• Unlike the NPR, which record even a foreigner staying in a locality for more than six months, the NRC is a citizenship enumeration drive that list only the legal citizens of the country, with necessary documents. • Earlier, following the SC’s order, the Government conducted the NRC in Assam and as a result of which over 19 lakh applicants failed to make it to the NRC list. • The Citizenship Act empowers the government to compulsorily register every citizen and maintain a National Register of Indian Citizens. A nationwide NRC, if undertaken, would flow out of NPR. • This does not necessarily mean that an NRC must follow NPR — no such register was compiled after the previous NPR in 2010. After a list of residents is created, a nationwide NRC — if it happens — could go about verifying the citizens from that list. • The Home Ministry issued a statement saying, “There is no proposal at present to conduct a nationwide NRC based on the NPR data. Further, the Home Minister said that the two were not connected and that NPR data would not be used for NRC. • However, statements linking the NPR and NRC have been made by the government in Parliament. And as per the 2018-19 Annual Report of the Home Ministry the NPR is the first step towards the creation of the National Register of Indian Citizens (NRIC) under the provisions of the Citizenship Act. Need For Nation-Wide NRC or NRIC • NRC will help identify a much-needed perspective on the extent of illegal migration. With this, the anxiety over illegal immigrants changing the demography of country will also be done away with. • There is also statutory obligation of the state under Section 14A of the Citizenship Act,1955 that provides that the Central Government may compulsorily register every citizen of India and issue national identity card to him. • This will also help in solving the immigration issue as it will deter future migrants from entering the country. • The introduction of nation-wide will also aid the border agencies in effective border management, especially with Nepal and Bangladesh. Arguments Against Nation-Wide NRIC • The existing provisions like the Foreigners Act, 1946 and Passport (Entry into India) Act, 1920 and tribunals are sufficient to detect, detain and deport them. • The introduction of such a provision also has to cross legal hurdle as NRIC scheme would thus be directly in violation of the K.S. Puttaswamy judgment on right to privacy. • The exercise also brushes aside the issues that cropped during Assam’s NRC like potential of statelessness, risk of deportation etc. • Many experts see it as a wastage of public resources and expenditure of the taxpayers’ money that could otherwise have been fruitfully deployed. • Further, there is lack of adequate detention facility and as per media reports detention camps are infamous for their inhumane living conditions. • There are fears that such an exercise could end up targeting minorities, poor and illiterate sections in the country. • There are also issues in implementation like it may take a gigantic toll on people’s time, money and productivity. • Lastly, the government has not prepared a post NRC implementation plan like deportation/ disenfranchisement etc. • With the government collecting data of such great magnitude across the country, there are data privacy concerns around it. Officials, however, insist that NPR information is confidential, meaning it will not be shared with third parties. However, there is as yet no clarity on the mechanism for protection of this vast amount of data that the government plans to collect. Conclusion • It is important for the government to balance its larger vision of providing a homeland to persecuted minorities in the immediate neighbourhood and its promise of non-dilution of indigenous identity of the citizens of North-East. • The government must also seek to address the larger question of illegal migration. The NRC should attempt to prevent further arrivals of illegal migrants. • To tackle issue of illegal migration comprehensively there is a need for a multi prong approach by focussing on comprehensive border management, assistance from international organisations such as United Nations High Commissioner for Refugees (UNHCR) among others

