UPSC CSE Demystified! A Civil Services 2019 Batch initiative Topic wise syllabus coverage in Maths optional – Kanishak Kataria (Rank 1) Hi everyone! Following on from my previous post I am giving a detailed topic wise syllabus coverage. It will give you some idea as to how should Maths be approached topicwise. It is advisable to read the previous post first before continuing here. MATHEMATICS AS AN OPTIONAL Topic wise coverage PAPER 1: It is lot easier than paper 2 but HIGHLY prone to silly mistakes. So do not take it lightly and practice as much as you can. Also, it has more scaling then paper 2. So any mistake will hurt you much more. Linear Algebra: Very scoring topic. With consistent practice you can assure yourself of full attempt. There isn’t much variation in type of questions asked. Important areas: Linear Transformation, Matrix of LT, Linear Equations, Bases and Dimension Proofs: Don’t waste too much time on them. Basic understanding of definitions is very important. Calculus: Do it in continuation with Real Analysis (As has been done in IMS notes). Important Areas: Lagrangian Multipliers, Jacobian Practice all types of problems involving Multiple Integrals . Single variable calculus is very easy. Remember important integrations to save yourself time. Keep a sheet of such integrations and revise them time to time. Beta and Gamma functions can become handy in solving integrations involving sin and cos functions. Do not fully ignore these topics. Curvature has been asked in the past. But keep it at lowest priority. Analytic Geometry: Till conicoids , It is a very intuitive and scoring topic with certain guarantee of attempting the question. Practice is important to recognise which type of parametric equation should you start with like assuming symmetric vs asymmetric form of line before starting the problem. Locus problems are quite common and you should be thorough in it. The Line is an important and scoring topic. Post conicoids, Subsequent topics are challenging for sure. Little amount of cramming is needed to remember various formulas and approaches. Short notes are very handy in this section. With practice you will be able to identify particular models. Learn how to start a given problem, many question are repeated in the exam. Do not leave conicoids. As per your bandwidth pick important topics based on PYQs. Atleast cover all the problems discussed in the test series. Ordinary Differential Equations: Very simple topic. Remember the formula and apply it. The only challenges are multitude of formulas and avoiding silly mistakes. I did a lot of silly mistakes in my 1st iteration from the notes. 2nd order LDE with Variable coefficients is a portion which needs much practice. Laplace transformation should also be covered as there is a tendency to ask questions from it. Some problems might seem easy but involve some tricks to integrate. Such tricks you can remember only when you solve the problem once. Keep a shortnotes book handy to note such examples. Dynamics and Statics Easier as compared to the other 2 physics topics from Paper II. Dynamics: SHM, Catenary, Cycloidal motion, Projectile etc — cover all different question types. They follow a specific procedure which you need to replicate in each problem. It can be a scoring alternative – an X factor – in your preparation if you are comfortable in them. But focus only if you have covered the other topics. Its marginal utility isn’t that high, more so if you get a favourable question distribution in final exam where you can ignore all the questions from these topics. Statics Virtual work is a very simple and scoring concept. If not all, cover atleast the previous year questions involving Principle of Virtual Work. You should be proficient in all the 10 pointer compulsory problems asked from these topics in UPSC and test series. An easy question from this topic might make your job of picking non-compulsory questions in Paper I — Part II much easier. Vector Analysis: Important topics: Serret-Fernet Formulae, Divergence and Curl are very important topics. Solve ALL the problems on the Green, Gauss and Stokes theorems asked in UPSC and in test series. The more you practice them, the lesser you will commit silly mistakes. Change of axes and showing invariance is important. Overall a scoring topic. Please cover it fully. PAPER 2: It has more challenging topics but not undoable. Lesser scaling than Paper 1, so if you attempt more, you will score more. Modern Algebra: One of the most feared topics. If you haven’t encountered the terms before, there are chances that you will feel lost. As a result, this topic will need more than average time. The only answer to the fear of Modern Algebra is revision, revision and loads of revision. Topics up to Homomorphism of rings are manageable and relatively easier to understand but you need practice to solve the problems. From Fields onwards, you have to struggle much more – but that’s why you opted maths, didn’t you?! If you cannot understand anything, please be more strategic and cover according to PYQs. Do not waste too much time by getting stuck. Try to be thorough with all the PYQs and test series questions. Discussions with friends also helps. With multiple revision you will begin to have more clarity. Keep handy negation examples in hand like Quaternion group! Such problems are very easy to score from. One important TIP: Homomorphism is a very very important topic and also one of UPSC’s favourite. If you understand it, a lot of problems become easier. Also IMS notes are sufficient, don’t start chasing textbooks. There isn’t much difference between the two. Almost everything important in the books is there in the notes. Just revise as much as you can. Clarity increases with more revisions. Real Analysis: Amongst the tougher topics. Try to cram all the convergence tests for sequence and series and practice as much as possible. Continuity is a favourite concept for UPSC. Reimann integral and Uniform convergence as well. You should not fret too much over proofs. They have very high CBA and