Looking for best maths optional coaching in Delhi? You are at right place. Elite Glean is the point that will help you in choosing an institute that is best for maths optional coaching in Delhi. Many institutes provide maths optional coaching in India but the quest to find the good coaching institute for maths optional in India is hectic. However, this article will assist you in choosing best institute for maths optional in Delhi.

Choosing the right optional subject for UPSC is essential decision and every UPSC aspirant has to choose an optional subject for Mains exam. The professionals give advice students to choose that subject in which they have interest and expertise. Mathematics as an optional subject is chosen by many aspirants. Maths is one the best subjects as optional because of its scoring nature and straightforward marking criteria. When you choose an optional subject, you always look for the best IAS coaching in Delhi for maths optional. Continue reading below to find which is the best IAS maths optional coaching in Delhi?

Every student needs UPSC maths optional coaching in Delhi and look for IAS maths optional best institute in India. Mathematics is all about grasping the subject’s essential concepts as well as the workings of mathematical applications, which can aid in developing interest in the subject’s core principles of operation.

Every year UPSC holds IAS examination. UPSC examinations give you opportunities to work in civil services sector and administrative departments, planning departments, revenue departments etc. and Mathematics is an important subject because all the calculations are operated under the umbrella of Maths. Many students choose Maths optional in Delhi because of their interest and expertise.  Lot of institutes provide maths optional coaching for IAS Delhi.

Maths optional for UPSC is a good option because it gives advantages such as –

Scoring in Nature– Maths is scoring subject as it is all about calculations. So, marking is straightforward in this subject.

Easy Concepts– If your maths optional teacher is intellectual and knowledgeable, he or she will make you understand the concepts and formulas completely. 

No Competition– Lesser students prefer maths as optional. So, there is likely absence of competition.

Familiar Subject– Students study mathematics since 1^st standards. As a result, they become familiar with the subject since the beginning. Mathematics has always been chosen widely as an optional subject. There is a lot you need to know about coaching for mathematics optional in Delhi for CSE.

Before you choose institute for maths optional coaching in Delhi, you should know about the institutes well. Have a glance at the best maths optional institutes in Delhi and then decide which institute you want to choose.

1) DIAS India
Among the best institute for maths optional in Delhi, the name of DIAS India outshines and it is considered as the best coaching institute for maths optional in India. Since inception, the institute is in the long journey of making name in the market for providing best coaching for civil services optional mathematics Delhi.

About DIAS India- DIAS is the best institute for maths optional coaching in Delhi as it provides best faculty for mathematics in Delhi IAS optional. Also, they have the right strategies and guidance for students that help in cracking maths optional exam easily.

About Faculty- DIAS India is proud to have the best teacher for maths optional in Delhi- Vajpayee sir. He is the best maths optional teacher in Delhi and this because of his innovative teaching methods and years of experience. DIAS India is popular for maths optional coaching in Delhi because of Vajpayee sir’s coaching classes.

Courses Offered by DIAS India
• Maths Optional Online Classes
• Maths Optional Test Series
• Maths Optional Modules wise Course

Maths Optional Online Classes at DIAS India
DIAS believes that study should be at halt. Amidst the Covid-19, they have started online classes for mathematics optional and many students have opted for mathematics optional coaching online. They are known for providing the best online coaching for mathematics optional for civil services.

Why choose DIAS India Maths coaching of Delhi

DIAS India is the best institute for maths optional coaching in Delhi offering top-notch maths coaching by professionals. There are many reasons because of which people choose that-
1) Experienced Faculty- Vajpayee sir is the best maths optional teacher for UPSC. He is highly experienced and has flexible teaching methods. His teaching methods are simple and understandable.

2) Affordable Fee- DIAS offers offline and online maths optional coaching in Delhi. Their course fee is nominal for online and offline classes.

3) Mentor’s Strategy- DIAS has experienced tutor who share his strategy of success with students so that they can score well. Vajpayee sir is experienced and knows how to prepare students for maths optional.

4) Provision of Notes- DIAS has the best teaching strategy. He provides UPSC maths optional notes PDF that helps students in understanding the formulas and concepts clearly and precisely.

DIAS Maths Optional Regular Foundation Course Details
• 150 + Lectures,
• 300 + Hours Compact Offer
• Entire Syllabus course in 10 Modules
• Fee for entire course is Rs. 40,000/-
• Exhaustive & Scientific Coverage of the whole syllabus.
• Tests at the End of Every Section.
• 6 Days a week Class.
• Focus on Answer writing Practice.
• 4 Sectional Tests at the End of Every Section.