Recently, the Government had passed Citizenship Amendment Act that was followed by the country wise protest in different parts of India. The issue further got muddied on the possible implication of the amendment post introduction of nation-wide National Register of Citizen (NRC). To understand the issue, let’s first know about the provisions of the act. The Citizenship Act, 1955 : • It provides for acquisition of citizenship by birth, descent, registration, naturalization and by incorporation of territory into India. • The Act prohibits illegal migrants from acquiring Indian citizenship. It defines an illegal migrant as a foreigner: (i) who enters India without a valid passport or travel documents, or (ii) stays beyond the permitted time. • It regulates registration of Overseas Citizen of India Cardholders (OCIs), and their rights. An OCI is entitled to multiple-entry, multi-purpose lifelong visa to visit India. • The earlier provision allowed Central government to cancel the registration of OCIs on grounds such as fraudulent registration, imprisonment for more than 2 years within 5 years of registration, sovereignty & security of country etc Provisions Of The Act • The Bill amends the Citizenship Act, 1955 to provide Indian citizenship to the persecuted minorities (Hindu, Sikh, Buddhist, Jain, Parsi & Christian communities) from Pakistan, Afghanistan and Bangladesh, who have arrived in India on or before 31st Dec, 2014 & are living in India without valid travel documents. • The amendment reduces the aggregate period of residential qualification for acquiring citizenship by naturalization from 11 years to 6 years, along with continuous stay for last 12 months. • The amendment Act also provides for cancellation of registration of Overseas Citizen of India (OCIs) for violation of any law in the country. Benefits For Persecuted Minorities 1. The Act is an atonement of the wrong that was done during India’s partition as it will safeguard all who had been victims of partition. 2. In Pakistan, Bangladesh and Afghanistan, religious minorities face severe discrimination that is often state sanctioned and institutionalized, especially in Pakistan. 3. Further, women face major brunt, sometimes stalked, molested and raped with no reprieve from state. Moreover, areas of residence are targeted during riots, bombings, terrorist attacks etc. 4. Several refugees living across the country have been victimized and were forced upon to convert, before fleeing to India. 5. Lastly, the Act is said to benefit many people by allowing them to take up self-employment, buy property, open bank accounts and Aadhaar. E.g. it will be of immense benefit to communities like Chakma and Hajongs of Bangladesh. Opposition To The Act : 1. The Act provides for differential treatment to illegal migrants on the basis of their religion, which may violate Article 14 of the Constitution guaranteeing equality to all persons, citizens and foreigners. 2. Another issue with listing out non-Muslim minorities is that it excludes various persecuted minorities. E.g. Rohingyas of Myanmar and Ahamadiya in Pakistan. 3. There is also an issue with the choice of countries as leaves out other neighbouring countries like Sri Lanka, Myanmar etc 4. The Act is in conflict with Assam Accord 1985 as on one hand NRC and the Assam Accord marks the line of eligibility for Indian citizenship as 24th March 1971. However, the Act marks the eligibility line as 31st December 2014. 5. The amendment also goes against the spirit of Clause 6 of the Assam Accord, which requires the government to provide safeguards to protect the culture & sociolinguistic identity of the Assamese people. 6. The local community fears that the prospect of citizenship will encourage migration from Bangladesh and might lead to outsiders dominating indigenous population. 7. Further, the amendment has revived an old divide between the Brahmaputra and the Barak river valleys. The large Bengali Hindu population of the Barak Valley have supported the amendment, whereas the residents of the Brahmaputra Valley see it as an instrument that may change the ethnic demography of the region. 8. The Act also grants the central government wide discretion to cancel OCI registration, even for minor offences like violation of a traffic law. 9. Lastly, the repercussions of the Act will also extend even to neighbouring country of Bangladesh. As the incumbent government in Bangladesh will find it difficult to face domestic opposition that the Act labels Bangladesh as the source country for illegal immigrants Assam Accord, 1985 : • It was a Memorandum of Settlement (MoS) signed between representatives of the Government of India and the leaders of the Assam Movement. • As per the provisions of the AccordI. All those foreigners who had entered Assam between 1951 and 1961 were to be given full citizenship, including the right to vote. II. The entrants between 1961 and 1971 were to be denied voting rights for ten years but would enjoy all other rights of citizenship. III. Those who had done so after 1971 were to be deported.

