#### Department Profile

### Department of Mathematics

#### Department Profile PG

#### About the Department

Year of Establishment: | 1990 |

PG MSC: | 2014 |

Post Graduation: | M.Sc (Maths with Computers) |

Faculty Strength (PG): | Full time: 10 |

#### Vision

To inculcate the spirit of talent and the power of practice.

#### Mission

- To Develop Critical thinking and analytical problem-solving capabilities.
- To enable them to realize that they are capable of becoming functionally numerate.

#### Best Practices, Uniqueness, Innovative Ideas

#### Programmes Offered

- Post Graduate Programme
- MSc Mathematics with Computer Science

#### Programme Objectives (PO’s), Programme Outcomes (PO’s), Programme Specific Outcomes (PSO’s)

#### Program Objectives PG MSC Mathematics with Computers

The Postgraduate degree programme MSC Mathematics with Computers in the Department was started in 2014 with an aim of interdisciplinary approach in line with current trends in scientific research, which is multi-disciplinary and adaptive. Postgraduates shall have a strong foundation in mathematics and computers, and can apply this knowledge to research, teaching, and the software industry.

#### Program Outcomes

- Apply mathematical concepts to solve problems in various areas of pure mathematics.
- Locate mathematical methods as needed in order to solve problems.
- Develop proficiency in the analysis of complex physical problems and the use of mathematical techniques to solve them.
- Communicate effectively by oral, written, computing, and graphical means.
- Able to pursue their careers in research and in the software industry.
- Students will be able to work on projects in collaboration with well-established software development organizations and acquire demonstrable experience in the design, development, and documentation of a software product of significant size and complexity.

#### PG- MSC (Maths with Computer Science)

#### PSO’s

#### Semester-I

##### Algebra

**Objective:** To lay a strong foundation in solvability in group structures, theorems on groups, ideals, homomorphism, and unique factorization domains.

**Outcome:** On successful completion of the course, students will recognize algebraic structures that arise in matrix algebra, linear algebra, and will apply the skills learned to understand various subjects, appreciate the value of abstraction, and meet many examples of groups and group actions from around mathematics.

##### Mathematical Analysis

**Objective:** A student is made to understand the concepts and theorems of metric space, limits of functions, Riemann-Stieltjes integral, and sequences and series of functions.

**Outcome:** Students will be able to prove basic set-theoretic statements, develop models, and apply the results of computations to the application domain. They will understand formal mathematical definitions and theorems, and apply them to prove statements about real-valued functions.

##### Discrete Mathematics

**Objective:** Introduce concepts of mathematical logic for analyzing propositions and proving theorems, using sets for solving applied problems, working with relations and their properties, investigating functions as relations, and introducing basic concepts of graphs, digraphs, and trees.

**Outcome:** After completion of the course, students will analyze logical propositions via truth tables, prove theorems using induction, understand sets, determine properties of relations, identify functions, and define graphs, digraphs, and trees.

##### Python Programming

**Objective:** Understand Python as a scripting language for developers, learn to design and program Python applications, work with lists, tuples, dictionaries, and more. Learn to design object-oriented programs, write loops and decision statements, and build Python modules for reusability.

**Outcome:** Become familiar with Python programming, input/output, algorithm design, file manipulation, and data storage. Students will build a portfolio of documented Python code, demonstrating their skills to potential employers.

##### RDBMS

**Objective:** Learn the basics of relational databases, write SQL code, update database content, retrieve data, and apply views to enhance security.

**Outcome:** Understand relational databases, write ANSI/ISO standard SQL, manage transactions, and process data with row and aggregate functions.

### Cloud Computing

#### Objective:

To provide students with the fundamentals and essentials of Cloud Computing. To provide students a sound foundation of Cloud Computing so that they are able to start using and adopting Cloud Computing services and tools in their real-life scenarios. To enable students to explore some important cloud computing-driven commercial systems and applications. To expose the students to frontier areas of Cloud Computing and information systems, while providing sufficient foundations to enable further study and research.

#### Outcome:

- Explain the core concepts of the cloud computing paradigm, the characteristics, advantages, and challenges of various models and services in cloud computing.
- Apply the fundamental concepts in datacenters to understand the trade-offs in power, efficiency, and cost.
- Identify resource management fundamentals, such as resource abstraction, sharing, and sandboxing, and their role in managing infrastructure in cloud computing.
- Analyze various cloud programming models and apply them to solve problems on the cloud.

