Approaching Mathematics as an Optional.

·   What to expect from this optional

Mathematics as an optional of CSE has been doing well off-late, if we look at the higher end of the spectrum of marks obtained by candidates. But at the same time I feel most of the candidates opting for this optional are not aware of the effort required for obtaining such high marks. If we set aside a few exceptional candidates, one would find that the top scorers of Mathematics (including myself) generally require multiple attempts at this exam before managing such high scores. 

This is not merely a coincidence in my opinion, and is probably a result of the numerous challenges this optional poses for a newcomer.

A few challenges which one may encounter during the course of studying this optional are :

1. Vast syllabus which may require 6-8 months of dedicated preparation
2. Some topics like Algebra, Fluid are difficult to master satisfactorily
3. Huge time investment in Mathematics which can end up affecting one's GS preparation
4. No correlation with other GS, essay papers
5. High degree of accuracy is needed in the examination as it has been generally observed that marking is binary (with little credit given for incomplete, incorrect answers)
6. High degree of competition exists in this optional and apart from the Top 30-40 scorers, others are heavily penalised as a result of scaling.

At the same time, there are a number of reasons why this optional is gaining favour with candidates in recent times : 

1. A major advantage of this optional is its predictability in the sense that one can be assured of a certain quantum of marks after leaving the examination hall based on calculation of one's correct attempts. 
2. Another factor supporting this optional is that across attempts one can expect an increase in marks which cannot be said with certainty in case of humanities optionals.
3. A lot of questions asked in the examination are repeated/on similar patterns as asked previously.
4. And finally, off late we are seeing marks in Mathematics to be among the highest across all optionals.

For those opting for mathematics it is a pre-requisite to have a strong interest as well as some background in Mathematics at the under-graduate or graduate level, in my opinion.

• One should not merely opt for this optional considering one's decent scores at the school level, as it may be misleading at times due to difference in syllabi of CSE and intermediate levels. 

Also one should opt for this optional with the full realisation that a greater investment of time and effort is required in Mathematics, when compared to other Humanities optionals. 

Preparing this optional is a long, arduous journey which one should be ever willing to undertake before opting for Mathematics in CSE. 

·      General principles to follow 

• Go for breadth rather than depth - try to cover as many, if not all topics before the exam. From each topic there can always be a question which you may not be able to answer in the exam so it is better to be ready with alternates at hand rather than trying to master a few topics.

• Always try to complete the syllabus or atleast 10-11 topics before prelims, as after prelims one is overwhelmed by the amount of work to be done to get ready for mains

• Confine your study to a single source and ensure multiple revisions/practice of the same source

• Since questions are often repeated, it is essential to cover the standard sources, previous years questions even if one has read the topic in their graduation

• Rather than dwell too much on difficult questions in each topic, focus on getting control over the easy/moderate questions {around 60-80% marks are always attainable by solving questions of this kind}

•  Focus on previous years questions and solutions 
• DIPS Academy solutions for some topics + online solutions for a few other topics are available at : https://sites.google.com/site/sunderlalchd/ 
• I mainly looked at the questions post the year 2000 (before which the pattern was significantly different)

• Make notebooks containing solutions to general and representative problems + difficult problems for each topic, which may be difficult to recall in the exam. 
• This allowed me to revise all the topics on the last day before Mains.

• Practise questions/give tests right upto mains 
• I gave a test on the day before the language papers to maintain a decent flow of problem solving

• Do not be discouraged/ complacent by seeing your scores of test series. They are in no way related to your final marks obtained. They should seen just as an indicator of whether you need a course correction in your preparation strategy or not, nothing more.

• Scaling in Mathematics : It is a non-issue as far as I am concerned. While it is true that you end up getting lesser marks than your correct attempts in the actual examination, the scaling factor is such that one still can end up higher than almost all other optionals even after scaling is done.
• Generally the factor is seen to be around 0.8-0.9 which depends on paper difficulty and other factors
• Around 400 correct attempt should easily get you 320-330 marks, and with around 450 correct attempts have obtained 350+ marks

• Coaching vs self study  : Mathematics as an optional of CSE is purely based on understanding of concepts and plenty of practise. While coaching can help one with the former, it is the practise part which is more important in my opinion. 
• Based on my experience I can say that there is no requirement of coaching in order to be successful in this optional. 
• However, this is a highly individualistic assessment and requirements of coaching may vary from person to person. 
• If one feels that they can handle the syllabus by reading from standard text-books then they should refrain from joining a coaching institute.
• One advantage of joining a coaching institute is that it enables a more streamlined completion of syllabus.
• However, after having discussed with many other candidates, I believe that total reliance on coaching institutes is not recommended. Any coaching if undertaken should be supplemented with standard textbooks in order to increase one's marks beyond a threshold.
• P.S : I did not join a coaching institute, so my views may be a bit skewed.

• Importance of test series : As mentioned earlier, mathematics requires a lot of practise and accuracy. 
• A test series enables one to familiarise with the actual exam setting, dealing with fixed space answer sheets, promptness in selecting the optional questions and time management. 
• Keeping these aspects in my mind, I joined Mathematics test series of an institute in both my attempts and I feel that test series has an important role to play in this optional.

• Answer writing for Mathematics :  
• For answer writing, one should follow the steps given in the solved examples of standard textbooks/notes. Continuous practise of problems while writing detailed steps should be sufficient to cover this aspect.
• While using the standard theorems which are given in the textbooks, one could merely write their statements, without providing their proofs, which may make the problem at hand unnecessarily complex, and would also reduce the effective space available to show the complete solution of the actual problem.
• At times in the examination, space given for a problem may be inadequate to list down all the necessary steps for the given problem. In such cases, one may chose to skip a few trivial steps in order to accomodate the critical steps involved in the solution.

• For first timers : One needs multiple revisions/ iterations of each topic before one starts feeling confident in this optional (lack of confidence/difficulty in recalling concepts in Maths before prelims for first timers is a natural feeling to have)