Indian Forest Service (abbreviated as IFS or IFoS) is one of the prestigious All India Services like Indian Administrative Service (IAS) or Indian Police Service (IPS). To get into IFS, a candidate has to sit for the same preliminary exam as civil service aspirants do. But what is the minimum educational qualification for Indian Forest Service (IFS/IFoS) Exam? Let’s see. Minimum Educational Qualification for Indian Forest Service (IFS/IFoS) Exam The candidate must hold a Bachelor’s degree in any of the following subjects/ disciplines. Bachelor’s degree with at least one of the subjects as Animal Husbandry & Veterinary Science. Bachelor’s degree with at least one of the subjects as Botany. Bachelor’s degree with at least one of the subjects as Chemistry. Bachelor’s degree with at least one of the subjects as Geology. Bachelor’s degree with at least one of the subjects as Mathematics. Bachelor’s degree with at least one of the subjects as Statistics. Bachelor’s degree with at least one of the subjects as Physics. Bachelor’s degree with at least one of the subjects as Zoology. Bachelor’s degree in Agriculture. Bachelor’s degree in Forestry. Bachelor’s degree in Engineering. Graduation should be from of any of Universities incorporated by an Act of the Central or State Legislature in India or other educational institutions established by an Act of Parliament or declared to be deemed as a University under Section 3 of the University Grants Commission Act, 1956, or possess the same qualification. Can last year students of graduation also apply? Candidates who have appeared at an examination the passing of which might render them educationally qualified for the Commission’s examination but haven't been informed of the results as also the candidates who shall appear at such a qualifying examination also will be eligible for admission to the preliminary exam . All candidates who are declared qualified by the Union Public Service Commission for taking the Indian Forest Service (Main) Examination will be required to produce proof of passing the requisite examination with their application for the most Examination failing which such candidates won't be admitted to the Indian Forest Service Main Examination. The applications for the most Examination are going to be called sometime within the month of July/August, through online mode. What is the regulation to use for Indian Forest Service (IFS/IFoS) Exam? A candidate must have attained the age of 21 years and must not have attained the age of 32 years on 1st August of the respective year of preliminary examination . But the upper regulation prescribed above are going to be relaxable – up to a maximum of 5 years if a candidate belongs to a Scheduled Caste or a Scheduled Tribe. up to a maximum of three years within the case of candidates belonging to Other Backward Classes who are eligible to avail of reservation applicable to such candidates. up to a maximum of three years within the case of Defence Services personnel disabled in operations during hostilities with any foreign country or during a disturbed area and released as a consequence thereof: up to a maximum of 5 years within the case of ex-servicemen including Commissioned Officers and ECOs/SSCOs who have rendered a minimum of five years Military Service as on 1st August, and are released (i) on completion of assignment (including those whose assignment is thanks to be completed within one year from 1st August) otherwise than by way of dismissal or discharge on account of misconduct or inefficiency, or (ii) on account of physical disability attributable to Military Service, or (iii) on invalidment. up to a maximum of 5 years within the case of ECOs/SSCOs who have completed an initial period of assignment of five years of Military Service as on 1st August, and whose assignment has been extended beyond five years and in whose case the Ministry of Defence issues a certificate that they're going to apply for civil employment which they will be released on three month’s notice on the selection from the date of receipt of the offer of appointment. up to a maximum of 10 years in the case of:- (a) Low Vision (b) Hearing Impaired (Partially deaf) and (c) Locomotor disability (sub-category : Leprosy cured and Acid attack) To know about further relaxations, refer the UPSC notification. The Plan of IFS/IFoS Exam The Indian Forest Service Examination will contains two successive stages. Civil Services (Preliminary) Examination (Objective type) for the choice of candidates for the Indian Forest Service (Main) Examination Indian Forest Service (Main) Examination (Written and Interview) for the choice of candidates for the Indian Forest Service. How can you make sure that you clear IFoS Exam? Due to limited vacancies, the cut-off score of IFS aspirants for the most exam is usually greater than that of government officials Exam Prelims. But once you clear Prelims, your chances of converting are very high thanks to various factors . Apply before the last date, if you're eligible. You can apply for Civil Services (IAS, IPS, IRS etc) and IFS on an equivalent online form.

