## Wednesday, 16 February 2022

### PI Day 2022

Dear friends,

Sinofcos, the math forum of TKMCAS is inviting suggestions for naming the upcoming π day program. 📝The suggestions should be shared along with your name, class and department.
🗳️Drop it in the box kept infront of Mathematics Department on or before 18th Feb 2022.
🎁Winner will be rewarded.
📎Alumini can send their suggestions via https://forms.gle/Bp5Y5vqchgyif3VM9

## Generators of multiplicative group $(\mathbb{Z}/2^{\alpha}\mathbb{Z})^*$

The set of all unit elements in the cyclic group $\mathbb{Z}/N\mathbb{Z}$ is a group under multiplication modulo $N$ of order $\phi(N)$, where $\phi$ is the Euler-totient function. It is denoted by $(\mathbb{Z}/N\mathbb{Z})^*$.
It is well known that $(\mathbb{Z}/N\mathbb{Z})^*$ is not always cyclic (Primitive element theorem) (See Chater 10, [1]). For example $(\mathbb{Z}/8\mathbb{Z})^*=\{1,3,5,7\}$ is not cyclic. $(\mathbb{Z}/2\mathbb{Z})^*=\{1\}$ and $(\mathbb{Z}/4\mathbb{Z})^*=\{1,3\}$ are trivially cyclic.

Question: Show that for $\alpha\geq 3$, $(\mathbb{Z}/2^{\alpha}\mathbb{Z})^*$ is generated by $-1$ and 5?
You may use the following sage code for validating the result:
Reference: [1] T M Apostol, Introduction to Analytics Number Theory

# Meet the Scholar Program (MTS-I-2021)

## Title of the Talk: Career Prospects of Applied Economics

Speaker: Dr. Vineeth Mohandas, Assistant Professor in Economics, Christ College, Bangalore

## Wednesday, 6 October 2021

### Is it true that square root of any positive integer greater than one, which is not a perfect square, is an irrational number?

This question was raised during a discussion with first year degree students.  The motivation was the proof showing the  irrationality of  $\sqrt{2}$.  The discussion took us to the following 'one line' proof: If $n$ is such a number having the rational expression $\sqrt{n}=\frac{a}{b}, \gcd(a,b)=1$, then by the fundamental theorem of arithmetic (unique prime factorization)  $b=1$ and $n$ is a square.

## Thursday, 18 March 2021

### Detailed Promo | Estrellas 2021 | π Day Celebrations | sin∮cos Math Forum

We are proud to announce the release of the ESTRELLAS 2021 Detailed Promo  here.

## REGISTER FOR EVENTS IN A CLICK

You can provide Academic, Financial and Social support for encouraging the Math Forum to conduct more creative events inorder to arouse the mathematical abilities of students.

Script/Camera/Editing/Direction : Jinu S Jacob

Asst. Director : Sarathlal S

Produced by : Prof.Nizamudeen Ashique (For Department Of Mathematics)

Coordinator : Kasyap L S

Cast

P1: Vishnupriya

P2: Parvathy

P3: Muhammed Ajmal

P4: Ashifa N

P5: Moomina

P6: Sreehari

P7: Amritha

P8: Keerthy

P9: Arya a

P10: Femina

P11: Jinu S Jacob

# ✨ 𝔼𝕤𝕥𝕣𝕖𝕝𝕝𝕒𝕤 2021 ✨.........π Day Celebrations..........

★ All Kerala Online Events for Secondary School & College Students

★Exciting Offline Events for Students of the Institution

★ Grand Cash Prizes and Assured Certificates

********************************************

#Detailed description of each event is available in its Registration Form

Online Events

DEXERTICA - Online Presentation Competition

ENIGMA - Online School Quiz Programme

Offline Events (*Only for the students of the institution)

EBULLIENCE

CALCULO

MATH RELAY

DRISHYAM-THE CLASSIC SOLVER

★ GUESSTIMATE (Open for participants of any of the above event)

Deadline for Online Events : 21/03/2021, 6 PM

Deadline for Offline Events : 22/03/2021, 6 PM

→ Contestants can register upto any number of events.

→ Registrants are required to upload a photo of their Valid Institutional ID.

→ PAYMENT IS RESTRICTED TO UPI Method Only (GPay, PayTM, PhonePe, WhatsApp Payment etc.)

→ Contestants should upload the Receipt or Screenshot of SUCCESSFUL Transaction in the concerned space in the form.

FOR ANY ENQUIRIES:

Coordinator : Adersh V K (+91 999 516 59 51)
Convener : Kasyap L S (+91 952 603 98 23)
EMail : studentcoordinatorsinofcos@gmail.com

## Sunday, 14 March 2021

### ESTRELLAS 2021 | Official Promo Release | π Day Celebrations

We proudly present the promotion video of ESTRELLAS 2021 π-Day Celebrations organized by sin∮cos Math Forum of TKM College Of Arts and Science, Kollam.

 ESTRELLAS 2021 | Official Logo

Stay tuned here for details of the event.

Video & Logo Credits: Jinu S Jacob, Joint Convener&Technical Head, IInd PG Mathematics, sin∮cos

## Monday, 21 December 2020

### National Mathematics Day 2020

As a part of National Mathematics Day on 22nd December 2020 sin∮cos is conducting a talk on Attractors for Reich IFS through fixed point theory.

The talk will be delivered by Dr. Aswathy MR, Assistant Professor of Department Of Mathematics of TKM College Of Arts and Science, Kollam and also one of the mentors of the Math Forum sin∮cos.

The talk is scheduled on 22nd December from 5:30 PM to 6:30 PM via Google Meet Application.

Interested individuals can join the talk on prescribed time and date using the link or join button below.

Join on December 22nd at 5:30 PM
(Join 10 minutes prior to avoid network traffic issues)

## Tuesday, 27 October 2020

### Quester 2020-Final Quizzing

Here the video link for the final phase of Quester 2020.

### Quester 2020 - Inauguration

Here is the video link for the inaugural session of Quester 2020, the all India quiz competition organised by sinofcos.