# Graduate Aptitude Test in Engineering (GATE)

If you’re interested in pursuing higher studies in Engineering, writing the GATE examination is a very good option.The GATE examination is conducted on the second sunday in february every year by the IITs and IISc. Admission to prestigious institutes like IITs, NITs and IISc are through GATE. If you are serious about pursuing a masters degree, then you have to write GATE. Information about GATE and how to apply can be found here.

I have written the GATE exam in Electronics and Communication engineering twice, once in my pre-final year and again in my final year BE. The exam tests your understanding of basic concepts. The syllabus contains all the subjects that are covered in undergrad generally upto the 3rd year. Attending coaching is not necessary, as self study usually suffices. It is necessary to clarify all concepts and have thorough understanding of all subjects. I had attended the mock tests conducted by Gateforum and found them to be very useful.

I went through mathematics first and then to the other subjects. That really helped since understanding the fundamentals in electronics does require math. Here are some of the books I referred to:

Math: Differential and Integral Calculus by Piskunov, Advanced engineering mathematics by Ray Wylie and Louis Barrett, Higher engineering mathematics by Grewal. Probability and random processes by Papoulis is good.

Network Analysis: Network analysis by Van Valkenburg

Electronic devices: Solid state electronic devices by Ben Streetman, Integrated electronics by Millman and Halkias(has almost all topics)

Analog circuits: Integrated electronics by Millman and Halkias
Digital circuits: Digital electronics by Givone

Signals: Signals and systems by Oppenheim and Willsky, DSP by Proakis

Control systems: Automatic control systems by Benjamin Kuo

Communications: Communication systems by Taub and Schilling (has almost all topics necessary), Simon Haykin.

Electromagnetics: Was a bit tricky, Read a little of Lectures on Physics by Feynman (awesome book) for basics, EM waves and Radiating systems by Jordan and Balmain, Samuel Liao and a bit of Pozar for TLW and microwave (waveguides, tees and such stuff)

The questions of the previous years are never repeated and solving previous question papers is required to only get comfortable with answering questions and managing time. It also helps in finding out which concepts you didnot understand properly.

It is also a good idea to make notes as you study as they help in last minute revision.

On the day of the exam

Reach the examination centre ahead of time. Do not read any new concepts on that day or the previous as it only leads to confusion. Revise concepts from the notes, if you have made any.

Attempt the questions with a cool head. Don’t solve them in a hurry. This was the mistake I made and lost quite a few marks in the process. Do not take too long to solve a problem either. If you can’t solve one, proceed to the next one and come back to it later.

After you solve all the problems, double check if all your answers are correct and you have marked the right options.. You can save quite a few marks that might otherwise be lost due to carelessness.

After the exam

Constantly check for any updates from the institutes for admission. IISc particularly starts handing out admission forms before the results come out. The last date for submission is generally only a few days after the results are announced.

For the record, I came 487th in my first attempt and 75th in my second.

I had applied only to IIT-Bombay (communication and control&computing -TA category), IIT Madras (math, control&instrumentation and communication -MTech) and IISc (CEDT, ME in telecomm and signal processing, MSc in ECE). IIT-M accepts students for MTech only through direct admission. IIT-B has direct admission in the first list(for TA). They then call for interviews.

I got a call for math in 1st list, Control&Instrumentation in the 3rd list at IITM.
I was called for interview by IITB for the TA category. There was a written test and then interview. The interview went well. I also had a conference publication in communication and that also added weightage. I was selected for MTech in communication.

I got interview calls from IISc for CEDT and MSc. I didnot get selected for ME. I did not attend the CEDT interview.

MSc (research) interviews at IISc are supposed to be tough. You are asked to go to the black(or white)board and grilled by the panel. At the ECE dept, you have to choose two math topics and also the topic you want to do research in from a check list. You will be asked questions based on your choice. Details can be found here.

I chose Linear algebra, probability as the math subjects and research topics: Information theory and Coding theory.

The interview went on for half an hour. I was asked very fundamental questions: vector space, field, linear independence, basis, dimension, rank, the rank-nullity theorem, some proofs and so on. In probability, they asked me about random processes, correlation, covariance, independent rvs, uncorrelated rv, stationarity, ergodicity, mean square convergence and so on. I was also asked to explain my conference publication. In Info theory and coding, I was asked about Shannon’s first theorem, source coding, which was the best source coding method, what is average code length, capacity and so on.

The interview went well and I answered most of the questions. Thankfully, I was selected for the MSc programme. After I got the call letter, I rejected the offers from IITM and IITB.

# Euclid’s algorithm

Euclid’s algorithm:

Theorem 1 Euclid’s algorithm: Given ${ m,n \in \: \mathfrak{N} }$ , ${ m \neq 0 }$, then there exist ${ q,r\in \: \mathfrak{N} }$ , ${ 0 \leq r < m }$ such that ${ n = mq+r }$.

Proof: We prove the statement using the principle of mathematical induction.

Denote ${ \mathcal{P} (n): \; n=mq+r }$

Fix m.

Clearly, ${ \mathcal{P} (0): \; 0=m0+0 }$ is true.

Suppose, ${ \mathcal{P} (n) }$ is true i.e. there exist m,r with ${ 0 \leq r < m }$ such that ${ \mathcal{P} (n): \; n=mq+r }$ is true.

Consider ${ n' = n+1 =mq+r+1 }$.

Since ${ 0 \leq r < m }$, ${ 0 \leq (r+1) < m+1 }$. Hence, ${ r+1 or ${ r+1=m }$

If ${ r+1, then ${ n' = mq+\hat{r} }$, where ${ \hat{r}=r+1 }$.

Hence, there exist ${ q,\hat{r} \in \mathfrak{N} }$, ${ 0 \leq \hat{r} < m }$ such that ${ \mathcal{P} (n') }$ is true.

Now, if ${ r+1=m }$, then ${ n' = mq+m }$.

${ n' = m \hat{q} +0 }$.

${ n' = m \hat{q} +\hat{r} }$, ${ \hat{r} =0 }$.

Hence, there exist ${ \hat{q},\hat{r} \in \mathfrak{N} }$, ${ 0 \leq \hat{r} < m }$ such that ${ \mathcal{P} (n') }$ is true.

By the principle of mathematical induction, ${ \mathcal{P} (n) }$ is true for all ${ n\: \mathfrak{N} }$. $\Box$