History Basic Books: NIOS course books for classes XI and XII on - Ancient India, Medieval India, Modern India, National Movement & Contemporary World and Culture of India. (All these are available in PDF format on internet) Advance Level Books: India’s Ancient Past by R.S. Sharma published by Oxford University Press A History of Ancient & Early Medieval India by Upinder Singh History of Medieval India (800–1700 AD) by Satish Chandra published by Orient Longman History of Modern India by Bipin Chandra (2009 Edition) India’s Struggle for Independence by Bipin Chandra & Others India After Independence (1947 - 2000) by Bipin Chandra & Others From Plassey To Partition And After by Sekhar Bandopadhyaya World History: The Story of Civilization, Part 2 by Arjun Dev, NCERT Contemporary World History for class XII (Old NCERT Book) Mastering Modern World History by Norman Lowe Geography Certificate Physical & Human Geography (Oxford) by Goh Cheng Leong NCERTs (New Editions) XI Standard: (1) India - Physical Environment (2) Fundamentals of Physical Geography XII Standard: (1) India - People & Economy (2) Fundamentals of Human Geography 3. School Atlas - Orient Black Swan 4. Indian Geography by D. R. Khullar Social Issues XI Standard NCERT on Indian Society (Chapters on Unity & Diversity and Population Issues) XII Standard NCERT (Chapters on Communalism, Secularism and Urban Issues such as Poverty, Housing, etc.) The Hindu or Indian Express Newspaper Indian Polity Constitution of India at Work (Class XI) NCERT Publication Indian Polity by Laxmikant The Hindu or Indian Express Newspaper Yojana Magazine Governance Issues From Government to Governance by Kuldeep Mathur Ethics in Governance, ARC Report Citizen Centric Administration (Chapters 2, 5, 6, 7 & 8 only and box items in the report) Developmental Issues Human Development Report & World Development Report Panchayati Raj in India by Kuldeep Mathur The Hindu or Indian Express Newspaper Kurukshetra & Yojana Magazines International Relations India’s Foreign Policy Since Independence by V.P. Dutt The Hindu or Indian Express Newspaper Indian Economy Indian Economic Development XI Standard NCERT Indian Economy by Sanjiv Verma Introductory Macro Economics XII Standard NCERT (Ignore all diagrams & mathematical formulas) The Hindu or Indian Express Newspaper Economics Dictionary published by Collins & Penguin Economic Survey 2017 - 18 & 2018 - 19 (to be out in Feb 2019, only recommended chapters) Ecology & Environment Certificate Physical & Human Geography by Goh Cheng Leong (Second Half of the Book) XII Standard NCERT Book on Biology (Chapters pertaining to Ecology) India Year Book (Chapters on Environment) Chapter on Climate Change from Economic Survey The Hindu or Indian Express Newspaper Security Issues India’s Security in a Turbulent World by Jasjit Singh, published by National Book Trust of India The Hindu or Indian Express Newspaper Science & Technology VIII, IX, X Standard NCERT books on Biology The Hindu or Indian Express Newspaper Monthly Magazine ‘Science Reporter for Science & Technology’ Ethics, Integrity & Aptitude Ethics in Governance, ARC Report Lexicon by Chronicle Publications The Book on Ethics, Integrity & Aptitude published by Access Publication Current Affairs The Hindu/ Indian Express

Dos: Revise, Revise and Revise: Whatever subject and topic you're studying, confirm to revise and remember so you are doing not make lose marks in those topics. Without proper revision, you'll probably carry more confusion into the exam hall and find yourself with a better negative score which will undo all the great work that you have otherwise done. Make assessment on Facts vs Concepts: The UPSC prelims over the previous couple of years in core subjects has become quite conceptual. So check out the last 4-5 year’s question papers and make an assessment of the sort of questions that are asked on each subject. For example, in Polity, you are doing not got to rote learn names of past Presidents, Election Commissioners etc. (Qs wont to be asked on them earlier but not anymore). The Economy paper is now highly conceptual and highly scoring. So concentrate on understanding the basics. Make assessment of all subjects. If your preparation may be a mismatch to the exam pattern, then you'll only be dalliance . Space out your current affairs preparation: Many students make the error of learning current affairs booklets within the previous couple of weeks hoping