About the Author

I am a software development manager residing in Noida, India. My primary interest is mathematics. Readers are expected to see a reasonable amount of mathematical content (although I will try to simplify things a little bit so as to make it more accessible to people).

My day job requires me to handle projects done mostly in C/C++ and I have been doing so for more than 13 years. My area of expertise includes multimedia technologies on Google's Android platform. I am also familiar with various video compression formats like MPEG-4, H.264, VC1, VP8, VP9 and HEVC.

I have a profile at math.stackexchange.com and also maintain a non-mathematical blog.

About this Blog

This blog uses MathJax for rendering all mathematical symbols and takes some time to load and therefore patience is advised to get the mathematical symbols rendered properly. Mathematical content can be zoomed to twice the size by double clicking it.

It is advisable to use desktop mode on the mobile browsers otherwise the MathJax content will be disabled. Moreover while using mobile devices it is preferable to use Firefox as it is the only mobile browser with support for CSS embedded web-fonts and thus renders the blog posts in exactly the same look as seen on desktop browsers.

All the content published on the blog is available for public use under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. Readers should feel free to make use of it in any way they want as long as they credit this blog for original creation and release derivative work with the same Attribution-ShareAlike license.

Comment Policy

Comments on this blog are moderated, but at the same time these are normally approved on ASAP basis unless the comments are completely irrelevant. Readers should therefore provide prompt feedback and suggestions if they so desire. Mathematical content (using $\mathrm\LaTeX$ commands) can be put in comments using one of the two common mechanisms provided by MathJax:
  • For inline mathematical content write like $\$$<math content>$\$$ (without the angle brackets)
  • For displaying large math equations use either of the two approaches below:
    • $\$\$$<math content>$\$\$$
    • $\$$\displaystyle <math content>$\$$
The comments also become a part of this blog and are therefore covered under the same license with attribution to the comment author.

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Paramanand Singh

24 comments :: About the Author

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  1. Dear Paramanand,
    I am happy to see your blog posts. I am also a math enthusiast though not very skillful at it. I happen to work in the same company as yours in the Bangalore multimedia team. I stumbled across your blog through my colleague Ganesh’s reference.
    I am happy to find a math enthusiast amongst the software engineers of today. Keep up the good work and I look forward to read your posts in the future.

    Have a great day.
    Hemanth Sethuram

  2. Dear Paramanand,

    I am also a software guy & like mathematics, i found ur blog today itself, and hope that i would enjoy it.

    Thanks in advance to keep up the good work.

    Also i wish ur single status to change to married very soon. :)

    Naveen Agarwal

  3. Liked the website. Please let me know where can we find good questions (with explanations and solutions) for IIT JEE mathematics.


  4. Remember that Fermat was a lawyer, not a professional mathematician! :-) Love your website – thanks.

  5. Sir I respect your view I am a student preparing for iit and I live in hyderabad first I thought that. You are from hyderabad and I had a idea of asking you to teach me calculus but unfortunately I found that you are in noida could you please tell me how to learn calculus in an effective way and use it effectively and please I requeat you to suggest a teacher in hyd or a good book and please also try to email me ragarding calculus and learning calculus please

  6. Hello Rajashekhar,
    I will not be able to help you with any tutor, but surely I can advise you a good book to read. Please get a copy of “A Course of Pure Mathematics” by G. H. Hardy and read it completely. By “read it” I mean read it and not start solving problems. If you manage to understand this book completely you will never have issues in calculus.


  7. Hello

    Hi This is K.Chandrasekran from Chennai. I am working as Assist.Professor in mathematics in Engineering college, myself and our friends are started working in modular equations for doctoral degree. your Notes are simple for understanding the concepts for beginners. I like you very much because even though your a software engineer, doing mathematics problems problems and posting in blogs.

    Is it possible to get one copy of the book “A Course of Pure Mathematics” by G. H. Hardy ” and need some more help regarding Latex software.



  8. Hello Chandrasekran,

    Hardy’s book is at an elementary level covering calculus concepts in a rigourous manner. It should be available online if you search enough. Unfortunately the printed form is difficult and costly to obtain (need to order from Amazon). It can also be available in some university library.

    About learning latex, the best is start using this fabulous software. Maybe you can start a blog on wordpress and try to use latex. Lot of tutorials are available online. A book “Math into Latex” is also very helpful.


