Introduction:
Preparing for Mathematics as an optional subject for UPSC can be a challenging task, but with proper planning and dedication, it can be a rewarding experience. Here are some steps to help you get started:

1. Understand the Syllabus:
The first step is to thoroughly understand the syllabus for Mathematics as an optional subject. It is important to know the topics and subtopics that need to be covered. Refer to the UPSC syllabus and make a list of all the topics.

2. Collect Study Material:
Gather relevant study material for Mathematics. There are various books and resources available in the market. Make sure to choose books that cover the entire syllabus comprehensively. Some recommended books for Mathematics optional include "Higher Engineering Mathematics" by B.S. Grewal, "Linear Algebra" by Bernard Kolman, etc.

3. Plan a Study Schedule:
Create a study schedule that is realistic and suits your daily routine. Allocate specific time slots for each topic and stick to the schedule strictly. Break down the syllabus into smaller parts and set deadlines for completing each part.

4. Practice Previous Year Question Papers:
Practicing previous year question papers is essential to understand the exam pattern and the type of questions asked. It will also help in improving time management skills. Solve as many papers as possible to get a good grasp of the subject.

5. Seek Guidance:
If you find certain topics challenging, seek guidance from experienced teachers or subject matter experts. Joining a coaching institute or enrolling in an online course can provide structured guidance and help in clearing doubts.

6. Regular Revision:
Mathematics requires regular practice to retain concepts and formulas. Set aside time for regular revision of topics that you have already covered. Revision helps in reinforcing concepts and improving retention.

7. Join Study Groups:
Joining study groups with like-minded aspirants can be beneficial. Discussing concepts, solving problems together, and sharing resources can enhance your understanding of the subject.

8. Analyze Mock Tests:
Take regular mock tests to assess your preparation and identify areas that need improvement. Analyze your performance in the tests and work on your weak areas.

9. Stay Positive and Consistent:
Mathematics can be challenging, but with a positive mindset and consistent effort, it can be conquered. Believe in yourself, stay motivated, and never give up.

Conclusion:
Preparing for Mathematics as an optional subject requires a systematic and disciplined approach. With proper planning, regular practice, and guidance, you can master the subject and score well in the UPSC examination. Remember to stay focused, stay positive, and give your best effort.