## 14 JunFermat’s Last Theorem

[caption id="attachment_3363" align="alignleft" width="418"] Google Doodle depicting Fermat's Last Theorem[/caption] We can find infinitely many solutions that can solve the equations \$\$x+y=z\$\$ and \$\$x^2+y^2=z^2\$\$ in integers, but what about the equation \$\$x^3+y^3=z^3\$\$ or more generally \$\$x^n+y^n=z^n\$\$, where n is an integer greater than 2 and x,y,...

## 10 JunReinventing the Indian (Hindu) Calendar

Summary: Following the Indian (Hindu) calendar, we Indians are celebrating the seasonal festivals on wrong dates. It is because in the Indian calendars, the seasons are out of phase with the real tropical phenomenon of the earth. This article analyses how and why we are doing that and what to do about it. In the Indian calendars, the Makar Sankranti which marks the transition of the Sun into Makar Rasi (Capricorn), generally falls around 14th or 15th January of the Gregorian calendar. Makar Sankranti also marks many of the Indian harvest festivals such as the Pongal of the Tamils, the Bhogali Bihu of the Assamese, the Maghi (Lohri) of the Punabis, Bhogi in Andhra Pradesh etc. Many communities start their new years on this date. Astronomically, Makar Sankranti is the winter solstice. It is the shortest day marking the beginning of the Uttarayan (the northern journey) of the Sun with gradual increase of the duration of the day. The Bhagavad Gita mentions great importance of the Uttarayan. This was the reason why Bhishma, when wounded in Mahabharata war, chose to await for the Makar Sankranti, before choosing to die. In the Jagannath temple at Puri the Uttarayana Yatra is celebrated on this Makar Sankranti day.

## 09 JunMath Unlimited : Eassys in Mathematics

Edited by R Sujatha, H N Ramaswamy and C S Yogananda, CRC Press, 2012, 350 pp.   Math Unlimited is a collection of essays that has been edited by R Sujatha, H N Ramaswamy and C S Yogananda, whose aim is to offer, to a wide audience, a flavor...

## 09 JunThe Tangled Origins of the Leibnizian Calculus

Richard C Brown World Scientific, 2012, xxi+310 pp.   As the title of the book suggests, this book attempts to unravel the threads that lead to the creation of the revolutionary symbolism of differential and integral calculus by the polymath Gottfried Wilheim Leibniz (1646–1716). We are all aware that...

## 12 MayGonit Sora Notes: Probability Theory

Gonit Sora is introducing a new initiative where we shall post class notes of various topics related to an undergraduate curriculum. These notes will be based on some actual course at some university and will follow the actual classes. The first of this series is a...

## 06 MayMathletics 2013 (Category IV) - Assam Academy of Mathematics

(Class XI and XII) Marks: 100 Time: 3 Hours [Answer in English. Two students of the group will discuss the solution of the problems and then write the answer in a khata for the group. No third person can help the group to solve the problems.] Answer the following...

## 06 MayMathletics 2013 (Category III) - Assam Academy of Mathematics

(Class IX and X) Marks: 100 Time: 3 Hours [Answer the following questions in English or in mother tongue. Two students of the group will discuss the solutions of the problems and write answer in a khata for the group. No third person can help the group to...

## 06 MayMathletics 2013 (Category II) - Assam Academy of Mathematics

(Class VII and VIII) Marks: 100 = 5X20 Time: 3 Hours [Answer the following questions in English or in mother tongue. Two members of each group will discuss the solutions of the problems and one of them will write the solutions in a khata for the group.] [তলত দিয়া...

## 06 MayMathletics 2013 (Category I) - Assam Academy of Mathematics

(Class V and VI) Marks: 100 = 5X20 Time: 3 Hours [Answer the following questions in English or in mother tongue. Two participants will discuss the solutions of the problems and they will write the answer in a khata for the group. None can help the group in...

## 16 AprThe Number of Solutions of a System of Linear Equations

The standard form of a linear equation in \$\$n\$\$ unknowns \$\$x_1,x_2,\dots ,x_n\$\$ is \$\$a_1x_1+a_2x_2+\dots +a_nx_n=b,\$\$ where \$\$a_1,a_2,\dots ,a_n\$\$ and \$\$b\$\$ are constants. Here constants mean some real numbers (these constants may come from any number field). A collection of one or more linear equations of same variables is called...