Mathematics Optional Group UPSC 2021 - ForumIAS

Mathematics Optional Group UPSC 2021

People with mathematics optional who are aiming for CSE 2021, please join this discussion forum so we can have relevant discussions on issues specific to our optional subject. I have been trying to look for people with math optional online, but it is quite difficult as it is a sparse population. Most people have Sociology, Pub Ad., History, Geography as optional subjects. Libraries have the same problem. There is no currently active group on forum either. I tried civilsdaily habitat platform but the math group is inactive there. 


We can discuss strategies to finish syllabus, topics to choose (rarely does someone study all the 13 topics), discuss best source materials and books, ask specific math problems, discuss previous year papers, etc.

MikeWozniak,shivshankar_iasand14 otherslike this
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89 comments

Maths meymey.. 

MikeWozniak,EiChanand6 otherslike this
3.6k views


chamomile,AJ_and4 otherslike this
3.8k views
@CelebornThanks for sharing! That was very elaborate. I find myself too slow with lengthy topics like 3D, modern etc where I start by solving most of the questions present in IMS notes. How do you plan on finishing the syllabus twice? Do you go through the books/IMS notes wholely or just following your own notes and compilation of selected questions?


By now for these topics (like Modern, 3D), I have already done IMS notes multiple times. So revision is a bit faster. In the notes, I don't go through everything. I have ticked certain questions that I need to read and revise + double ticked some questions that are complicated and I need to wrote/solve to revise. I don't look at the remaining portion. 

Before I begin revision though, I'll make a rough estimate of how much time it will take. If I have less time, I'll just revise the short notes (Kanishak Kataria notes). If I have a bit more time, I'll do IMS notes. Last year (2020 attempt), I didn't have time so I did only the short notes + 2019 test series questions topic wise. This year, I'll do IMS notes for certain topics (Modern, Real analysis + calculus, 3D) and short notes for all other topics. 

I am planning to go over my IMS notes, revise PYQs, revise my short notes and one Test Series. Preferably I want to also cover one test series of 2020. Essay and GS4 I have covered earlier so I'll only be revising that and write tests.


How realistic does this seem considering that you have given earlier attempts with maths? :P 

Before I say anything, keep in mind that I'm no expert. I scored 153 in Maths in my first attempt. This time I'm hoping for somewhere between 240-280 (based on IMS key). So whatever I say, it comes from a place of failure, not success. Hence take my words with a pinch of salt. 

Your task list seems doable, although a bit ambitious. Here are some conditions though:

1) In doing all this, you'll have to prioritize Maths over GS. This is mentally hard to do since GS is vast. Further GS is the common link for all aspirants so every institute will bring out some material/programme for GS. FOMO is your enemy here. Decide early on what's absolutely necessary and stick to that. 

2) You won't be able to write and practice every question. Try to read and mentally solve questions while revising for most of the material. This will save time. 

3) Make a priority list at the beginning for instance say IMS notes >Test Series 2021 >Short notes >PYQs >Test Series 2020. This way if you lack time, drop whatever is having a lower priority. 

4) This time there is 3-4 weeks lesser time than earlier. So from the very beginning you'll have to be at your most productive.

5) Estimate from the beginning how much time you'll devote item by item (say 6 days for IMS notes of Modern + 2 days for Modern PYQs - something like that). Do this for everything, including GS. This will help you realise very soon if you're taking more time and help you adjust accordingly. 

All being said, you are in a good spot. Your GS4 and essay is done so that potentially saves 10-15 days. You've done your PYQs and just need to revise them so you can do that in half the time than usual. 

So I hope you'll be able to pull this off. All the best! 


chamomile,Archandand3 otherslike this
4.3k views
How do you guys revise as mathematics syllabus is huge?

Make short notes for every chapter with important formulas, theorems, important questions. I used Kanishak Kataria's short notes since he also used IMS notes to study. Along with these, in the IMS notes or Test Series answers or even solved PYQs, I've marked certain questions that are important.  I revise them all too. 

When you solve PYQs or Test Series questions, highlight (in your short notes) the formulae/theorems used in them. Over time you'll notice certain portions have been repeatedly asked. They'll be barely 20-25% of your notes but they're the most important. Make sure you remember them. In the other 75-80% portions, you may not be able to remember everything so do what you can. 