to end . Reality is that it'll be overload of data and your memory might not be ready to cope up with the sudden load. So spend a couple of hours everyday from now itself on current affairs and confirm again to revise regularly. Even if you're unable to end all current affairs, don't worry. Study and revise what you can. Same applies to map work - allot alittle slot for it daily and keep revising. Practice tons of Test papers: confirm to select up some test series booklets and attempt them no matter the extent of your preparation. This will assist you assess the extent of your preparation, your ability to end on time, and therefore the quite basic errors you commit like improper reading of the questions or options etc. Make a routine to be most active during exam hours: During the last weeks leading up to the exam, confirm you're studying or practising with intense concentration in the two slots of 9am-12pm and 2am-5pm. Your brain will get familiar with being most active during those hours. Check out the venue before the exam day: You (or someone who's getting to accompany you) must physically go and visit the exam venue once before the exam day, so that there are no surprises that day. You will also understand the simplest mode of transportation. Also, if you propose on getting into a cab, remember that there'll be huge demand for the cabs then you ought to keep a buffer of 10-15 minutes. Reach the venue well on time: confirm you reach the venue 45 min to 1 hour before the scheduled time. Last minute rush and anxiety to succeed in the venue could negatively impact your concentration. Dont's Do not be afraid: The paper is same for everybody . Trust your preparation and give your best. Any anxiety before or during the exam will hurt your performance. Close your eyes, exclude everything and take deep breathes for a moment to seek out calmness. Even if initially look, the paper looks tough and you are feeling you recognize nothing, don't get scared. Keep calm and undergo the paper question by question and you'll find ample number of questions that you simply can answer. Do not think you're unprepared or under-prepared: Your preparation is an objective reality and can't change on the day of the exam. Once you opt to offer the paper, don't let thoughts of your preparation enter your mind. Focus only on what you recognize and make a sensible attempt of the paper. Do not lose momentum going into the exam: you would like to be concentrating and studying the maximum amount time as you'll within the days leading up to the exam. The psychological state leading up to the exam is extremely important. Do not leave OMR sheet filling to the end: Students often ignore the very fact that filling OMR sheet not only takes time but is that the most vital a part of the prelims. If you are doing not want to travel to the OMR sheet after every question, confirm you fill it up after every 45-50 minutes a minimum of . This will not only confirm you are doing not lose out for not filling OMR sheet but also assist you plan your paper better towards the top . Also, while filling OMR sheet, confirm to read out the amount of question in your mind; serial filling without watching question numbers could lead on to an enormous tragedy. Do not make mistakes attending sheet: you'll got to fill an attendance sheet during the exam where you furthermore may will need to fill out circles. Be very careful and it only takes 1-2 minutes. Although, the exam centers assist you if you create an error , it'll not only lose you time but also create additional anxiety. It is quite common scene to ascertain students making mistakes in exam sheets. So, be very careful. Do not leave any question before watching the options: confirm to read a minimum of once all questions and options. There will always be 2-3 questions which you'll answer just by reading the questions and options carefully. Even with minimal information, you'll be ready to eliminate 2-3 options. Do not over-attempt: Do not ever think you will have to attempt a predetermined number of questions. You will be ready to make a mental assessment on how difficult the paper is after having attempted the paper. If the paper looks very tough and your preparation has been good, then attempting around 70 questions (in paper-I) well may additionally be enough. So, again, there's no fixed number but don't feel compelled to aim like 90-100 questions simply because some toppers did so.