Courses Taught by India’s Best Maths Faculty for UPSC
1) Dynamics -> 12 Classes by Vajpayee Sir
2) Fluid Dynamics -> 12 Classes by Vajpayee Sir
3) Rigid Dynamics -> 12Classes by Vajpayee Sir
4) Vector Analysis -> 8 Classes by Vajpayee Sir
5) Differential Equations (ODE & PDE) -> 20 Classes by M. Maheep Sir
6) Complex Analysis -> 12 Classes by M. Maheep Sir
7) Calculus -> 12 Classes by M. Maheep Sir
8) Modern Algebra ->20 Classes by Shukla Sir
9) Linear Algebra & Matrices->15 Classes by V. Deorishi
10) Real Analysis->10 Classes by Shukla Sir

IAS Maths Optional Faculty at DIAS INDIA
• Vajpayee Sir
• M. Maheep Sir
• Shukla Sir
• V. Deorishi Sir

Address: Second Floor, 18, Pusa Rd, Near Metro Pillar No. 95, Karol Bagh, New Delhi- 110005
Contact No: +91-9318384883
Website: www.diasindia.com
Directions: DIAS India Direction

2) IMS 4 Maths
IMS is an institute known for providing maths optional coaching in Delhi. IMS is another maths optional coaching students choose because of experience and good results. They provide multiple fast track course. They have experienced faculty for maths optional coaching and are known for producing the top results in maths as an optional subject in UPSC.

They have simple process of admission and provide good coaching for maths optional in Delhi. They offer regular classroom programmes, offline and online test programs, postal study material and test series. You can visit their website or contact them to know more details.

Course Fees: Not Available on Site
Duration: 5-6 Months
Faculty: K. Venkanna Sir
Website: www.ims4maths.com
Address: 25/8, Old Rajender Nagar Market, New Delhi, Delhi 110060
Contact NO: +91-9999197625

3) Analog Education
Analog education is also one of the popular institutes for maths optional coaching in Delhi. The institute is known for providing maths optional coaching by experts that gives results. Analog Education aims to provide high quality coaching for maths optional.

This institute is headed by Mr. Srikanth Vinnakota who is experienced and MTech. He thrice qualified civil services interview opting Psychology and maths as optional subjects. They have experienced faculty who hold expertise in their respective niches. From general essays to sociology and Maths, they teach every subject. You can also choose them for maths optional coaching.

Course Fees: ₹40,000/-
Duration: 4 Months
Faculty: Srikanth Vinnakota Sir
Website: www.analogeducation.in
Address: 25/24, 2nd Floor, Bada Bazar Marg, Old Rajinder Nagar, New Delhi, 110060
Contact NO: +91-8800283132

4) Vajiram and Ravi
In the field of UPSC maths optional coaching, Vajiram and Ravi are also prominent figure in tutoring students for maths optional. They are experienced people working in this field. They provide UPSC optional subject coaching online, GS Course online and also prelims test series. They provide different courses coaching and have three sessions for coaching batches.

They have systemized and structured syllabus for maths optional and teach in an efficient manner. The latest batch is available from October. Keeping the current scenario and adhering to protocols, they are delivering online classes.

Course Fees: Not Available on Site
Duration: Not Available on Site
Faculty: Not Available on Site
Website: www.vajiramandravi.com
Address: 9-B, Bada Bazar Rd, Old Rajinder Nagar, New Delhi- 110060.
Contact NO: (011) 41007400

5) Mathematics Optional
Mathematics Optional is the specific institute for maths optional coaching. They only teach maths optional online classes and pen drive maths optional course. They are not providing offline classes because of covid protocols. They are offering online classes and help you in the right preparation of the examination.

They are offering Maths optional coaching for many civil services examination like IAS, CSE, IFoS, UPSC maths. Their teachers are well-educated and experienced and provide guidance to the students. They are offering maths optional coaching pan India. The institute offers online classes at affordable and nominal fee.

Course Fees: ₹58,500/-
Duration: 6 Months, 135 Lectures.
Faculty: Ramanasri Sir
Website: www.mathematicsoptional.com
Address: 20/24, Near Yashoda Dairy, Old Rajinder Nagar, New Delhi- 110060
Contact NO: +91-8750706262

Union Public Service Commission (UPSC) civil services examination has Mains exam where a student has to choose optional subject. The optional subject has two papers. Similarly, Maths as optional also has 2 papers and each paper is of 250 marks. Maths optional syllabus is comprehensive and easy. Maths optional UPSC syllabus consists of algebra, calculus, geometry, ordinary equations, dynamics & stats, real and complex analysis.

