International Conference on "Interdisciplinary Research on Mathematics & Statistics" ICIRMS-2024

 

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Mandelbrot set

                 

Mandelbrot set:

               The Mandelbrot set is a famous fractal that exhibits intricate and self-similar patterns at every level of magnification. It is defined by a simple iterative algorithm involving complex numbers. The set is named after the mathematician Benoît B. Mandelbrot, who studied and popularized it in 1980.

Definition:

The Mandelbrot set consists of all the complex numbers 

$c$

$$z_{n+1} = z_n^2 + c$$

does not escape to infinity when iterated starting with 

$z_0 = 0$$c$$z_n$$n$

Key Concepts:

• Complex Numbers: A complex number is of the form 
  $c = a + bi$$a$$b$

• Escape Time Algorithm: To check if a complex number belongs to the Mandelbrot set, we repeatedly square 
  $z_n$$c$$|z_n|$$z_n$

• Visualization: When visualizing the Mandelbrot set, points that are in the set are typically colored black, while points that escape are colored based on how fast they escape. This creates a beautiful and complex image that shows spirals, filaments, and other intricate shapes.

Steps to Generate a Mandelbrot Set Image:

1. Choose a region of the complex plane: Typically, you choose a rectangular area of the complex plane (e.g., real values between -2 and 2 and imaginary values between -1.5 and 1.5).
2. Iterate over each pixel: For each point in the grid, treat the 
   $x$$c$$y$
3. Apply the iterative formula: Start with 
   $z_0 = 0$$z_{n+1} = z_n^2 + c$
4. Check if the point escapes: If 
   $|z_n| > 2$
5. Plot the points: Points that remain bounded are part of the Mandelbrot set and are typically plotted in black. 
6. What does the Mandelbrot set represent?
7. 

   The Mandelbrot set is an example of a fractal in mathematics. It is named after Benoît Mandelbrot, a Polish-French-American mathematician. The Mandelbrot set is important for chaos theory. The edging of the set shows a self-similarity, which is perfect, but because of the minute detail, it looks like it evens out.

Properties of the Mandelbrot Set:

1. Self-Similarity: The set shows self-similarity at different scales. As you zoom into any part of the boundary, you continue to find structures similar to the whole set.

2. Fractal Nature: The Mandelbrot set is a fractal, meaning its boundary is infinitely complex and detailed. As you zoom in, you reveal more intricate patterns.

3. Connectedness: The Mandelbrot set is a connected set. This means that it is "one piece" and does not break into multiple disconnected parts.

4. Complex Boundary: The boundary of the Mandelbrot set is highly intricate, containing infinitely many filaments and intricate structures.

Applications and Uses:

• Mathematics and Chaos Theory: The Mandelbrot set is often used in mathematics to explore complex dynamics, nonlinear systems, and chaos theory.
• Art and Visualization: Its stunning visuals make it a favorite in artistic representations of mathematics and fractals.
• Computer Graphics: It serves as a standard example for algorithms in computer graphics and fractal rendering.

Would you like me to generate an image of the Mandelbrot set for you, or do you need more detailed explanations on specific aspects of it?

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Monthly Report of May (23-24)

 

MARUDHAR KESARI JAIN COLLEGE FOR WOMEN

PG and Research Department of Mathematics

Activities for the Month of May

2023-2024

ACADEMIC

·         BOS meeting held on 07.05.24.

·         BOS syllabus correction updated on 17.05.24.

·         Autonomous Syllabus has been framed for the next academic year for I UG & I PG.

DEPARTMENT ACTIVITY

·         Staff  meeting was conducted on 14.05.24, 17.05.24, 23.05.24.

·         Prepared the documents for NAAC.

·         Prepared and submitted the documents for SSR on 31.05.24.

·         Staff meeting with principal held on 25.05.24.

·         Invited alumni for the Mega Alumni Meet through phone upto 2020 batch.

·         Website work has been updated.

·         Ms. A. Shoba newly joined on 15.05.24.

·         Ms. J. Ayesha Siddiqa Newly Joined on 16.05.24.

·         Ms. Noorlin newly joined on 28.05.24.

·         Admission work carried out by our department staff members.

·         Alumni meeting with principal held on 11.05.24, 16.05.24.

·         University exam completed for the I UG on 16.05.24.

·         University exam completed for the III UG on 17.05.24.

·         University exam completed for the I PG on 23.05.24.

·         University exam completed for the II UG on 30.05.24.

·         NPTEL mark entry has been completed on 31.05.24.