should be done only if you have too free time! The only way out is practice and revision. To put things into perspective, I would just say that in the 5 day gap during Mains, 50% of my time was devoted to Modern Algebra and Real Analysis. Complex Analysis: This topic is trickier than it looks. Much practice is needed. Cauchy theorem and Contour integration are the frequently asked concepts. Learn all the tricks in contour integration problems. Other important concepts: Taylor and Laurent expansions , convergence and singularities . In addition to IMS notes, you might need to refer to Krishna book for better understanding of few topics. Atleast try to look at the solutions to select PYQs provided by IMS. Partial Differential Equations: Linear PDE with constant coefficients is quite similar to ODE. Non Linear PDE problems are little difficult. Learn Charpit’s method (even though not in syllabus) and cram Cauchy characteristics method. Cauchy method should be used only when explicitly asked in exam. If nothing is mentioned, use Charpits. Physics application problems should be practiced as they are asked as 15-20 pointers and are quite scoring and follow a fixed pattern. Reduction to canonical form questions are also quite frequent. Linear Programming Problems: The easiest topic to prepare but HIGHLY PRONE to silly mistakes. In a paper with limited space, any silly mistake means 0 marks because with all the tables, there isn’t any space to correct mistakes and redo the problem. Solve ALL the PYQs. There are many edge case problems given in the notes, you should have done them atleast once. Be thorough in all the problems and don’t intermix the steps and get confused. Try to improve your overall speed and accuracy. Computer Programming and Numerical Analysis: CP was easy for me to prepare plus IMS notes are little excess which can lead to time wastage. Try to cover from PYQs. Maxterm and Minterm concepts should be known. Algorithm and flow charts should be done only after reading Numerical Analysis. Draw all the flowcharts by yourself. And don’t just read from books/notes. Numerical Analysis is a scoring yet difficult chapter. Biggest challenge is to remember all the formulas correctly. Error approximation is being given importance now and should not be untouched. Try to do for standard methods like Newton-Raphson etc Fluid Dynamics and Mechanics 10 pointers are manageable and 15-20 pointers are repetitive. If you get hold of this topic, again it can act as an X factor but don’t spend too much time into it. Do a thorough Cost Benefit Analysis with respect to other topics and GS prep. If you do have time, cover this topic by solving the PYQs. Repeat attempters shouldn’t ignore it. Moment of Inertia, Lagrangian and Hamiltonian in Mechanics along with Continuity equation, Sources and Sinks in Fluids are easier topics. Lagrangian and Hamiltonian problems are very scoring and follow a fixed pattern. If you can learn that, a lot of scoring options open up in Paper II-Part II. I covered these topics from Vajpayee Sir’s DIAS videos and IMS notes (solved examples). The videos aren’t that conceptually enriching but they do help in boosting the confidence. My biggest take away was that in topics like Fluid, 10 pointers are scoring whereas 15-20 pointers repeat. So, if I cover all PYQs and few model problems, there is a chance that I might actually attempt a few difficult problems in exam and get some partial marks. I got the videos from a friend of mine. They are probably available on Neostencil. Still I would say that they are not worth spending time and money into! If you can manage them easily, good for you else leave them. Recommended order of topics to finish syllabus: Topic(approximate number of days to complete) 1. Ordinary Differential Equation (10 days) 2. Partial Differential Equation (10 days) 3. Vector Analysis (10 days) 4. Linear Programming Problems (7 days) 5. Modern Algebra (30 days) 6. Linear Algebra (15 days) 7. Real Analysis + Calculus (45 days) 8. Complex Analysis (15 days) 9. Analytic Geometry (15 days) 10. Computer Programming and Numerical Analysis (10 days) 11. Dynamics and Static (10 days) 12. Mechanics and Fluid Dynamics (15 days) First 4 topics are to get into rhythm of solving maths problems. They are more “application of formula” based. Next 4 topics are little taxing but you will be at peak of studies and can sustain it. Some portions of Modern Algebra and Linear Algebra also overlap like Vectorspaces and Groups. Linear Algebra and Calculus provide little relief from theoretical problems. Complex Analysis has a minor overlap with Real Analysis (convergence etc.) which might be helpful. Analytic Geometry and Computer Programming and Numerical Analysis again get you into that application based topics, thus breaking your saturation from theoretical topics. Remaining physics topics should be done as per your own level of overall preparation. Doing them at last won’t break your rhythm in other topics. Few topics like PDE, Complex etc should be done as prerequisites to Fluid Dynamics. Also you can mix topics depending on your comfort level. You can put either Analytic Geometry or Numerical Analysis in between Modern Algebra and Real Analysis so that you get refreshed between two heavy weight topics. LPP and Vector Analysis are floating topics which can be done anytime. Total estimated time is around 6-7 months. This is just a rough approximate. You can reduce this time depending on your time allocation to optional vis-a-vis GS at the start. I would advise you to devote at least 6 hours daily during initial days, so that you can finish the syllabus on time. If your 1st revision is done before Prelims, you are in a wonderful position from Mains perspective and the burden of optional would reduce substantially. In my last two posts, I have tried to cover as many dimensions as possible. I have always focused on finding my own path. These posts should only act as a guiding light in case of confusion. You are the best judge for yourself, so try to formulate your own strategy.
