**National Conference **

**on **

**Mathematical and Computational Analysis**

** **

**January 28 – 30, 2023**

Organised by

Ramanujan Society of Mathematics and Mathematical Sciences

at

Department of Mathematics, T.D.P.G. College, Jaunpur-222002 (UP)

**About the Conference:**

Ramanujan Society of Mathematics and Mathematical Sciences is going to organise a National Conference on “Mathematical and Computational Analysis,” during January 28 – 30, 2023.

The Conference is to bring together eminent Mathematicians, research scholar and students from different parts of the Country. In these three days National Conference young mathematicians and research scholars will be benefitted by getting ideas of the recent development in Mathematical and Computer Analysis through invited talks/plenary lectures of the senior and eminent mathematicians. The programme covers broad spectrum of topics to the several applications of mathematics in different field of subjects. It also provides a premier interdisciplinary platform for researchers, practitioners, and educators to present and discuss the most recent innovations, trends, and concerns as well as practical challenges encountered and solutions adopted in the fields of Mathematical and Computer Analysis Conference.

**Theme of the Conference**

**Mathematical Analysis**

The name "mathematical analysis" is a short version of the old name of this part of mathematics, "infinitesimal analysis"; the latter more fully describes the content, but even it is an abbreviation (the name "analysis by means of infinitesimals" would characterize the subject more precisely) Analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Mathematical analysis is of high importance to the mathematical sciences as a whole, linking many areas of pure mathematics to applied areas. For example, there are strong interactions with: algebra. applied mathematics. An analysis is important because it organizes and interprets data, then structures that data into presentable information useful for real-world applications. For example, a marketing analysis interprets buying patterns, market size, demographics and other variables to develop a specific marketing plan. Analysis is a branch of mathematics that depends upon the concepts of limits and convergence. It studies closely related topics such as continuity, integration, differentiability and transcendental functions. These topics are often studied in the context of real numbers, complex numbers, and their functions. In the 18th century, Euler introduced the notion of mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the modern definition of continuity in 1816, but Bolzano's work did not become widely known until the 1870s. In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, particularly by Euler. Instead, Cauchy formulated calculus in terms of geometric ideas and infinitesimals. Thus, his definition of continuity required an infinitesimal change in *x* to correspond to an infinitesimal change in *y*. He also introduced the concept of the Cauchy sequence, and started the formal theory of complex analysis. Poisson, Liouville, Fourier and others studied partial differential equations and harmonic analysis. The contributions of these mathematicians and others, such as Weierstrass, developed the (ε, δ)-definition of limit approach, thus founding the modern field of mathematical analysis. Around the same time, Riemann introduced his theory of integration, and made significant advances in complex analysis.

Towards the end of the 19^{th} century, mathematicians started worrying that they were assuming the existence of a continuum of real numbers without proof. Dedekind then constructed the real numbers by Dedekind cuts, in which irrational numbers are formally defined, which serve to fill the "gaps" between rational numbers, thereby creating a complete set: the continuum of real numbers, which had already been developed by Simon Stevin in terms of decimal expansions. Around that time, the attempts to refine the theorems of Riemann integration led to the study of the "size" of the set of discontinuities of real functions.

Also, various pathological objects, (such as nowhere continuous functions, continuous but nowhere differentiable functions, and space-filling curves), commonly known as "monsters", began to be investigated. In this context, Jordan developed his theory of measure, Cantor developed what is now called naive set theory, and Baire proved the Baire category theorem. In the early 20th century, calculus was formalized using an axiomatic set theory. Lebesgue greatly improved measure theory, and introduced his own theory of integration, now known as Lebesgue integration, which proved to be a big improvement over Riemann's. Hilbert introduced Hilbert spaces to solve integral equations. The idea of normed vector space was in the air, and in the 1920s Banach created functional analysis.

Mathematical analysis includes the following subfields:

- Real analysis, the rigorous study of derivatives and integrals of functions of real variables. This includes the study of sequences and their limits, series, and measures.
- Functional analysis studies spaces of functions and introduces concepts such as Banach spaces and Hilbert spaces.
- Harmonic analysis deals with Fourier series and their abstractions.
- Complex analysis, the study of functions from the complex plane to the complex plane which are complex differentiable.
*p*-adic analysis, the study of analysis within the context of*p*-adic numbers, which differs in some interesting and surprising ways from its real and complex counterparts.- Non-standard analysis, which investigates the hyperreal numbers and their functions and gives a rigorous treatment of infinitesimals and infinitely large numbers. It is normally classed as model theory.
- Numerical analysis, the study of algorithms for approximating the problems of continuous mathematics.