  9. Hello Paramanand,
    I found your notes on elliptic integrals very interesting and clear.
    To make it easier to navigate through your notes, I was wondering if there is a way of having a start page with an index to all your notes.

  10. Thanks for the suggestion. I will see what I can do, but currently I don’t have access to modification of template or CSS in WordPress. I am planning to move to http://paramanands.blogspot.com/ where I have full control on the CSS and templates.

  11. I saw only later that you have moved already some of the notes.
    On an unrelated subject: would (a variation of) the Landen’s transformation work also for integrals with integrand of the type $\displaystyle \int(1-k^{2}\sin^{2}\phi)^{-n-1/2}\,d\phi$?

  12. Hello Michele,
    I think the integral you are asking belongs to third type of elliptic integrals. There are many books available to treat this subject. If I get time to deal with this topic, I will definitely put on the blog.


  13. @paramanand
    I don’t see the reply button to your remark but I thought it would have been rude not to thank you.

  14. Updated with latest pic.

  15. Hello Parmanand!

    I am an engineering undergraduate in third year at BITS Pilani who spends all his time doing mathematics. I wish to pursue Masters in Mathematics. I can somehow relate to you. I blog too- cozilikethinking.blogspot.com

    I feel had you too made the decision to switch to mathematics in place of doing a job, you'd have been happier. Or not. But it was really good reading your blog.

  16. @Ayush Khaitan

    I am glad that you can "somehow relate to me" by just reading my blog. Just to satisfy your curiosity the decision to go for software job was based on financial concerns. But luckily mathematics is such a subject which can be studied without the need of any establishment like schools and universities (after a certain stage).

    The fact that you made an effort to read my blog and also to comment on it gives me great satisfaction and that is enough reason to be happy.

    Wish you best of luck for higher mathematical studies!

  17. Dear Paramanand,

    Do you have any suggestions for this question?


  18. Dear Paramanand Sir, I wish to contact you, please share your mobile number.Thank you.

  19. @Srinivasa Raghava,

    It is an accepted good behavior not to share personal information like mobile number online. However there are many other equally powerful channels of communication available online. You can ask me any information about this blog (or any other stuff related to mathematics) via comments to this blog. Since the comments here are moderated you can perhaps give your email in comments so that I can contact you (and this comment containing your email will not be published here).


  20. Your blog is very good.(Though I do not know enough math to understand the content, but can see the beauty of math.)

    This is the second blog that I bookmarked. (I bookmark seriously)
    I also loved the design of your blog.

    Here are some questions related to blog:
    1. How did you create the design? I mean this is not a template. (I'm noob)
    2. How do you write your content? As you also provide PDF version, so I'm asking do you write it in blogger editor or first write in some software and then paste into blogger editor?

  21. @रोहित हिल

    Thanks for bookmarking this blog. I am glad that someone likes it even if he does not yet understand all the content here.

    The design of the blog is based on an existing template and some modifications in the script. It was done a long time ago so I don't remember the exact details.

    I exclusively use the blogger editor (HTML mode) to type all my content and once it is published I then print the webpage into PDF and give a link to this PDF in the blog post. The PDF link is designed so that it is not visible in print preview.


  22. Parmanand, Great blog! You are obviously a very smart guy. I am just an interloper between businesses (happily unemployed!) and spending all my time in doing everything I could not do when I was under pressure getting through B.Tech (IIT KGP) and then building my career .. so spending time reading history and mathematics ... :) Thanks for your great work .. (curious, are you IIT alum?)

  23. Dear Sir, I stumbled upon your solution to the below mentioned problem . Due to certain technical issues I couldnt comment my doubts in the platform. Please help me with this doubt.
    "α,β are roots t2−t−1=0 and hence we can write 1−x−x2=(1−αx)(1−βx)" Could you please explain how this can be written?

  24. @Adithya
    You can observe that if $\alpha, \beta$ are roots of $t^{2}-t-1=0$ then we have $$t^{2}-t-1=(t-\alpha)(t-\beta)$$ and putting $t=1/x$ (and multiplying the equation by $x^{2}$) we get $$1-x-x^{2}=(1-\alpha x) (1-\beta x) $$ so maybe it was not so obvious but at the same time not too difficult either.