The syllabus for maths as optional in UPSC is easy if you got UPSC best coaching in Delhi for maths optional and best teacher for maths optional in Delhi because the role of mathematics optional teacher in IAS is undeniable.

UPSC Maths Optional Syllabus for Paper-I

(1) Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; row and column reduction, echelon form, congruence 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 integrals; 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 linear equations with constant coefficients, complementary function, particular integral and general solution. Second 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 & 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 equations. Application to geometry: curves in space, curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.

UPSC Maths Optional Syllabus for 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 functions, 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-Jordan (direct), Gauss-Seidel(iterative) methods. Newton’s (forward and backward) interpolation, Lagrange’s interpolation. Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runge 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: Generalized 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.

In the journey of preparing maths optional, the role of maths optional study material is essential and if you are looking for maths optional book list you can get it online. UPSC maths optional notes pdf is also available for the students. When you join maths optional UPSC coaching in Delhi make sure that you join the best institute that provides you exceptional IAS maths optional coaching in Delhi and also maths optional booklist for UPSC.

The UPSC maths optional books vary from Paper I and Paper II. The books are recommended for topics like algebra, calculus, linear programming, real analysis and others.

• Complex Analysis by Schaum Series or J N Sharma
• Differential Equations by Schaum Series
• Linear Algebra by Schaum Series
• Real Analysis by Shanti Narayan
• Vector analysis by Shanti Narayan
• Analytic Geometry by Shanti Narayan
• Ordinary and Partial Differential Equations by Dr. M.D. Raisinghania
• VECTOR ANALYSIS: Schaum’s Outlines Series by Murray Spiegel
• A Textbook on Dynamics by Ray M and G.C. Sharma
• Integral Calculus by Narayan Shanti and Mitta
• Linear Algebra by Kenneth M Hoffman
• Differential Calculus by Santhi Narayan
• Numerical Analysis by S S Sastry

7.5

Complex Analysis by Schaum Series or J N Sharma Best Values

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Schaum’s Outline of Theory and Problems of Differential and Integral Calculus

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Valuable Study Guide which Provides a Modern Introduction to Linear Algebra

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In-depth Knowledge of Vector Analysis for Better Knowledge

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From Coordinates to Interpretation Of Equations Loci, you get it all!

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Ordinary and Partial Differential Equations is a Comprehensive Treatise on the Subject

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Perfect Book of Vector Analysis to Help Study Faster & Learn Better!!!Content

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Most Appropriate Guide to Central Force, D’Alembert’s Principle & so on…

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Ideal Book On Integral Calculus to Enlighten the Subject Concept!

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Linear Algebra by Kenneth M Hoffman Best Price

Comprehensive Book to Clarify the Computational Aspect of Linear Algebra

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Differential Calculus by Santhi Narayan Best Offer

Textbook Begins With a Brief Outline of Development of Real Numbers & Much More!

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Numerical Analysis by SS Sastry Best Values

Have a Complete Idea of the Numerical Analysis

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Maths optional question papers are significant for students as they help in giving them an insight to question paper pattern and revision. You can get maths optional previous year papers topic wise online and can prepare well with maths optional UPSC question paper.

When you search for maths optional question papers on the internet, you will get access to numerous UPSC IAS Mains optional question papers mathematics. These papers help a student in getting idea about the type of questions that had asked in the examination. Get UPSC question paper for maths and prepare well for your examination.

Q. Which is the best IAS maths optional coaching in Delhi?
A. DIAS IAS is providing the best IAS maths optional coaching in Delhi. They are professional and experienced in this field and provide the best coaching for maths optional. They have the best maths optional faculty in Delhi. Join DIAS for the best math optional coaching in India.

Q. How is DIAS Delhi for UPSC maths optional?
A. DIAS Delhi is the best institute for maths optional in Delhi. DIAS is a well-known institute for civil service examination offering the best maths optional coaching in Delhi. They are known for providing good coaching institute for maths optional in Delhi. Since the inception, they put hard endeavors and made DIAS a brand in the field of UPSC maths optional coaching.

Q. How is Vajpayee Sir Mathematics Optional Classes?
A. Vajpayee Sir Mathematics Optional Classes are perfect for the individuals looking for best maths optional coaching in Delhi. DIAS institute is known for providing the best online coaching for maths optional and offline also.

Q. Is calculator allowed in UPSC maths optional?
A. Calculators are essential in UPSC maths optional subject. As it is mathematics subject that revolves around calculations so calculator is necessary. UPSC allows the aspirants to use calculators for complicated calculations in both Paper I & Paper II.

Q. How to prepare for maths optional for UPSC?
A. Preparing for maths optional is not a herculean task. All you need is the right teacher who can provide you strategies and the best institute that can give you notes, previous year question papers and rigorous training.

