# Blogs by other Toppers.

Will update as and when I get to know about others.

# Solutions to previous years questions : Linear Algebra, Abstract Algebra, Calculus, Complex Analysis

Dr. Sunder Lal, Retired Professor of Mathematics (Punjab University) has prepared solutions for previous years question papers spanning nearly 30 years. It has solutions for questions from Linear Algebra, Abstract Algebra, Calculus and Complex Analysis. Candidates are advised to go through them.

# Self-Study guide on Lagrangian and Hamiltonian

As many aspirants were facing difficulty in this topic, I have prepared a *self-study guide*. As I felt *proofs* will not be asked, I have directly given the equations, which you should *memorize*. Also if you are unable to understand anything in this guide, you can post you doubts.

# Collection of Solved Problems : Abstract Algebra

# Problems and Solutions : Part 2

Second set of problems for Linear Algebra and Real Analysis.

# Problems and Solutions – Part 1

This word document contains solved problems from different topics, in a random manner. It has many good problems largely for Linear Algebra and Real Analysis. I had collected these problems from various sources and complied them during my last attempt.

First finish these two topics from previously mentioned books and they refer to the above document.

# Few of my answer scripts

I am sharing few of my answer scripts. I wrote them during last year online test series at IMS.

# Choosing Mathematics as an optional !!

**Who can take Mathematics as an optional?**

A large number of aspirants called or messaged me saying that they have decided to or wanted to take Maths and asked me to share my strategy. When I asked them why they wanted to choose Maths, most of them told that it was because of *good performance* of Maths in recent years.

**Is Mathematics really performing well in recent years?**

On the surface it might look that Maths is doing well. This time around 25-30 candidates have got in the range 290-310. But the problem with Maths optional is *scaling*. Due to *scaling* (I don’t know how UPSC does it), a very few number of candidates get high and remaining ones get very low. The ones who get high would have obviously done better than the rest. But due to scaling, difference in marks between the highest and the lowest increases drastically. If the difference in *correct *attempts is say 60-70, then after scaling the difference becomes 110-120. Thus in Maths, marks are *binary*. Either you get high or you get low. There are no average marks in Maths, unlike humanities optional. Therefore one should *not* get attracted to Maths by marks obtained by a *few* successful candidates. A huge majority would have got very low marks in Maths. Thus Maths is performing *well *for say around 10% and *poor *for 90%.

**Who are the ones who usually take Maths as an optional?**

A large number of those who take Maths as optional come from reputed institutions like IITs, BITS and NITs etc. Due to this the competition is very high.

So back to first question, **who can take Maths as an optional**?

I feel only those who are *very strong* in Maths and have *genuine interest* should take Maths. Unlike humanities optional which can be taken by anybody, Mathematics requires *aptitude*. As there is huge competition, unless one is at the topmost part of the pyramid, Maths would result in low marks. I have seen many people who take Maths in haste, waste attempts and later change optional.

I was not from any IIT, BITS or NIT. I still went for Maths because I felt I am good in Maths. Mine previous performance in Maths boosted my confidence. I had got 99/100 in 10^{th} (Cbse), 100/100 in both 11^{th} and 12^{th}, 10/10 grade in all four semesters in Engineering Maths. This is not to boast about myself, but to press the point that Maths should be taken only *if you have good track record* in Maths.

Also given the complexity of topics and huge syllabus, I don’t think any coaching institute will be able to fully cover all the topics. I feel coaching has a limited role and own effort matters more.

# General Observations

GENERAL OBSERVATIONS:

- The fixed space for each question in Mathematics causes lot of disadvantage vis-à-vis other optional, particularly humanities. If you made a mistake while solving a problem and have consumed most of the available space, then despite knowing the correct method you would not have space to rectify your mistake. To tackle this, practice solving problems and write many mock tests. By greater practice you will be able to reduce unforced errors. Also if the problem is new or unfamiliar, I used to briefly solve it in the last page with pencil, later transferring it to main page.
- A lot of aspirants face the dilemma of how much time to give for Maths compared to GS. There is no hard and fast rule. I used to give 50% of my time (say around 5 hrs per day) for Maths and 50% for GS. Owing to huge syllabus of Maths, candidates generally tend to neglect GS and Essay. This has to be avoided.
- It is very important to complete atleast 80% of syllabus before prelims. Also between prelims and mains, try to do both Maths and GS everyday. Don’t lose touch of Maths. The last one month before Mains is very important. During this period keep on revising formulas and practicing problems.
- Join Test Series programme between Prelims and Mains. This helps you to complete the syllabus in time, gives you practice, improve your speed and accuracy etc. I had joined Venkanna’s (IMS)
*test series*4 times (2011,12,13,14) and found them very helpful. I did not attend their classroom coaching and went only for test series programme.