UPSC CSE preparation demands not just being aware about the News related to any topic published on a particular date, but also everything related to it that was in News in the past some time or will be in News till the exam date. This is known as maintaining track of ‘Backward/Forward Linkages’ related to all the current affairs topics. Also, there are instances when for some subjects you need to keep updating your study material in sync with the happenings taking place at present. The best way to do this is to make short notes from the newspaper by maintaining a separate register or a folder/file of paper sheets for newspaper notes. Divide the file into separate parts based on various sub-topics of syllabus. For example, have a separate section for Agriculture related topics of GS III syllabus. More often than not, newspaper articles cover only specific aspects of an issue or topic. On that particular day, make notes on the most important points covered in that article. Thereafter, whenever you come across more articles on that topic or related topics, try to add those points in your notes. Either fortnightly or on a monthly basis, take out time for revision of those notes and organize/re-compile all the points under a topic into a more structured form. In this process you will learn how to establish the links between various topics and how to prepare backward as well as forward linkages on any given topic. For example, on the topic of Food Processing Industry, try to link this syllabus topic to the problems of agriculture and how to make agriculture remunerative for the farmers, how FPI can lead to value addition of agricultural products, whether Contract Farming can be a solution to the supply chain problems of FPI, etc. Remember that questions asked by UPSC involving backward linkages, require you to have a holistic understanding of the topic. The intention behind asking such questions is to assess whether the aspirant has a good background knowledge of the surrounding issues, what are the problems, wherein lies the solution, how to approach an issue to be able to have a comprehensive and sustainable impact in the future, etc. Thus, even though the issues/topic may be a part of current affairs, but to prepare them holistically for the exam, you will need to supplement the newspaper articles with other preparation material such as Yojana magazines, Economic Survey, government reports, etc. which in turn will help you frame the best answers in exam.

This is a question that concerns most of the UPSC IAS Exam aspirants. General Studies, that's compulsory for both Prelims and Mains within the UPSC Exam features a wide selection of subjects to hide and most of the time aspirants find it difficult to tackle subjects that they need not been in-tuned with after school. Same applies to aspirants who have opted an Optional Subject that they need not studied during their graduation days. For example, a science graduate finds it tough to hide the large syllabus of humanities subjects. What one must confine mind here is that the UPSC doesn’t expect the aspirants of Civil Services Exam to be experts/specialists in each of the themes of its syllabus, rather have a generalist knowledge about all the topics. So first of all, take the fear out of your mind that a topic is necessarily difficult simply because you don’t have any background in it. You need to possess the proper approach towards studying each subject otherwise any subject can convince be difficult. Some details to organize a topic for UPSC CSE With No Background In It First things first, you would like to urge your basic fundamentals right. That is why it's recommended that one should start with the NCERT books. They contain simple lucid explanations of all the important concepts and thus provide one with the proper base to create upon from other sources too. Once the essential understanding of concepts are clear one can advance to a number of the quality textbooks thereon subject. Keep in mind to limit your sources for the topic to the foremost important ones and revise them multiple times, instead of having multiple sources and not even doing one properly. Also undergo the previous years’ question papers to know what quite questions are asked and check out to understand the need of the topic from an exam point of view. This requirement may differ for all the three stages of the exam. Thus, you'll got to plan your preparation accordingly. Supplement your textbook knowledge with current affairs from newspapers (Hindu and Indian Express) and magazines (Yojana, EPW, etc.) for the themes that need to be in sync with the newest happenings going around. Also ask government websites, inspect government reports, cover Economic Survey and Budget in good detail, etc. Don’t just read these extra sources and jot points, but also attempt to make linkages with the syllabus topics and gain a holistic understanding. Try making your own short notes for easier revision and better retention purposes. Whether you've got a background during a subject or not, answer writing practice may be a very essential a part of the preparation. The more you write, the higher your overall understanding of the topics and therefore the subject as an entire will become. The only thing is to try to to away with any quite fear or inhibitions. When you start writing, your initial answers might not be up to the mark, but don’t hand over and stop writing. Try to think and analyse how you'll have written it better and with time you'll become excellent at it. The key is to keep writing and improving.