Classical analysis would normally be understood as any work not using functional analysis techniques, and is sometimes also called hard analysis; it also naturally refers to the more traditional topics. The study of differential equations is now shared with other fields such as dynamical systems, though the overlap with 'straight' analysis is large.

**Computer Analysis**

Computer analysts, also called systems analysts, plan and develop computer systems. Their work includes installing new systems or upgrading existing systems to meet changing business needs. They also computerize tasks that are still being done by hand or in some other less efficient way.

The use of computers in the field of mathematical modeling is necessary. Computer simulation is the most important application in mathematical modeling. The specific tools are used. Including mathematical software, image processing software, statistical software and programming software. The operation of computers started only after advances in mathematics and logic. The mathematical foundation of computers is logic. Other fields like calculus, probability theory, and set theory are mathematical fields that are applied in computers programs but are not very important.

Math matters for computer science because it teaches students how to use abstract language, work with algorithms, self-analyze their computational thinking, and accurately modeling real-world solutions. In view of this, computer science fundamentals and path-breaking research in conceptual computer science and engineering will also be one of the facets of interest for this conference. Some of the upcoming areas of research like computational intelligence, big data analytics and deep learning, in addition to several others, will be the prime focus of the conference, with specific attention being paid to scope for future research in these fields. This conference will give academia and industry professionals a platform to share their experiences, research results and challenges faced, paving way for the development and evolution of state-of-the-art technologies.

**Applications of Mathematics in Computer Science:- **Math is one of the foundations of computer sciences. It’s also one of the more crucial elements in computer sciences. So how is mathematics really applied in computer science? Despite *advanced* mathematics not applied frequently, basic mathematics, most importantly algebra, is the main ingredient for a successful computer scientist. Many of the functions and operators in all programing languages require some knowledge in mathematics. For example, these operators include arithmetic, comparison, logical, assignment and conditional operators. All of the aforementioned tasks need mathematics for them to be used and properly applied, specially the arithmetic and conditional operators.

Computer sciences heavily rely on algorithms, which the latter in turn heavily relies on mathematics. ‘Theoretical computer science’ strongly involves discrete mathematics. Discrete mathematics is basically the study of mathematical structures that are discrete rather than continuous, and so this ‘theoretical’ branch of computer sciences involves a lot of mathematics, in the form of graphs, algorithms, computational geometry, quantum computation, algebra, computational number theory. In fact, the use of mathematics in computer sciences depends on the latter’s department. A beginner in programming may not need mathematics, but as the programmer advances through the level of difficulty, he / she will have to use more advanced mathematics.

Even though we don’t see any, computers operate using binary digits, which is basically mathematics. Physics plays a role in certain computer science branches. And since mathematics and physics are hugely related, this only provides us with more proof on how much mathematics is in computer sciences. More mathematical applications in computer science are sets, probability and Boolean algebra. Many applications such as calculators, video games and graphical applications are compelled to the use of mathematics. In my opinion, without proper mathematics, any computer scientist would be on the path to failure. For many programs to be created and written, logic is the central necessity, which in turn is mainly rooted to mathematics and mathematical principles. Hence, mathematics provides the right pathway towards success in computing.

**Aim of the Conference and Targeted Audience**

This conference aims to bring together researcher, academicians, scholars and students to exchange & share their experiences, new ideas and researches about all aspects of Mathematics research in diverse fields. This conference is going to benefit directly to 150 academicians who will attend this conference and indirectly too many people though social media (Advertisement, News papers, Social Sites, proceedings etc.).

**About Ramanujan Society of Mathematics and Mathematical Sciences:**

India celebrated the **“Mathematics Year”** in 2012 and **Ramanujan Society of Mathematics and Mathematical Sciences (RSMAMS)** was established in the same year. The main aim of the society is the promotion of Mathematics Educations and its applications in different field of Sciences and also to create interest among students, research scholars and young teachers towards mathematics. Since its foundation in 2012 **“RSMAMS”** has done excellent work to improve mathematics Educations and research in India. In 2012, 2013, 2014, 2015, 2016,2017, 2018, 2019, 2020, 2021, and 2022 **“RSMAMS”** has organized symposiums, conferences, and workshops successfully to achieve its goal. The society is continuously organizing lectures of eminent Mathematicians for students and research scholars. During this short tenure the name and fame of the society has spread across the frontiers of the country and also in abroad.