Q. How is Vajpayee sir for maths optional?
A. Vajpayee sir maths optional classes are the best and optimum for maths optional in IAS in Delhi. He has a proven record of making students score well in maths. Vajpayee sir is highly experienced and knows how to train students for UPSC maths optional. He has flexible teaching methods and pays attention to every student. He is a true facilitator and guide for the aspiring candidates.

Q. Can I take maths as optional in IAS UPSC exam?
A. Choosing maths as an optional in IAS UPSC exam is not a bad choice. Maths is a scoring subject and student from any background study can opt for maths as an optional subject. There is no restriction or eligibility to choose it as an optional subject in UPSC Mains exam.

Q. How is maths as an optional in UPSC?
A. Maths as an optional in UPSC is a better choice because this subject comes with several benefits. Above all the benefits, the subject is scoring, concepts are easy to understand and everyone is familiar with this subject. So, choosing maths as an optional in UPSC is a good choice.

The post Best Maths Optional Coaching in Delhi first appeared on Elite Glean.

Every year, around or more than ten lakhs students appear for the UPSC exam. To make sure that their preparation goes well, picking maths as optional subject for UPSC would be the best option. Only the general thumb rule for this is that you will have to be a student who has come from a mathematics background.

Let us learn a lot more about why mathematics is the best. Also, we will tell you how to prepare for maths optional. Apart from this, we have also mentioned the best maths optional coaching in Delhi so that you can help whenever needed. So, now let us begin with it!

Maths is and has always been one of the most chosen optional subjects amongst the UPSC aspirants. When you are planning to choose maths as an optional subject, it is very important that you come from the same academic background.

It is obvious that the students who come from the mathematics stream will find this subject much more interesting than the other aspirants. Hence, in case, if you have graduated with maths as your subject or love studying the subject; then ensure that you choose mathematics optional for UPSC.

There is a lot that you need to know about the maths optional subject for the exam. Choosing this subject as your chance to crack the civil service exam is a wise decision for those who have a strong grasp over the subject.

In this article, we will be helping you out to know how maths optional subject can be beneficial for you. Along with that, we have also mentioned the top 5 maths optional coaching institute in Delhi.

A lot of aspirants every year choose maths optional for UPSC exam. It is usually those who come from a non-medical background. Often many students seem to be a bit hesitant while choosing mathematics as optional, due to the vast maths optional syllabus and the time needed to prep-up for the exam.

However, there are so many obvious reasons for why this subject is the best. We will be discussing the ins and outs of maths as the right choice for the mains exam in UPSC. Also, this will clear a lot of things for you, as well. Now, let us talk about two main points, which are, firstly, why UPSC maths optional is the best and second what exactly IAS maths optional includes in the exam. Let us have a clear idea of both these points in the below section.

There are ample numbers of reasons for why an aspirant can choose maths as optional subject for UPSC. Let us have an insight to all the benefits of making it your priority for the mains.

• Easy-To-Understand Concepts

The best thing about choosing the maths optional for IAS is that the exam questions are simply picked up from the books. All the graduated students appearing for the UPSC can easily solve all the questions. Hence, we can say that questions and concepts asked when you choose maths as optional in IAS exam is very common and easy.

• Can Score Good Marks

Maths will always remain the easiest subject when it comes to scoring good marks when you choose maths as an optional for UPSC or some other exam. If you’ve practiced the questions of maths as UPSC optional subject properly and answered the questions right, you’ll certainly score good marks points.

• No Competition

You will be at peace knowing that not many students appearing for exams prefer choosing mathematics optional for UPSC. Hence, this way, you will have the advantage, as there is going to be lesser competition when you choose mathematics as optional subject for the UPSC exam.

• Students Can Analyze their Performance

There is still an aspect of relativism present in other topics such as science or humanities, with the personal biases of the examiner coming into effect. Two different examiners can score separately for much the same answer.

However, this is not true in case you choose mathematics optional, which is known to be an exact thing. The answer is either correct or incorrect. So, when you take the test, you will get a pretty good picture of how you go.

• Static Subject

One of the best things about selecting mathematics as optional for IAS is that this subject is constant and stable. It is not relevant to current affairs. So, once you’re done with the syllabus, you don’t have to continually refresh your experience; you just need to rewrite it.

Whenever beginning to prepare for mathematics, make sure that you know how to prepare for UPSC maths optional.

• Learn About the syllabus of maths optional subject

The first aspect you need to consider when you prepare for the mathematics optional is to make sure you are well informed with the exam pattern. You then have to know about what the UPSC maths optional paper syllabus is.