### Automata Theory

#### Objective:

To acquaint the students with an overview of the theoretical foundation of computer science from the perspective of formal languages. Employ finite state machines to solve problems in computing, explain deterministic and non-deterministic machines, and comprehend the hierarchy of problems arising in computer science.

#### Outcome:

- Understand the theoretical foundation of computer science in computing to employ finite state machines to solve problems in computing.
- Understand deterministic and non-deterministic machines and their applications.
- Understand the hierarchy of automaton machines, the grammar generated, and the set of languages accepted by it.

### Mobile Computing

#### Objective:

The course objective is to cover the nomenclature and implementation of mobile computing and mobile communication. Coverage includes 2G, 2.5G, 3G, 3G+, and 4G communication systems, mobile satellite communication networks, mobile IP, mobile TCP, digital audio-video broadcasting, and mobile TV.

#### Outcome:

- Define mobile technologies in terms of hardware, software, and communications.
- Utilize mobile computing nomenclature to describe and analyze existing mobile computing frameworks and architectures.
- Evaluate the effectiveness of different mobile computing frameworks.
- Describe how mobile technology functions to enable other computing technologies.

### Semester-IV: Integral Equations and Calculus of Variations

#### Objective:

The objective of these contents is to provide some important results like:

- Initial value problem reduced to Volterra integral equations.
- Method of successive substitution to solve Volterra integral equation of the second kind.
- Method of successive approximation to solve Volterra integral equation of the second kind.
- Resolved kernel as a series.
- Laplace transform method for a difference kernel.

#### Outcome:

- Understand methods to reduce initial value problems associated with linear differential equations to various integral equations.
- Categorize and solve different integral equations using various techniques.
- Describe the importance of the Green’s function method for solving boundary value problems.
- Learn methods to solve various mathematical and physical problems using variational techniques.

### Compiler Design

#### Objective:

Discuss the major phases of compilers and use the knowledge of the Lex tool. Develop parsers, experiment with different parser designs, and understand intermediate code representations.

#### Outcome:

- Acquire knowledge of different phases and passes of the compiler, and the use of tools like LEX, YACC.
- Design different types of compilers and parsing tables.
- Implement compilers using syntax-directed translation methods.
- Understand the target machine’s runtime environment, instruction sets, and code optimization techniques.

### Numerical Analysis

#### Objective:

Adequate exposure to learn alternative methods and analyze mathematical problems to determine suitable numerical techniques.

#### Outcome:

- Identify and interpret the fundamental concepts of polynomials and roots of equations.
- Apply numerical methods to solve algebraic and transcendental equations.
- Solve ODEs using spline interpolation and other numerical techniques.

### Basic Mathematics for PG Chemistry Students (2018-2020)

#### Objective:

This course provides basics of calculus, limits, continuity, differentiation, integration, and elementary differential equations useful for solving chemistry problems, especially in physical chemistry.

### IDE: Arithmetic and Aptitude for PG Students

#### Objective:

This course is offered to all PG students in their second year and is designed to enhance arithmetic and aptitude skills, useful for competitive examinations.

#### Details:

Course | Objective | Outcome |
---|---|---|

Cloud Computing | Provide fundamentals and essentials of Cloud Computing. | Explain core concepts and apply data center fundamentals. |

Automata Theory | Overview of formal languages and finite state machines. | Understand theoretical foundations and applications. |

Mobile Computing | Cover nomenclature and implementation of mobile technologies. | Define and evaluate mobile technologies and frameworks. |

Integral Equations | Provide important methods for integral equations. | Reduce initial value problems and solve integral equations. |

Compiler Design | Discuss phases of compilers and parser design. | Acquire knowledge of compiler tools and optimization techniques. |

Numerical Analysis | Learn alternative numerical methods for problem-solving. | Apply methods to solve algebraic and transcendental equations. |

### Faculty Details

Name | Qualification | Designation | Experience |
---|---|---|---|

P. Sarada | M.Sc, M.Phil, MCA | Assistant Professor | 18 years |

Ms. K. Arun Jyothi | M.Sc | Assistant Professor | 24 years |

Miss P.R. Jaya Sree | M.Sc | Assistant Professor | 1 year |

Ms. B. Sirisha | M.Sc Mathematics, SET Qualified | Assistant Professor | 1 year |