**Call for papers:**

The organizers of the Conference invite papers for presentation. The abstract not exceeding 200 words intended for presentation should be sent latest by January 20, 2023 preferable by e- mail to

Dr. Satya Prakash Singh,

263, Line Bazar, Jaunpur – 222002 (U.P.) India.

Contact No.: 05452 – 261922

Mob. No.: 09451159058, 09451161967

E-mail: jrsmams@yahoo.com; jrsmams@gmail.com

**Proceeding of the Conference: **

The proceedings of the Conference will be published. The full length paper in duplicate along with a file formatted in AMS latex/ MS word/ Pdf may be submitted during the Conference by January 20, 2023.

**Travel and Local Hospitality**

Financial support for travel (AC III class fare) will be provided to invited speakers. Teachers/Research Scholars presenting paper in the Conference will be given fare. Each participant and accompanying person will be provided local hospitalities. *Please inform will in advance about your travel programme to facilitate the organising committee and volunteers.*

**Expected Invited Speakers**

Prof. M.S.M. Naika (Banglore University) Prof. A.K. Agarwal(Punjab Univer.)

Prof. S.S. Mishra (BHU, Varanasi) Prof. Hukum Singh (NCERT, Delhi)

Prof. K. Srinivasa Rao (IMSC Chennai) Prof. M.A. Pathan (Aligarh)

Prof. Sunderlal (Agra University) Prof. U.C. De (Kolkata University)

Prof. K.C. Prasad (Ranchi University) Prof. P.K. Banarji (Jodhpur University)

Prof. Manoj Kumar Singh(BHU, Varanasi) Prof. T. Singh(BITS Pilani, Goa)

Prof. Rishi Ranjan Singh (IIT Raipur) Prof. Deepmala (IIIT Jabalpur)

Prof. Sanjay Singh (IIT BHU) Prof. A.M. Mathai, (CMSS Pala)

Prof. Vishnunarayan Mishra (Amarkantak) Prof. Umesh Singh (BHU, Varanasi)

Prof. Ahmad Ali (BBD Lucknow) Ms. S. Gangwar(Purvanchal Univer.)

Prof. Sandeep Bhakat (Kolkata) Prof. BP Mishra (Mumbai University)

Prof. M.I. Qureshi (Delhi) Prof. Prakriti Rai (Delhi)

**Registration fee:**

Participants: Rs. 1000, Research Scholars:Rs. 500, Accompanying person: Rs. 800

**Advisory Committee**

- Prof. Nirmala Maurya (Vice Chancellor Purvanchal University, Jaunpur)
- Prof. Sunder Lal (Ex-Vice-Chancellor, V. B. S. Purvanchal University Jaunpur)
- Prof. Alok Kumar Singh (Principal T. D. P. G. College, Jaunpur)

Prof. Sudhir Srivastava (Gorakhpur) Prof. M. A. Pathan (Aligarh)

Prof. P. K. Banerji (Jodhpur) Prof. K. C. Prasad (Ranchi)

Prof. U. C. De. (Kolkata) Prof. M.I. Qureshi (New Delhi)

Prof. B. P. Mishra (Mumbai) Dr. A.K. Singh (DST New Delhi)

Prof. Tarkeshwar Singh (Goa) Prof. G.C. Chaubey (Jaunpur)

Prof. Umesh Singh (BHU) Prof. Pankaj Srivastava (Allahabad)

**Contact persons**

**Dr. S. P. Singh (Convenor)**

Department of Mathematics, T. D. P. G. College, Jaunpur – 222002 (U.P.) India

Contact No.: 09451159058, E. mail: snsp39@yahoo.com

**Dr. S. N. Singh (Emeritus Scientist)**

Department of Mathematics, T. D. P. G. College, Jaunpur – 222002 (U.P.) India

Contact No.: 09451161967, E-mail: snsp39@gmail.com

**Dr. Brijendra Singh,**

Department of Mathematics, T. D. P. G. College, Jaunpur – 222002 (U.P.) India

Contact No.: 09415895789

**Dr. Manoj Kumar Srivastva**

Department of Mathematics, T. D. P. G. College, Jaunpur – 222002 (U.P.) India

Contact No.: 09415334577