• Choose the Best Study Materials

Any applicant preparing for the UPSC mathematics optional syllabus knows that study material has to be collected from various outlets, so don’t fall into the trap of having to read a bunch of maths optional books and get confused and irritated. Decide on a few of the best UPSC maths optional books and stick to them.

• Plan Your Goals

Planning the objectives and timetable is a must for all UPSC maths optional subject applicants. If you want to make sure that you pass the exam on the first try, you need to make a schedule.

You are supposed to have a daily routine where you spend a certain number of hours training. Set regular or weekly goals and aim to meet them.

• Proper Practice

Mathematics demands you to practice questions every day. Thus, make sure that you study it properly and also practice it every day until the last day before the exam.

• Attempt Mock Tests

Attempting mock exams and practicing UPSC maths optional previous year question papers will let you know what is normally done in the exam.

It will also let you understand where you are in mathematics optional UPSC syllabus preparation and make you more focused. It also helps you to know how much time you spent on each question.

• Do Not Get Confused

Note that if you appear for such exams, never make the error of taking shortcuts or preparing at the last minute. So, begin your preparation for maths optional on time. You should also start taking mathematics optional UPSC online coaching to support and offer better advice.

After making a choice of having mathematics as an optional subject, the next thing that you need to work on has to be the UPSC maths optional syllabus. The maths optional syllabus will make it very easy for you to complete the subject and its revision on time.

However, before we begin with giving you description of the maths optional syllabus UPSC, it is the mandatory that we tell you how important it is for you to be of maths background.

Whenever choosing to opt for maths as your optional subject, it is important that you have had excellent performance in the subject earlier. It would be easy for you to complete studying the UPSC CSE maths optional syllabus, only when you are aware of the subject before.

The maths optional subject is divided into two papers – Paper I and Paper II. Both the papers are of 250 marks, which totals as 500 marks. The IAS maths optional syllabus of both Maths paper I and II, as given in the UPSC Official Notice, is as follows:

Paper I –

• Ordinary Differential Equations
• Dynamics & Statics
• Vector Analysis
• Linear Algebra
• Calculus
• Analytic Geometry

Paper II –

• Ordinary Differential Equations
• Dynamics & Statics
• Vector Analysis
• Partial differential equations
• Numerical Analysis and Computer programming
• Mechanics and Fluid Dynamics
• Algebra
• Real Analysis
• Complex Analysis
• Linear Programming

Here is Details of UPSC Mathematics Optional Syllabus

PAPER – I

(1) Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; row and column reduction, echelon form, congruence 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 integrals; 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 linear equations with constant coefficients, complementary function, particular integral and general solution. Second 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 & 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 equations. Application to geometry: curves in space, curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.

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 functions, 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-Jordan (direct), Gauss-Seidel(iterative) methods. Newton’s (forward and backward) interpolation, Lagrange’s interpolation. Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runge 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: Generalized 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.

If you’re always curious that all the aspiring UPSC exam students make a lot of effort to crack the last ten years of UPSC maths optional previous year question papers before the exams. What are the advantages of this? Let’s discuss this.

• Helps You Practice Complete Syllabus

Trying to solve the maths optional previous papers of the last few years will make one better since they constitute a large part of the syllabus. You should get your hands to these mathematics optional previous year question papers and prepare rigorously for the exam.

• Strengthen Weak Areas

It might seem easy to grasp your weaknesses when you are practicing the mathematics optional previous year papers. So, solving the question paper would certainly help you achieve a perfect score when you choose mathematics as optional subject.

• Consistent Practice

Regular practicing of mathematics optional question paper can make you sure that you can answer any tough question. It’s the ultimate tool to conquer your shortcomings and do well in the tests.

Are you one of those who have begun with their UPSC preparation with mathematics optional? If yes, then it is very important that you start moving forward to purchasing the UPSC maths optional book. There is so much that you need to do, when you are looking for the best IAS maths optional book.

Many IAS aspirants often take this task of choosing the most appropriate maths optional books very lightly. However, this is not at all suggested, as there are so many things that you need to focus on.

There are certain advantages of having the best UPSC mathematics optional books at your convenience. For example, you can get to solve different and new questions related to the subject. Next, with the books for mathematics optional for UPSC you can get a lot of information and formulae at one place.

Take a peek at the suggested maths optional book list. Below is a collection separated into Paper I and Paper II as per the optional UPSC math syllabus and divided topic-wise.