EiChan,chamomileand3 otherslike this
4.5k views
@RonWeasley Even if you define scalar multiplication as modulo 7, the axioms of a vector space won't hold. 
For example, one of the axioms is (a#b)*v= a*(b*v). Here # is the multiplication operator of the field F (as a and b are both scalars) and * is scalar multiplication. In this case, # is multiplication mod 5 and * is multiplication mod 7.
[This differentiation of operators is important as you'll realise at the end of this text. This is the standard definition. For clarity you can glance at this -> https://www.math.arizona.edu/~cais/223Page/hout/236w06fields.pdf specifically at page 5 axiom 6 ]

Coming to the example, let a = 2, b = 3, andv=6. Here 2,3 belong to Z5 and6belongs to Z7.
Now (2#3)*6 = (6 mod 5)*6 = 1*6 = 6.    2*(3*6) = 2*(18 mod 7) = 2*4 = 8 mod 7 = 1
    So LHS =/= RHS.
Here the different values come because you have to take mod 5 when multiplying two scalars, and not mod 7 (as per standard definition of Vector Space)

Long story short, Z7 is not a vector space over Z5 no matter what operator you take for scalar multiplication. In fact, according to some comments here (https://math.stackexchange.com/questions/1927048/is-z7-integer-modulo-under-addition-a-vector-space-over-z5), you cannot define a scalar multiplication operator for this.

Also, don't worry about such questions. A quick google search reveals that the proof of why Z7 is not a vector space over Z5 uses concepts and theorems not in our syllabus. So it won't come in the exams. 

chamomile,AJ_and3 otherslike this
5.2k views


It took me 10 minutes to figure it out. Is maths even suitable for me?! :P :P
Falcon,Infinitybeyondinfinityand2 otherslike this
3.5k views
@CelebornThanks for sharing! That was very elaborate. I find myself too slow with lengthy topics like 3D, modern etc where I start by solving most of the questions present in IMS notes. How do you plan on finishing the syllabus twice? Do you go through the books/IMS notes wholely or just following your own notes and compilation of selected questions?


By now for these topics (like Modern, 3D), I have already done IMS notes multiple times. So revision is a bit faster. In the notes, I don't go through everything. I have ticked certain questions that I need to read and revise + double ticked some questions that are complicated and I need to wrote/solve to revise. I don't look at the remaining portion. 

Before I begin revision though, I'll make a rough estimate of how much time it will take. If I have less time, I'll just revise the short notes (Kanishak Kataria notes). If I have a bit more time, I'll do IMS notes. Last year (2020 attempt), I didn't have time so I did only the short notes + 2019 test series questions topic wise. This year, I'll do IMS notes for certain topics (Modern, Real analysis + calculus, 3D) and short notes for all other topics. 

I am planning to go over my IMS notes, revise PYQs, revise my short notes and one Test Series. Preferably I want to also cover one test series of 2020. Essay and GS4 I have covered earlier so I'll only be revising that and write tests.


How realistic does this seem considering that you have given earlier attempts with maths? :P 

Before I say anything, keep in mind that I'm no expert. I scored 153 in Maths in my first attempt. This time I'm hoping for somewhere between 240-280 (based on IMS key). So whatever I say, it comes from a place of failure, not success. Hence take my words with a pinch of salt. 

Your task list seems doable, although a bit ambitious. Here are some conditions though:

1) In doing all this, you'll have to prioritize Maths over GS. This is mentally hard to do since GS is vast. Further GS is the common link for all aspirants so every institute will bring out some material/programme for GS. FOMO is your enemy here. Decide early on what's absolutely necessary and stick to that. 

2) You won't be able to write and practice every question. Try to read and mentally solve questions while revising for most of the material. This will save time. 

3) Make a priority list at the beginning for instance say IMS notes >Test Series 2021 >Short notes >PYQs >Test Series 2020. This way if you lack time, drop whatever is having a lower priority. 

4) This time there is 3-4 weeks lesser time than earlier. So from the very beginning you'll have to be at your most productive.

5) Estimate from the beginning how much time you'll devote item by item (say 6 days for IMS notes of Modern + 2 days for Modern PYQs - something like that). Do this for everything, including GS. This will help you realise very soon if you're taking more time and help you adjust accordingly. 

All being said, you are in a good spot. Your GS4 and essay is done so that potentially saves 10-15 days. You've done your PYQs and just need to revise them so you can do that in half the time than usual. 

So I hope you'll be able to pull this off. All the best! 


Failure is almost always a better teacher than success. I'm sure it will be great this time :D


Absolutely agree with almost everything that you have said. FOMO is such a big problem for me, I'm planning to work on my content consolidation instead of answer writing (Except to continue the mains test series I'm enrolled in) but that is at a lower priority than mathematics. 