Dr. K. Rakmaiayya | M.Sc Mathematics, Postdoctoral in Mathematics | Assistant Professor | 4 years |

Dr. K. Vijaya Lakshmi | M.Sc, Ph.D. | Assistant Professor | 25 years |

Mrs. G. Srivani | M.Sc | Assistant Professor | 17 years |

Mr. Sudhaker | M.Sc Mathematics | Assistant Professor | 15 years |

Mr. Tirupathi | M.Sc Mathematics | Assistant Professor | 6 years |

G. Usha | MCA | Assistant Professor | 10 years |

### Highlights of the Department of Mathematics:

- ★ The Department conducted one international e-Webinar in 2019. The participants included individuals from the Philippines, Ibra, Sakhonnakhon (Thailand), Muscat, and the Al Sharqiyah region north.
- ★ One International e-Workshop was organized in 2020. Registered participants came from various Indian states and countries like Muscat, UAE, Philippines, Thailand, Dubai, Norway, New York, Dadra & Nagar Haveli, Morocco, and the UK.
- ★ The Department celebrates National Mathematics Day every year.
- ★ The department has 50 Mathematical Models that were learned and prepared by students in 2017-18. These models are exhibited and presented by students during Science Day Celebrations every year.
- ★ A course on Vedic Mathematics, which has its roots in ancient times, is offered as an Add-on course to all streams of U.G. The objectives of this course are:
- ● It is useful in competitive examinations.
- ● It motivates students of any level to learn mathematics.
- ● It helps students lose their fear of mathematics.

- ★ Paper presentation at the International Congress of Mathematicians held in Hyderabad, 2010.
- ★ One of the members has a Guinness World Record for Coir Singing (Annamayya Laksha Gala Archana).

### Activities of the Department

#### Intercollegiate Workshops Organized

#### Guest Lectures Organized:

S.No | Name of the Resource Person | Topic | Year |
---|---|---|---|

1. | Shri G Sethumadhavara Rao | What is Real Analysis | 22.12.2018 |

2. | Dr K Rakmoji Rao, Postdoctoral Research Associate from Osmania University | Numerical Techniques to all Degree final year Students | 06.03.2019 |

3. | Mrs T Vamsi Mohana from Department of Computer Science, RBVRR College | Usage of Software Tools in Software Engineering to all PG Students | 11.03.2019 |

4. | Mr R Arjun Rao, Associate Professor from the Department of Computer Science, Aurora Degree PG College | Online Webinar on Online Programming Tools Using Linux | 20.07.2021 |

5. | Mrs Swetha from Department of Mathematics, RBVRR College | A Guest Lecture in Numerical Analysis for the Students of Degree Final Year | 16.05.2022 |

6. | Mr Arjun Rao, Associate Professor, Aurora Degree and PG College | Linux Operating System Tools for PG MSc(MCS) I and II Year | 30.05.2022 |

#### Conference / Seminars / Workshops Organized / Attended:

S.No | Date | Conference/Seminar/Workshops Organized/Attended | International/National/State |
---|---|---|---|

1. | 02.03.2019 | Ms PR Jaya Shree: “Sustainability of Agriculture through Horticulture” and “Green Corner (Horticulture Show)” | One Day State Level Seminar |

2. | 28/03/2019 | Mrs P Sarada: OUTCOME BASED EDUCATION | One Day Workshop, IQAC of Bhavans Vivekananda College |

3. | 27/12/2019 & 28/12/2019 | Ms PR Jaya Shree attended a two-day workshop ABISSA 2K19 on MATLAB, Megastat, and Solver organized by the Department of Mathematics and Statistics, Avanthi Degree and PG College | – |

4. | 15.04.2020 | Mrs P Sarada attended a Webinar on “Creation of Webinars during COVID-19 Pandemic” | – |

5. | 17.05.2020 | Mrs P Sarada attended an International Webinar on Strategies and Challenges in Higher Education during COVID-19 in India with reference to the world | International |

6. | 06/06/2020 | P R Jaya Shree attended a National Level Online Quiz on Fundamentals in Information Technology – ICT Tools | National |

7. | 18/06/2020 to 21/06/2020 | P R Jaya Shree attended a four-day International e-Webinar on “Regression, Inference and Mathematical Building, Data Science and Applications on Regression with Python, Fibonometry, Importance on Mathematics” | International |