• Linear Algebra – A.R.Vasishtha
• 3-D Geometry – P.N. Chatterjee
• Vector Analysis – A.R. Vasista, Shanti Narayan, PK Mittal
• Dynamics, Statics and Hydrostatics – M. Ray
• Differential Calculus – Shanti Narayan, PK Mittal
• Analytic Geometry – Shanti Narayan, DK Jha, HC Sinha, and Sharma
• Coordinate Geometry – R. L. Soni
• Differential Equations – Schaum Series (Frank Ayres)
• Analytical Solid Geometry – Shanti Narayanan, PK Mittal

Mechanics and Fluid Dynamics – M.D. Raisinghania, R.K. Gupta, J.K. Goyal, and K.P. Gupta

Complex Analysis by Schaum Series or J N Sharma Best Values

Get An Insight to Theory of Functions of a Complex VariablesAn Introduction to Social Anthropology

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Differential Equations by Schaum Series Most functional

Schaum’s Outline of Theory and Problems of Differential and Integral Calculus

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Linear Algebra by Schaum Series Best Price

Valuable Study Guide which Provides a Modern Introduction to Linear Algebra

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Vector analysis by Shanti Narayan Best Values

In-depth Knowledge of Vector Analysis for Better Knowledge

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Analytic Geometry by Shanti Narayan Best Values

From Coordinates to Interpretation Of Equations Loci, you get it all!

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Ordinary and Partial Differential Equations by Dr. M.D. Raisinghania Best Values

Ordinary and Partial Differential Equations is a Comprehensive Treatise on the Subject

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VECTOR ANALYSIS: Schaum’s Outlines Series by Murray Spiegel Best Values

Perfect Book of Vector Analysis to Help Study Faster & Learn Better!!!Content

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A Textbook on Dynamics by Ray M and G.C. Sharma Best Values

Most Appropriate Guide to Central Force, D’Alembert’s Principle & so on…

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Integral Calculus by Narayan Shanti and Mitta Best Values

Ideal Book On Integral Calculus to Enlighten the Subject Concept!

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Linear Algebra by Kenneth M Hoffman Best Values

Comprehensive Book to Clarify the Computational Aspect of Linear Algebra

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Differential Calculus by Santhi Narayan Best Values

Textbook Begins With a Brief Outline of Development of Real Numbers & Much More!

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Numerical Analysis by S S Sastry Best Values

Have a Complete Idea of the Numerical Analysis

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Almost every year, more than 300-400 students choose maths as optional subject for UPSC. For all of them, here we are with some of the very common mathematics optional pros and cons so that they can make better choices.

Maths optional subject pros

• Scoring Subject – As mentioned earlier also, that mathematics optional is a scoring subject. There is no theory, as it involves only question solving problems. If you have studied carefully and can write answers properly and reliably, you will achieve full points, as much as any subject in humanities.
• Stable and Static – One of the best benefits of choosing maths as optional is that this subject is stable and static. There are no constant updates on the subject.
• Less Competition – There is very little competition in the mathematics optional for UPSC.
• Easy to Assess – You can very easily assess or evaluate your performance in the maths optional in IAS.
• Direct Questions – Finally, the questions asked in the maths optional for UPSC are directly taken from the textbooks.

Maths optional subject cons

• Time-Taking – Preparation can take longer as the syllabus needs to be completed fully and absolutely if you are to do well. Furthermore, math can only be studied by practicing amounts of money. There’s no getting around that.
• No Scores for Attempting – There seems to be little room for error in mathematics optional for UPSC. If your reply is incorrect, you can lose a significant score. Only if your attempt is in the correct direction will you be given any bonus marks for your attempt.
• Technical – Mathematics should only be considered by the applicants who are graduated in mathematics or engineering or graduates.

No Overlap – There is no chance of any overlap of this subject with the general studies paper.

We all know that the maths optional toppers have always been an inspiration for all of us. Scoring such good marks in this subject must have been tough for the mathematics optional topper in UPSC. Let us now have a look at the list of toppers with maths optional.

 Source – byjus.com

Also, now let us take a look at how many students take maths as an optional subject for UPSC.

 Source – byjus.com

There are many UPSC aspirants who choose mathematics as optional subject and managed to qualify the exam with excellent scores. Today let us end this blog by having a glimpse at the maths optional strategy for UPSC directly from the toppers.

• They always have focused on choosing the standard books for studying static subjects. Also, they preferred using internet sources for studying and being updated for dynamic subjects.

• They always say that one should take maths as optional, only when they are strongly inclined towards the subject.

• For getting good marks in maths optional subject, you need to put a lot of hard work into the preparation. You will need to solve as many questions as possible.

• Never copy the solution of maths optional subject for IAS from the books; rather, try solving them on your own. You will be able to learn only when you practice the questions yourself.

For your convenience, we have provided you a list of maths optional toppers blog which will help you for sure.

