doubts related to the subject. Apart from this whenever you have
doubts you can also post it in the groups sci.math in
groups.google.com. Many professors respond to your questions.
Preferrable install matlab or scilab and work on this. This will help
you to concentrate on concepts and do the needed computations in
scilab/matlab.
Keep consolidating which is a key strength. For example a partially
completed
Linear
Algebra consolidation.
The preparation time will be around 3-6 months for naive mathematics
students.
Sample interview questions can be found below.
Datastructures And Algorithms
The books that we followed are
Data Structures and Algorithm Analysis in C (Second Edition) by Mark
Allen Weiss. Low price edition around Rs. 300
Introduction to Algorithms by CLRS. Low price edition around Rs. 350.
Watch the videos from the website
ocw
mit website. Work out exercises. You are having lots of resources
on the web for Datastructures and Algorithms.
The key thing in Datastructures and algorithms is about consolidation.
The various datastructure and its comparison will be questioned. Also
you will be questioned based on comparison on various algorithms. For
reference I have put the consolidation of
sorting
and
datastructures
and operations.
Try to form a group and take sessions among yourselves and discuss as
much as possible. Try to solve various question papers available in the
internet.
You can post your doubts to algorithm geeks group in groups.google.com.
Also there are many forums and can post your questions to individual
professors.
Proposal
Concentrate on your proposal for sometime. Work with your research
supervisor and internal guide from the organization and ensure you are
in the right track. Discuss with the professor's students. You can
expect similar questions during interview also. This will not only help
you during interview but also speeden your research after you join IISc.
About Interview
The interview is intended to be a test of the candidate's aptitude and
suitability for research in the area of specialization to be pursued
and thoroughness of background in related core subjects. A
typical interview lasts for 30 minutes and the candidate can expect
questions on the proposed research project, one or two subjects of
candidate's choice in Mathematics and possibly Computer Science, data
structures, algorithms and
programming.
The emphasis will be on testing the depth of candidate's understanding
of fundamental concepts.
Thumb of rule : Perform excellent in simple subjects(algorithms,
probability, linear algebra) rather than performing average/poor in
advanced topics(optimization, calculus, machine learning etc)
Sample Interview Questions
Best Practices (Do's and Dont's)
- Dont use jargons unnecessarily. Use plain and simple english
- Use board extensively and think aloud. This will help the
interviewers to help you.
- Dont write anything wrong in haste. Think once or twice before
saying/writing anything.
- Always believe with your basic knowledge you will be able to
solve the problem.
- Approach the problem step by step. Split the board into many
sections and write the things you know related to the problem in one
side of the board. The right mixture of what you know should be enough
to solve the problem.
- Have complete knowledge on fundamentals. More than computation
under concepts. Read the first two pages in chapter thoroughly before
starting the chapters.
- Dont read with the objective of interview in mind but read for
understanding the subject. This will get you through the interview.
- There can be various starting points (for linear algebra it is
eigen value, orthogonalization, symmetric matrix, types of matrix,
system of linear equation etc.). Based on the starting point the
direction of the interview will be decided. You can give a preference
of your starting point if it is offered to you.
Linear Algebra
Starting Points : eigen value, orthogonalization, symmetric matrix,
types
of matrix, system of linear equation, Vectors.
. For sample I am giving the starting point as eigen value.
- What is a eigen value?
- What are equivalence matrices? Prove.
- What is positive definite matrix? Prove.
- How will be the eigen values of different matrices (orthogonal,
symmetric etc). Prove.
- Applications of eigen values in differential equations
- How will you compute eigen values of higher roots
- Cayley Hamilton theorem. Prove
- Eigen values of A^2, A^-1, 2A, A-2 etc.
- Application of diagonlization.
- Difference between factorization, decomposition, diagnolization
etc.
Datastructures and Algorithms
Starting Points : Graphs, Trees, Sorting, Hashing, Complexity. I will
be
giving here some sample questions for Complexity and Graphs here.
Graphs :
- What is the Graph?
- What is Shortest Path?
- What are the algorithms you know for shortest path?
- What is the difference between Djikstra and Bellman Ford
- What is a minimum spanning tree?
- What are the algorithms you know for MST?
- Compare and Contrast Kruskal and Prims
- Can MST yield Single source shortest path(SSSP)
- What is the difference between MST and SSSP?
- What is a greedy algorithm? Give an example where it fails
- Types of Graphs and their properties
Complexity:
- What is the complexity of an algorithm?
- What are all the representation of complexity of an algorithm?
- What is big-oh, theeta, and omega notation?
- Given an equation compute big-oh, theeta and omega notation
- What is masters theorem?
- Where will masters theorem fail?
- Given a recurrence relation draw a recurrence tree. find big oh,
theeta and omega by substitution, masters theorem and telescopic series
- Few more questions to test your understanding
- A program/algorithm may be given and asked to compute complexity
- From this place it can either get into graphs or sorting
Proposal
It is the toughest part. Dont make any major screw ups in this. This is
the first place where you start your interview. However good you do in
other subjects this has a great bearing in the interviewers mind. Be
confidence
in your delivery. Mostly they will try to probe your understanding on
the
problem and your confidence.
Even in case if you dont get through first time dont loose your heart.
To do research you dont need to be a student of IISc. Your professor
will
always be happy to have discussion with you and help you in nourishing
at Research. For any further clarification mail to me.
The next important phase after getting into IISc is your general test.
Kindly refer to
Karthik
Subbian's note on General Test.