I'm going to star this and come back to it once I (hopefully!) clear prelims. Thanks a lot, and all the best to you too :)

chamomile,Celebornand2 otherslike this
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2020 was definitely tougher. In fact the past few years, Maths is definitely getting tougher. You can feel the difference in solving PYQs. 

I just hope there's reversion to the mean and Maths comes easier next couple of years :p


Hahaha, totally. Irrespective of that, you're going to do really well this time. Perhaps then we'll pester you with even more doubts :P


All the best :D

chamomile,Celebornand2 otherslike this
2.1k views

How are you guys planning to move with maths in the post-pre-phase? Have thought of any sequence of topics to be followed post pre. Are you planning to take up tough/lengthy topics first or the relatively better ones first?


P.S. Asking since it's almost time to get into the prelims mode and this is what I've been procrastinating about lately :P

The last two times I've gone by the order of the syllabus (paper 1 linear algebra till paper 2 fluids in sequence). My weakness both times in the exam has been Paper 2 so this time I'll start with Paper 2 first and then Paper 1. I'll start with the tougher topics (Modern Algebra, Real analysis, Fluids). Then move to the lighter topics.

This time I plan on revising my notes + solving PYQs + taking part in the test series. My plan is to complete one revision + solve PYQs in 2 months; solve test series according to schedule and then revise everything in the last month (notes + PYQs + Test series questions). If I lack time, I'll drop the PYQs. If miraculously I've more time, I might read through previous years solved IMS test series and attempt certain tough questions. Based on my experience though, I'll barely have time to complete my primary targets.

EiChan,chamomileand2 otherslike this
4.5k views
@DHARNA This is a confusing part for me. 'c' appears to be many things at once - it is the parameter of the catenary, it is the distance between the vertex and the origin and also horizontal tension at lowest point = wc.

As far as I can tell, here's how it evolved.
The starting point is the horizontal tension T0. If we take w as the weight per unit length, there must be some length of the string such that T0 = wc ( To understand this, let us assume T0 = 80 and w = 10 as measured somehow. Then we can take a string of length 8 such that weight of this string = 10x8 = 80 = T0. ). In other words we chose c depending on the given horizontal tension and weight per unit length. 
This is the physical significance of 'c'. 

Now if we put T0 = wc , we can derive the intrinsic equation of catenary in terms of c and other variables (like angle psi). This is how c becomes the parameter of catenary.

Finally when we derive the cartesian equation of the catenary, there are steps where integration is involved. Here we take c as the height y from origin where angle psi = 0 (i.e. the vertex) to calculate the constants. Thus c becomes the distance between origin and vertex. In other words, we find c first from the tension and then fix the origin such that the distance from the vertex to the origin is also c. 


I hope this is right. If there's something faulty, do correct.

chamomile,AJ_and2 otherslike this
8.7k views


Just want to confirm if this approach is correct? The IMS solution for the PYQ contains partitioning of matrices. I don't see why we need that here. Thanks!

Was going through this question a few days back and upon a few failed attempts stumbled upon this solution on the internet. It’s as simple and crisp as it gets.

chamomile,BurtMacklin_FBIand2 otherslike this
2.1k views
@ArchandFeels like I never leave the godforsaken procrastination club :P


Archand,peterparkerand1 otherslike this
4k views
@CelebornThanks for sharing! That was very elaborate. I find myself too slow with lengthy topics like 3D, modern etc where I start by solving most of the questions present in IMS notes. How do you plan on finishing the syllabus twice? Do you go through the books/IMS notes wholely or just following your own notes and compilation of selected questions?


By now for these topics (like Modern, 3D), I have already done IMS notes multiple times. So revision is a bit faster. In the notes, I don't go through everything. I have ticked certain questions that I need to read and revise + double ticked some questions that are complicated and I need to wrote/solve to revise. I don't look at the remaining portion. 

Before I begin revision though, I'll make a rough estimate of how much time it will take. If I have less time, I'll just revise the short notes (Kanishak Kataria notes). If I have a bit more time, I'll do IMS notes. Last year (2020 attempt), I didn't have time so I did only the short notes + 2019 test series questions topic wise. This year, I'll do IMS notes for certain topics (Modern, Real analysis + calculus, 3D) and short notes for all other topics. 

chamomile,Archandand1 otherslike this
4.4k views

Did anyone solve this question? Shouldn't p and q be same from symmetry? Wasn't statics and dynamics section very difficult in 2020?

@Celeborn @Archand 

Don't consider the weight to be uniformly distributed. Assume a centre of gravity at a certain length and then solve by taking moments accordingly. Let me know if you'll need anything else. 


