"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." – William Paul Thurston
The selection of an optional subject for the UPSC civil services exam can be a tough decision. There are numerous factors to consider, such as your prior knowledge, interest, and the subject's scoring potential. If you have a strong mathematical background and a passion for the subject, choosing Mathematics as your optional subject could be a wise choice. This article provides comprehensive insights into how to approach Mathematics as your optional subject for UPSC civil services.
In the UPSC mains examination, the optional subject consists of two papers, Paper I and Paper II. Each paper carries 250 marks, making a total of 500 marks. To understand the syllabus in detail, refer to the IAS Notification 2022 .
UPSC Mathematics Optional Syllabus:
PAPER – I
- Linear Algebra
- Calculus
- Analytic Geometry
- Ordinary Differential Equations
- Dynamics & Statics
- Vector Analysis
PAPER-II
- Algebra
- Real Analysis
- Complex Analysis
- Linear Programming
- Partial differential equations
- Numerical Analysis and Computer programming
- Mechanics and Fluid Dynamics
You can review the detailed UPSC mathematics optional syllabus at the given link.
Benefits of Choosing Mathematics as an Optional Subject
High Scoring Potential
Mathematics is a subject that offers a high scoring potential in UPSC exams and others, provided your preparation is solid and the answers are accurately presented.
Straightforward Questions
The questions in the mathematics paper are often directly derived from standard textbooks. A well-prepared mathematics graduate should find the questions ranging from easy to medium difficulty level.
Less Competition
A smaller number of UPSC candidates opt for Mathematics as an optional subject, resulting in less competition compared to subjects like History or Sociology.
Clear Evaluation
Unlike humanities subjects, which have a degree of subjectivity in evaluation, Mathematics is an exact science. The answer is either correct or incorrect. Therefore, you can have a fairly accurate idea of your performance soon after the examination.
Stable Syllabus
The Mathematics syllabus is fairly stable and doesn't require frequent updates related to current affairs. Once you have covered the syllabus, your focus should be on revision.
Drawbacks of Choosing Mathematics as an Optional Subject
Time-Intensive Preparation
Mathematics requires active engagement and problem-solving, rather than passive reading. As the famous mathematician Paul Halmos stated, “The only way to learn mathematics is to do mathematics.”
No Overlap with General Studies
Unlike subjects like History, Geography, or Polity, Mathematics doesn't overlap with the General Studies syllabus.
No Marks for Attempting
Unlike some other subjects, Mathematics does not award marks for incorrect attempts. Only when your solution is in the right direction can you expect to score.
Recommended Books for UPSC Mathematics Optional:
- Linear Algebra: A.R.Vasista, Schaum Series
- Calculus and Real Analysis: S.C Malik and Savita Arora, Shanti Narayana
- 3-D Geometry: P.N. Chatterjee
- Ordinary Differential Equations: M.D. Raisinghania, Ian Sneddon
- Vector Analysis: A.R.Vasista, Schaum Series
- Algebra: Joseph A. Gallian, Shramik Sen Upadhayay
- Complex Analysis: Schaum Series, J.N. Sharma, Ponnu Swami, G K Ranganath
- Linear Programming: Shanti Swarup, Kanti Swarup, S D Sharma
- Numerical Analysis: Jain and Iyengar, K. Shankar Rao, S. S. Sastry
- Computer Programming: Raja Raman
- Dynamics & Statics: A.R.Vasista, M. Ray
- Mechanics and Fluid Dynamics: M.D. Raisinghania, R.K. Gupta, J.K. Goyal and K.P. Gupta, Azaroff Leonid
You can access previous year mathematics optional question papers at the provided link.
Tips to Maximize Scores in Mathematics Optional Papers
- Practice: The importance of practice in Mathematics cannot be overstated. Regular problem-solving enhances speed and accuracy.
- Avoid Silly Mistakes: Be cautious of common errors such as overlooking a ‘+’ or ‘-’ sign or making simple computational mistakes. Practice until you achieve perfection.
- Understand the Problem: Before attempting a solution, ensure that you fully understand the problem. Write down the given data and solve the problem step by step.
- Clear Presentation: Present your solutions in a clear, step-by-step manner. A neatly written answer is easier to evaluate.
- Conceptual Understanding: Always strive to understand the underlying concepts rather than memorizing procedures. This approach is more effective in Mathematics.
- Understand the Question: Before you start solving, make sure you understand the question correctly. Incorrect attempts can waste valuable space in your answer booklet.
- Formula Sheet: Prepare and keep a formula sheet handy for quick reference. This can help you memorize important formulae required for problem-solving.
- Relax: Always approach mathematical problems with a calm mind. Anxiety can lead to confusion and mistakes.
Mathematics is a fascinating subject that permeates every aspect of our lives. As the renowned mathematician, Johann Carl Friedrich Gauss, put it, “Mathematics is the queen of the sciences.”
Respect this queen of sciences, and you will be rewarded in your IAS exam !
Also read:
Mastering the Civil Services Aptitude Test Paper (GS CSAT Paper II)
| IAS Eligibility | UPSC Books |
| UPSC 2023 | UPSC Notes |
| UPSC Online Application | UPSC Syllabus |