Choosing the right optional subject for UPSC CSE Mains is a very crucial decision that every UPSC aspirant has to make. A general thumb rule is that you should take the subject in which you have some academic background and a genuine interest. Along with this, some other factors like – past performance of the subject in UPSC, time frame required to prepare the subject, contribution of the subject towards General Studies syllabus and coaching available in the subject should also be considered in deciding the Optional Subject. Same criteria apply to opting Mathematics as an Optional Subject for UPSC CSE Mains. First of all, an aspirant need to have studied Maths in his/her graduation. Maths only till class 12th as a subject is not enough for UPSC Mains, no matter how well one had performed. Secondly, an aspirant must have a genuine interest and passion for the subject, as the syllabus will seem humungous for someone lacking love for the subject. But a student who has a passion for Maths will not find developing concepts and practising them, hard at all. This article discusses in detail all you need to know about Mathematics Optional for UPSC Civil Services. Syllabus of Mathematics Optional for UPSC CSE Mains In UPSC Mains Exam, the Optional Subject has 2 Papers – Paper I & Paper II. Each paper of the optional subject is of 250 marks, making it a total of 500 marks. The syllabus of both the papers of Maths optional as per UPSC Official Notification is as follows: Mathematics Paper I (1) Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimensions, Linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues. (2) Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables; Limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian. Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integral; Double and triple integrals (evaluation techniques only); Areas, surface and volumes. (3) Analytic Geometry: Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to Canonical forms; straight lines, shortest distance between two skew lines, Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties. (4) Ordinary Differential Equations: Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut’s equation, singular solution. Second and higher order liner equations with constant coefficients, complementary function, particular integral and general solution. Section order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters. Laplace and Inverse Laplace transforms and their properties, Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients. (5) Dynamics and Statics: Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; Constrained motion; Work and energy, conservation of energy; Kepler’s laws, orbits under central forces. Equilibrium of a system of particles; Work and potential energy, friction, Common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions. (6) Vector Analysis: Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equation. Application to geometry: Curves in space, curvature and torsion; Serret-Furenet's formulae. Gauss and Stokes’ theorems, Green's identities. Mathematics Paper – II (1) Algebra: Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem. Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields. (2) Real Analysis: Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series. Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals; Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima. (3) Complex Analysis: Analytic function, Cauchy-Riemann equations, Cauchy's theorem, Cauchy's integral formula, power series, representation of an analytic function, Taylor’s series; Singularities; Laurent’s series; Cauchy’s residue theorem; Contour integration. (4) Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality. Transportation and assignment problems. (5) Partial Differential Equations: Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy’s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions. (6) Numerical Analysis and Computer Programming: Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods, solution of system of linear equations by Gaussian Elimination and Gauss-Jorden (direct), Gauss-Seidel (iterative) methods. Newton’s (forward and backward) and interpolation, Lagrange’s interpolation. Numerical integration: Trapezoidal rule, Simpson’s rule, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Eular and Runga Kutta methods. Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal Systems; Conversion to and from decimal Systems; Algebra of binary numbers. Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms. Representation of unsigned integers, signed integers and reals, double precision reals and long integers. Algorithms and flow charts for solving numerical analysis problems. (7) Mechanics and Fluid Dynamics: Generalised coordinates; D’Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions. Equation of continuity; Euler’s equation of motion for inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid. Benefits of taking Maths as an Optional Subject in UPSC Mains Exams Static Syllabus - The syllabus of Maths Optional for UPSC is the curriculum followed by most of the universities and institutes in India. Anyone with Maths as a subject at undergraduate level whether they are engineering students or B.Sc/B.A students are familiar with most of the topics already. All that is left to be