1. Anubhav Singh (Rank-8/UPSC-2017) – https://mrunal.org/2018/07/upsc-topper-ias-anubhav-singh.html
2. Kanishak Kataria (Rank 1 in UPSC CSE 2018) – http://demystifycse.in/mathematics-as-an-optional-kanishak-kataria-rank-1/
3. Bhavesh Mishra ( Rank 58 ) – https://www.iasabhiyan.com/maths-optional-strategy-bhavesh-mishra-rank-58/
4. Ganesh Kumar Baskar (UPSC AIR 7 ) – https://blog.oureducation.in/upsc-cse-2019-rank-7-ganesh-kumar-baskar/

Whenever beginning with the maths optional UPSC preparation, there are lots of resources available online with which you can study. Make sure that you go through them by heart. Here we will have a look at some mathematics optional toppers blog and so much more that can help you prepare the subject.

1. Mathematics Preparation Strategy – https://www.youtube.com/watch?v=ANBG0k9Ui_E
2. Linear Algebra – https://nptel.ac.in/courses/111/106/111106051/
3. Linear Algebra – https://www.math.pku.edu.cn/teachers/anjp/textbook.pdf
4. Differential Calculus – https://www.pdfdrive.com/shanti-narayan-e83435486.html
5. Numerical Analysis – https://rahulpatel121.files.wordpress.com/2018/07/s-s-sastry-introductory-methods-of-numerical-analysis-2012-phi-learning-pvt-ltd.pdf
6. UPSC Maths Optional Linear Algebra Class-01 | Online UPSC Maths Optional | Ramanasri – https://www.youtube.com/watch?v=7lyEylol9g0
7. Introduction to Vector Analysis – Mathematics Optional By Venkanna Sir – https://www.youtube.com/watch?v=PcVXFLBF29E

We have talked about the five best maths optional coaching in Delhi. Now let us have a look at each of them in detail.

1. Delhi Institute For Administrative Services (DIAS)

About: DIAS is a well-known Institute for facilitating and coaching the applicants for CSE and IFS examination held by the Union Public Service Commission (UPSC) under the umbrella of DIAS India Edutech (Pvt) Ltd, a corporation governed by the Companies Act.

We can say that DIAS mathematics optional coaching in Delhi has been the most chosen one amongst the students who are prepping up for the UPSC exam. If you are also planning to begin with the preparation, then you can certainly join the institute for assistance and better prep-up.

Address: 18, Pusa Road, Near Karol Bagh Metro, New Delhi 110005

Contact Number: 011-40079000, 9350934622

Mathematics Course Fees: Rs. 40,000

Mathematics Preparation Methods: Online / Offline Class, Class Test, Tutorial Sheets, Mains Test Series, IAS IFoS Maths Option

Faculty: Vajpayee Sir, M.Maheep Sir, Shukla Sir, V. Deorishi Sir

Coaching Results: Pratibha Sharma, Archit Chandak, K. Varun Reddy, Sagar Kumar, Himanshu Gupta

Website: https://diasindia.com/

Directions: DIAS Directions

• Institute of Mathematical Sciences

About: IMS is here to help its students in getting thoroughly expert in the mathematics subject. This institute makes sure to provide the best maths optional coaching institute in Delhi to its students.

K. Venkanna sir is here at IMS in Delhi to help every student do their best in the exam. Every student that joins IMS makes sure that their success is attributed to the K.Venkanna sir.

Address: 25/8, Old Rajender Nagar Market, Delhi – 110060

Contact Number: 01145629987, 09999197625

Mathematics Course Fees: Mathematics Classroom Programme – Fee – Rs. 63,000/-

Mathematics Optional Study Material – Fee – Rs. 14,000 /-

Mathematics Test Series Programme – Fee – Rs. 16,000/-

Faculty: K. Venkanna sir

Mathematics Preparation Methods: Maths Notes, Mathematics Classroom Programme, Mathematics Optional Study Material, Mathematics Test Series Programme

Coaching Results: Hardik Agarwal, Ganesh Kumar Bhaskar, Nidhi Bansal, Suji Shankar, Chirag Jain

Website: https://www.ims4maths.com/

Directions: IMS Directions

• Analog IAS Academy in Delhi

About: Analog IAS Academy was founded to ensure that the best knowledge can be imparted to the students. Being one of the best institutes for IAS maths Optional in delhi , we can say that this coaching institute has produced all the toppers due to its effective and helpful teaching methods.

With its arrival in Delhi, it has managed to get hands-on with lots of students due to its excellent past performance.

