The UPSC Mathematics optional paper consists of 500 marks which are divided into 2 papers. For the last 6 years, the conducting body has given Ordinary Differential Equations and Calculus the most important as they have an average weightage of 80.6 marks and 78.4 marks.

To prepare for IAS (UPSC CSE) Mathematics Optional, just practice will not be enough. Start your preparation by practicing the NCERT Mathematics books of Class 11 and 12. This will help you to clear the concept.

In the following article, for better understanding, the mathematics optional paper, the topic-wise preparation tips, best books for each topic, and reference books along with preparation strategy has been given.

Maths Weightage

The topic-wise weightage has been given in the following table. The order has been maintained as per the weightage of the topic each year.

Topics | 2015 | 2016 | 2017 | 2018 | 2019 |
---|---|---|---|---|---|

Ordinary Differential Equations | 70 | 70 | 87 | 106 | 70 |

Calculus | 93 | 75 | 60 | 95 | 70 |

Numerical Methods and Computer Programming | 45 | 60 | 75 | 75 | 90 |

Mechanics and Fluid Dynamics | 65 | 70 | 50 | 50 | 80 |

Real Analysis | 55 | 65 | 65 | 65 | 65 |

Linear Algebra | 58 | 70 | 70 | 45 | 70 |

Dynamics and Statics | 84 | 75 | 60 | 22 | 70 |

Partial Difference Equations | 75 | 70 | 60 | 60 | 45 |

Analytic Geometry | 49 | 65 | 70 | 60 | 60 |

Vector Analysis | 46 | 45 | 53 | 72 | 50 |

Complex Analysis | 65 | 45 | 55 | 55 | 45 |

Linear Programming | 45 | 30 | 60 | 60 | 35 |

Abstract Algebra | 50 | 60 | 35 | 35 | 40 |

Maths Books

Rather than following several books on each paper, candidates can take specific books for each topic. This will help to complete each topic in depth.

Here are the topic wise preparation books for the Mathematics Paper-I. Candidates will be able to find the below-mentioned books in the offline market and the online market as well.

Topics | Name of Books | Author/Publishers |
---|---|---|

Linear Algebra | Schaum Series | Seymour Lipschutz |

Linear Algebra | Hoffman and Kunze | |

Calculus | Mathematical Analysis | S C Malik and Savita Arora |

Elements Of Real Analysis | Shanti Narayan and M D Raisinghania | |

Analytic Geometry | Analytical Solid Geometry | Shanti Narayan and P K Mittal |

Solid Geometry | P N Chatterjee | |

Ordinary Differential Equations (Ode) | Ordinary And Partial Differential Equations | M D Raisinghania |

Dynamics And Statics | Me Statics & Dynamics | Vasishtha |

Vector Analysis | Schaum Series | Murray R. Spiegel |

For the topics in the Paper-II of UPSC Mathematics Optional, candidates can choose the following books for the mentioned topics:

Topics | Name of the Books | Author/ Publisher |
---|---|---|

Algebra | Contemporary Abstract Algebra | Joseph Gallian |

Real Analysis | Elements Of Real Analysis | Shanti Narayan and M D Raisinghania |

Complex Analysis | Complex Variable (Schaum's Outlines | Speigel, Lipschitz, Schiller, Spellman |

Linear Programming | Linear Programming And Game Theory | Lakshmishree Bandopadhyay |

Partial Differential Equations | Advanced Differential Equations | M D Raisinghania |

Numerical Analysis And Computer Programming | Computer-Based Numerical And Statistical Techniques | M.Goyal |

Numerical Methods | Jain, Iyengar, and Jain | |

Digital-logic And Computer Design | M. Morris Mano | |

Mechanics And Fluid Dynamics | Fluid Dynamics | Krishna Prakashan |

Other than the above-mentioned books, candidates can use these books as reference:

- Problems in Calculus of One Variable – I. A. Maron
- Coordinate Geometry – R. L. Soni
- Mathematics Dictionary – RC James
- Differential Equations – Schaum Series (Frank Ayres)
- Textbook of Coordinate Geometry – Rai Ballabh
- Analytical Solid Geometry – Shanti Narayanan, PK Mittal
- Text Book on Differential Calculus – Gorakh Prasad

Previous Papers

The previous year’s question papers are essential for the IAS (UPSC CSE) exam. To download the previous year papers from 2016 to 2020 free of cost, click on the links given below:

Years | Paper-I | Paper-II |
---|---|---|

2020 | Download | Download |

2019 | Download | Download |

2018 | Download | Download |

2017 | Download | Download |

2016 | Download | Download |

We will now share paper-wise tips for different important topics which are often repeated over the years in IAS (UPSC CSE) Mains Maths Optional Papers.

- Paper-I is easier than paper-II as it comprises topics that are in the higher secondary level and more based on calculation than derivations.
**For analytical geometry**, emphasis on problems related to skew lines, cones, and conoids, and sphere. Check the solved problems provided in the books and try to follow the same pattern while solving a new sum related to these topics. The questions may be asked differently, but the approach of solving the question will remain the same once you understand what you are expected to find.**In calculus**, focus more on the calculus of many variables - this topic is common for paper-I and II with slight differences which means you can prepare the topic simultaneously for both the papers.**Statistics and Dynamics**is an important topic, so try to solve as many problems of different difficulty levels, as you can from this chapter.- Ordinary differential equations are relatively simple even though the topic appears very vast. Once you complete practicing sums for all types of differential equations the section is done and since the sums are of the same pattern and rather simple, this topic does not take too much time to prepare.
**For vector analysis,**you must have a thoroughly clear conception of the theorems associated with it so that you can do the applications accordingly.

**Paper-II**is more conception-based and has sums related to the derivation and proving theorems, which make it difficult for many candidates. If you can master these types of problem-solving, this paper will prove to be an advantage for you and also enhance your preparation for paper-I.- In
**abstract algebra,**you have to memorize all the theorems. But you can skip practicing the derivation of large theorems which are usually not asked in the paper. - In
**real analysis,**emphasis on Riemann Integral, Series and Sequence of functions and Improper Integrals which are repeated on several occasions for maths optional in the past few years. **Linear Programming**is another very important topic, and you cannot leave out any part of this while practicing the sums.**Mechanics and Fluid Dynamics**had a fair share of questions in the previous year. In UPSC you will often get questions that are a mix of PDE,**Numerical analysis, and Fluid Dynamics**which make it much trickier. See all the solved examples from your reference books and lay special emphasis on sums related to Kinematics of Fluids in Motion, Sources and Sinks, Vortex motion, and equation of motion of Inviscid Fluids.**Complex analysis**is an important but also very easy section from this paper and Cathy’s Theorem is particularly important from this topic.- The
**computer programming**section requires adequate practice but on the brighter side, it comprises basic programming which is easy to master.

The IAS (UPSC CSE) Mathematics can be prepared with the UPSC prelims 2021. This will boost your preparation as well as you will have more time to prepare for the exam. We hope the tips shared above will assist your preparation and wish you all the very best!

IAS FAQs

**Ques. Does UPSC allow calculators in Mathematics Optional Exam?**

**Ans. **Yes, scientific non-programmable calculators are allowed in mains for any subject even for English Literature. UPSC doesn't want to bias towards any one particular optional so it has allowed the use of calculators for all.

**Ques. Who got the highest marks in Mathematics Optional in IAS (UPSC CSE) Mains exam?**

**Ans.** In 2017, Anubhav Singh got the highest score for the Mathematics Optional subject. He scored 375 out of 500.

*The article might have information for the previous academic years, please refer the official website of the exam.