·         Stationary requirement submitted on 23.05.24.

·         ISO documents have been uploaded by all the staff members through Higrade software.

·         All the staff members applied for the SET exam.

·         Mega alumni group photos taken on 18.05.24.

·         VIT / Nishvartha scholarships applied by the first year students.

·         UMIS number registration completed for II UG, III UG and II PG.

·         Three staff members relieved on 31.05.24.

·         Academic works carried out by the staff members.

·         Stock verification completed on 20.05.24.

·         Alumni fund & Staff fund was collected and submitted on 29.05.24.

·        Industrial visit details submitted on 09.05.24.

·      All the staff members prepared their notes for the upcoming semester.

STUDENTS ACHIEVEMENT

·         Internship carried out by 11 students of I PG in State Bank of India, Vaniyambadi during their summer vacation..

·         Internship carried out by one student from I PG in St. Park Hr. Sec. School, Bargur during her summer vacation.

·         Internship carried out by the 3 students from I PG in Govt. Hr. Sec. School, Gajalnayaganpatti, during their summer vacation.

 

STAFFS ACHIEVEMENT

·         One staff member passes with score of  81% in NPTEL exam on Linear Algebra.

 

Alumni Group Photos taken on 18.05.24

 

One staff completed the NPTEL course on Linear Algebra with 81%

 

BOS meeting held on 07.05.24

 

Monthly Report of April

 

MARUDHAR KESARI JAIN COLLEGE FOR WOMEN

PG and Research Department of Mathematics

Activities for the Month of April

2023-2024

ACADEMIC

·         Prepared the documents for NAAC.

·         University exam timetable received on 18.04.2024.

·         Internal Audit held on 26.04.24.

DEPARTMENT ACTIVITY

·         Staff  meeting was conducted on 12.04.24, 17.04.24, 23.04.24.

·         e notes prepared for first years & second years.

·         Invited alumni for the Mega Alumni Meet through phone upto 2020 batch.

·         Result analysis prepared for the CIA III.

·         University practical conducted from 01.04.2024 to 03.04.2024.

·         University practical mark entry completed on 05.04.24.

·         Syllabus has been completed on 09.04.24.

·         Curriculum feedback has been posted by the students and staff members.

·         University exam fee payment completed by the students and the discrepancies has been updated.

·         Website work has been updated.

·         Project viva for III UG held on 10.04.24.

·         Project viva for II PG held on 09.04.24.

·         Hall tickets issued to the students on 23.04.24.

·         Common breakage amount submitted to the office on 15.04.24.

·         Staff achievement submitted to the IQAC on 22.04.24.

·         Syllabus Autonomous has been framed for the next academic year-I UG & I PG.

·         Stock verification completed on 26.04.24.

·         Staff interview held on 25.04.24.

·         II UG & II PG university exam started from 26.04.24.

·         I UG university exam started from 28.04.24.

·        I PG university exam started from 30.04.24.

 

 

STUDENTS ACHIEVEMENT

Pi day prizes were distributed on Students Achievers Day

EVENT NAME: GROUP DISCUSSION

I PRIZE:

1.      R.Narmatha – II M.Sc Maths

2.      S.Madhumitha – I M.Sc Maths

3.      K.Priyadharshini – III B.Sc Maths

4.      M.Saranya – II B.Sc Maths

5.      A.Nivetha – I B.Sc Maths

II PRIZE:

1.      D.Mahalakshmi – II M.Sc Maths

2.      S.Snega – I M.Sc Maths

3.      S.Lakshmi Sruthi – III B.Sc  Maths

4.      R.Jeevitha – II B.Sc Maths

5.      T.Mythili – I B.Sc Maths

III PRIZE:

1.      M.Mamtha – II M.Sc Maths

2.      R.P Madhumitha – I M.Sc Maths

3.      R.Dharshini – III B.Sc Maths

4.      C.Abinaya – II B.Sc Maths

5.      C.Saadhavidhya – I B.Sc Maths

EVENT NAME: POSTER PRESENTATION

           I PRIZE  :  M.Vinothini – I M.Sc Maths

           II Prize    :  M.Soumiya – I M.Sc Maths

           III Prize   : P.Sujaritha – I B.Sc Maths

 

STAFFS ACHIEVEMENT

·         Five staff members participated in online Seminar titled Mathematical Modeling in Image Processing held on 23.04.24 at Dr. M. G. R. Educational and Research Institute.

·         One staff acted as observer for NPTEL exam held at Sacred Heart College, Tirupattur.