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

Is Z7 a vector space over Z5 ? If we take scalar multiplication as trivial multiplication, then, it will not be a vector space. But, if we take scalar multiplication as modulo 7, then it seems to be a vector space. Can anyone please explain how to go about this question?

3.5k 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
@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

Hello everyone 

I am revising maths and finding some good mates who are on same page  or near by as it is difficult many times to appreciate doubts on mechanics if one is working on real analysis. If any one interested in making group of 2-3 people on such line ,can msg on my whatsapp no.6284231773 . Moreover,Thank you to all  the people who have discussed their valuable experience in above discussions.

3.2k views

Can anyone who has first hand experience of IMS test series please tell us how was it ?


3.1k views
How do you guys revise as mathematics syllabus is huge?
3k 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

2.7k 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
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

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
@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?


THE_MECHANIC,
2.6k 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
@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 

chamomile,
2.5k 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! 


chamomile,Archandand3 otherslike this
4.3k 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
3.7k views

I have found this group quite helpful, may try.

https://t.me/MathematicsLevelUp
2.4k views

Maths meymey.. 

MikeWozniak,EiChanand6 otherslike this
3.6k views


chamomile,AJ_and4 otherslike this
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