Address: 25/24, 2nd Floor, Bada Bazar Marg, Old Rajinder Nagar, New Delhi, 110060

Contact Number: 01149785868, 8800283132

Mathematics Course Fees: Rs. 40,000/-

Faculty: Mr. Srikanth Vinnakota

Mathematics Preparation Methods: Maths Notes, Maths Optional Classes

Coaching Results: Hardik Agarwal, Ganesh Kumar Bhaskar, Nidhi Bansal, Suji Shankar, Chirag Jain

Website: https://www.analogeducation.in/

Directions: Analog IAS Academy in Delhi Directions

• VajiRam and Ravi IAS Academy in Delhi

About: Vajiram & Ravi is one of the most reputed coaching institutes in Delhi for maths Optional known for prepping up the students for IAS exams. They make sure to help the students in the best way by providing them the needed study materials and notes.

Address: 9-B, Bada Bazar Rd, Old Rajinder Nagar, Rajinder Nagar, New Delhi, Delhi 110060

Contact Number: (011) 41007400, (011) 41007500

Mathematics Course Fees: Rs. 62,000/-

Coaching Results: Gunjan Dwivedi, Durishetty Anudeep, Sachin Gupta, Kothamasu Dinesh Kumar, Tina Dabi, Athar Amir Khan, Artika Shukla

Website: https://www.vajiramandravi.com/

Directions: VajiRam and Ravi IAS Academy in Delhi Directions

• Ramanasri UPSC Maths Optional Coaching

About: While looking for the best online coaching for Maths optional in delhi, we came across this institute, which certainly is the best. There are many students in Delhi studying here and have scored good marks to date.

Address: 20/24, Near Yashoda Dairy, Old Rajinder Nagar, New Delhi-110060

Contact Number: 08750706262

Mathematics Course Fees: Offline Maths Optional – Fee – Rs. 58,500/-

Online Maths Optional – Fee – Rs. 55,500/-

Pendrive Maths Optional – Fee – Rs. 52,500/-

Faculty: Ramanasri Sir

Mathematics Preparation Methods: Maths Notes

Coaching Results: Saurabh Kumar, Kranthi Kumar, Awani Bhushan, Sitanshu Pandey

Website: www.mathematicsoptional.com

Directions: Ramanasri UPSC Maths Optional Coaching Directions

Hope that all the details that we have talked about in the preceding section about the maths optional subject for IAS will be of great help to you!

Does UPSC maths allow optional calculators?

Yes, UPSC does allow calculators for the applicants that have chosen mathematics as an optional subject. Keeping in mind the impartiality towards every optional subject, UPSC does allow the aspirants to enter exam hall with calculators. The students can carry the scientific non programmable calculator when appearing the UPSC mains with maths as optional subject.

How do I start preparing for maths optional?

Often, a lot of students ask how to prepare for maths optional. Hence, we are here with a small and easy answer. Make sure that you go through it properly.

• Be aware of your entire mathematics optional syllabus for better preparation.
• Choose the best maths optionsl books for studying which have been suggested by the experts.
• Prepare your Mathematics optional study plan, as per your convenience.
• Make sure to curate your own study notes along with studying. These will help you for last-minute revision.
• Regular practicing of the UPSC maths previous year question paper.
• Appear for the online or offline maths optional test series to gain insight to your preparation.

How much time does it take to prepare for mathematics optional?

To get ready for your UPSC mains, it will take at least 4-5 months for you to be well-acquainted with mathematics properly. Make sure that you study 5-6 hours a day and there you will be done with the preparation. Also, rest depends on how good you are at grasping concepts and facts. There are many factors in combination to decide the time for your preparation.

Who should opt for Mathematics?

Students who may have completed a B.Sc. in Mathematics or a B. Tech. will take maths as optional subject in this examination. Indeed, Mathematics is one such choice that provides you with the benefit of a much more score than what you might obtain with other humanities subjects, raising your odds of getting the top ranks.

What are the tips to score good marks in Maths optional?

Here are some must-remember tips which will help you score good marks in mathematics optional in the exam.

• Make sure that you practice more and more maths previous year questions, as it will increase your accuracy and help you score more.
• Maths is a subject, in which you always need to be careful and avoid making silly mistakes.
• Presentation matters in answer writing, hence, keep your answers clean and neat. Do not rush through the important steps or write the solution haphazardly.
• Math is a practical subject, so never attempt to memorize solutions or formulae. Understand the theoretical process and strengthen the concepts; this will accompany you in answering all types of questions.

Mathematical formulae are the base of the subject. So, create a formula sheet with all of the formulae on it so that you can easily revise it at any time.

The post Maths Optional for UPSC- A Complete Guide about this Optional first appeared on Elite Glean.