# TKM CAS Math Forum

A platform for sinofcos activities

## Wednesday, 16 February 2022

### PI Day 2022

## Thursday, 27 January 2022

### On generators of multiplicative group

## 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*

## Thursday, 14 October 2021

## Wednesday, 6 October 2021

### Some rational thoughts on Irrationality.

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

## Thursday, 18 March 2021

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

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

**Download this Video in HD 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.

**Go to sin∮cos Support Forum click here**

**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: Ahad j

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 REGISTRATION

# ESTRELLAS 2021 has come to an end...

# Thank You All....

# ✨ **πΌπ€π₯π£πππππ€ 2021** ✨

**.........Ο 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*)

**★ CALCULO**

**★ 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)

## Sunday, 14 March 2021

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

We proudly present the promotion video of

**ESTRELLAS 2021**Ο-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.

For experiencing this video in high quality, click here

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

## Monday, 21 December 2020

### National Mathematics Day 2020

**Attractors for Reich IFS through fixed point theory.**

## Tuesday, 27 October 2020

### Quester 2020 - Inauguration

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