done is concept building and a thorough revision. This is unlike other optional subjects especially for engineering students, where they have to study the subject from scratch. Also as the syllabus is not linked to current affairs, so once you are done with the syllabus you don’t have to constantly update your knowledge, you just need to revise. Well balanced syllabus - We all know how anyone can end up doing a careless (silly) mistake in Maths like 2+3 = 6 which can be heart breaking and unavoidable unless the student checks and double checks the calculations. The great thing about UPSC maths syllabus is that it is well structured and balanced with emphasis on theorems and their proofs as well as the application part. Generally about 20-30% of both the papers each is based on providing proofs and knowing the theory. Obviously once the students know how to approach the proof it is only about logically writing all steps and concluding. This gives a break to the calculations and helps one increase their efficiency by reducing the chances of error. High Objectivity and hence Scoring - Maths is and has always been a scoring subject, be it in the UPSC exam or any other exam. In the past few years consistently students with maths optional have performed well and obtained very good ranks. The style of presentation matters as much as content in UPSC, especially in Maths. If a student learns how to present a solution in steps highlighting the main points one can easily predict the score in that question. Since the questions are not subjective or opinion based but factual it is not up to the examiner to give marks if content and presentation are both up to the mark. Less emphasis on memory - Of course some amount of remembering is required like basic formulae and key steps in the theorems but nothing compared to the amount students have to remember for prelims/mains/other optional subjects. This makes it attractive for those who are not so fond of cramming. Moreover the things to remember in maths is only about 10% of the entire syllabus which anyway one ends up keeping in mind because of practice and usage in majority of the questions. Less time to prepare the subject - If a student spends enough time and energy on building strong fundamentals in Maths and learns how to categorise/ recognise the problem types he/she can easily cover most types of possible questions that can be asked from that topic. It is a myth that maths takes more time to cover, yes the syllabus is quite a lot but due to the static nature if one topic is fully covered one needs to put in effort to only regularly revise that same portion and not learn newer things. So in retrospect if organised and managed well it can very well be covered in six months time (2-3 hours of class followed by same duration practice at home). Also what people usually call a disadvantage i.e., not having any portion common with the GS papers should be seen as an advantage as students can devise a study plan with distinct timings for remembering and practically doing questions. Tips to score high in Maths Optional If your teachers in school and college constantly told you to practice maths problems a lot and avoid silly mistakes to score high, then they were absolutely right. These are the basic keys to score high in Mathematics. Here, we have compiled some tips for you to score high in Maths Optional subject in UPSC Mains Exam. Practice more – Practicing makes you faster in problem solving and helps you improve speed and accuracy which ultimately will help you score high in exam. Avoid Silly Mistakes – Noting down even one symbol/number wrong can cost you a lot. So, stay calm and focused while solving questions to avoid such silly mistakes. Again, practicing a lot will help you in avoiding such mistakes. Also, few minutes for revision should be kept aside just before the exam ends so that you can cross check your answers and make correction if required. Be Systematic – Presentation matters a lot along with the right solution. So, write the solution neatly and in proper steps. Do not skip any important step in hurry or do not haphazardly write the solution. Do not cram maths – Maths is a very logical subject, so do not ever try to cram solutions or theorems. Just understand the logical flow and build your concepts strong, this will help you solve all types of questions as you will be able to apply logic in exam and won’t skip any important step of the solution. Formula Sheet – This is one thing that every aspirant with Maths as an optional subject should keep with her/him. Formulae are like the backbone of maths. So, prepare a formula sheet with all the formulae in it so that it is easy for you to revise at any time, any place. Book list for UPSC CSE Mains Maths Optional It is important to refer the right set of books while preparation as this keeps your preparation on track always and you don’t end up wasting time studying something that was not even required in the first place. Remember, referring to the right study material is as crucial as studying the material itself. Check the below given link for the book list of both Maths Optional Paper – I and Paper – II: UPSC CSE Mains Maths Optional Book List Maths is an amazing subject to study and concerns everything around us. Just study it with a relaxed mind and avoid panic while solving and you definitely can score high.