I remember that the last two questions have very difficult (or maybe seemingly difficult) questions. That does limit our choices but the general consensus seems to be that 2020 was more difficult than earlier years across chapters. Haven't given any mains so perhaps Celeborn can clarify it for us :)


2020 was definitely tougher. In fact the past few years, Maths is definitely getting tougher. You can feel the difference in solving PYQs. 

I just hope there's reversion to the mean and Maths comes easier next couple of years :p


chamomile,Archand
2.6k views

@Archand @Celeborn Do you have the 2021 solutions? Please share if you do

https://drive.google.com/drive/u/0/folders/1ZDgBKYD9ztSaRowzVD2fu_Xgtq-lD89B


Hope this helps :)


MikeWozniak,Celeborn
620 views

How are you guys planning to move with maths in the post-pre-phase? Have thought of any sequence of topics to be followed post pre. Are you planning to take up tough/lengthy topics first or the relatively better ones first?


P.S. Asking since it's almost time to get into the prelims mode and this is what I've been procrastinating about lately :P

Hey! 


Yet to write my first mains so take what I say with a pinch of salt. My plan is to follow the IMS test series schedule. The first round of tests has sectional tests, I'm going to follow that. Of course, there are topics that need more effort than what I'll be able to give them in the first round but I intend to compensate for that as the test series moves ahead. 


Also, welcome to the procrastination club :P

chamomile,AJ_
4k views

Hi there!

I wanted to check about the sources / reference material that one should use for math optional. I got IMS class notes, but have been finding it difficult to follow them. Should I get the standard books instead? What books / material have you guys been doing?

You can follow the blogs of previous year toppers. 

https://nitishhebbar.wordpress.com/2015/07/23/booklist-and-strategy-for-paper-2/

IamThat,psyduck
8.4k views
» show previous quotes

This seems like a really cool and intuitive approach.
I did it by the brute force method. Though the calculations got a little bit tedious but got the result in 5 steps (of which two were quite tedious and confusing where we find the determinant of the matrix C :P).


Hey, thanks! I took some inspiration from the IMS solution, was too scared to go the brute force route! :P


Haha, I'll now do it by your method just for the fun of it. I can totally see myself spending 30 minutes only to find a teensy calculation mistake! 

It is almost cathartic when all the terms of the determinant (involving 12 variables in total and 4 variables per term)

cancel each other.

Feels great even when you know that you balanced and changed the subscripts of some terms just to get you to the right answer :P :P

Archand,arjunas
1.3k views
I gave 2020 mains. Paper was somewhat same in difficulty. Par i felt ki practice achi khaasi chahiye. Lagrange interpolation aur baaki kuc questions me i fucked up. Kuc silly mistake hui to kuc question aise the jo time hote to aa jaate aur kuc question to aaye hi nahi. Mai yahi kahunga jo aate hai unhe jaldi attempt kar lo aur time bachao baakiyo ke lie jisme problem hori ho. 
EiChan,IamThat
9.7k views
@RonWeasley Even if you define scalar multiplication as modulo 7, the axioms of a vector space won't hold. 
For example, one of the axioms is (a#b)*v= a*(b*v). Here # is the multiplication operator of the field F (as a and b are both scalars) and * is scalar multiplication. In this case, # is multiplication mod 5 and * is multiplication mod 7.
[This differentiation of operators is important as you'll realise at the end of this text. This is the standard definition. For clarity you can glance at this -> https://www.math.arizona.edu/~cais/223Page/hout/236w06fields.pdf specifically at page 5 axiom 6 ]

Coming to the example, let a = 2, b = 3, andv=6. Here 2,3 belong to Z5 and6belongs to Z7.
Now (2#3)*6 = (6 mod 5)*6 = 1*6 = 6.    2*(3*6) = 2*(18 mod 7) = 2*4 = 8 mod 7 = 1
    So LHS =/= RHS.
Here the different values come because you have to take mod 5 when multiplying two scalars, and not mod 7 (as per standard definition of Vector Space)

Long story short, Z7 is not a vector space over Z5 no matter what operator you take for scalar multiplication. In fact, according to some comments here (https://math.stackexchange.com/questions/1927048/is-z7-integer-modulo-under-addition-a-vector-space-over-z5), you cannot define a scalar multiplication operator for this.

Also, don't worry about such questions. A quick google search reveals that the proof of why Z7 is not a vector space over Z5 uses concepts and theorems not in our syllabus. So it won't come in the exams. 

Thanks a lot. It cleared a lot of my concepts.

Celeborn,
5k views
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