8. | 20/06/2020 | Mrs P Sarada attended a Quiz on Fundamental Concepts of Mathematics | – |

9. | 21/06/2020 | K Arun Jyothi attended a National Level Online E-Quiz | National |

10. | 25/06/2020 | P R Jaya Shree attended an E-Quiz at Keshav Memorial Institute of Commerce and Sciences | – |

11. | 26/06/2020 to 27.06.2020 | P R Jaya Shree attended “Teaching in Times of COVID-19: Computing in Sciences” at Aurora’s Degree & PG College, Chikkadpally, Hyderabad | – |

12. | 27/06/2020 to 30/06/2020 | P R Jaya Shree attended “National Level E-Quiz on Pure and Applied Mathematics” at Shrimit Indira Gandhi College | National |

13. | 30/06/2020 | P R Jaya Shree attended an Online Aptitude Test at Puratchi Thalaivar Dr. MGR Government Arts and Science College, Uthiramerur, Kanchipuram Dist, Tamil Nadu | – |

14. | 01/07/2020 | P R Jaya Shree attended a seminar on “Ordinary Differential Equations – The Natural Decomposition Approach” | – |

15. | 05/07/2020 | P R Jaya Shree attended “Blended Learning and Mathematics Relevance to Real World Applications” | – |

16. | 05/07/2020 | Ms P R Jaya Shree attended an Online COVID-19 Quiz | – |

17. | 06/07/2020 to 10/07/2020 | P R Jaya Shree attended “Mathematical Perspectives on Computational Science and Engineering” | – |

18. | 13/07/2020 to 16/07/2020 | P R Jaya Shree attended an International e-Webinar on “Vedic Mathematics” | International |

19. | 11/09/2020 to 15/09/2020 | K Arun Jyothi attended an International e-seminar on Recent Research in Mathematics | International |

20. | 26.09.2020 | Ms PR Jayashree attended a National Level Mathematics E-Quiz on Real Analysis | National |

21. | 26th and 27th June 2020 | Mrs P Sarada attended a seminar on Cryptography and Randomness, a security prerequisite | – |

22. | 29.06.2020 | Mrs P Sarada attended a seminar on Consequences of Banach and Junk Fixed Point Theorem | – |

23. | 10.07.2020 | Impact of Indian Culture on World Civilization Special Reference to Trinidad | – |

24. | 22.06.2020 to 26.06.2020 | Mrs P Sarada attended an FDP on Pioneering AI Technology: A Case Study Approach | – |

25. | 5th to 10th Sept 2020 | Mrs K Arun Jyothi attended an FDP on Real Analysis | – |

26. | 5th to 9th July 2021 | Mrs K Arun Jyothi participated in a five-day e-workshop on LaTeX | – |

27. | 10th and 11th February 2022 | Mrs K Arun Jyothi attended a two-day webinar on Role of Statistics in Industry and Research | – |

28. | 14th to 16th October 2022 | Mrs P Sarada along with students attended a three-day workshop on 8 Elements of Wellness | – |

29. | 22.12.2018 | On account of the 131st Birthday Celebrations of Srinivasa Ramanujan, a guest lecture “What is Real Analysis” was organized | – |

30. | 15/03/2019 | Conducted a One Day Seminar on “New Trends and Advances of Mathematics and Statistics in Technology” | – |

31. | 18/06/2020 & 21/06/2020 | Department of Mathematical Sciences conducted a four-day international webinar, Sameekaran | International |

32. | 13/07/2020 to 16/07/2020 | Department of Mathematics and Statistics conducted a four-day international e-workshop on Vedic Mathematics | International |

#### Field Visits

S.No | Location | Date |
---|---|---|

1. | Osmania University-Open House | 25-03-2022 |

#### Students Projects Completed

- Students Projects Completed in 2022-23: 29
- Students Projects Completed in 2021-22: 29
- Students Projects Completed in 2020-21: 36
- Students Projects Completed in 2018: 15

#### Paper Presentations

NIL

#### V. Collaboration

##### Resource Persons

S.No | Date | Resource Person | International/National/State |
---|---|---|---|

1. | 18-21 June 2020 | Dr Ramesh Kolluru, Senior Statistician Fluent Grid Pvt Ltd, Vizag, AP | International |

2. | 18-21 June 2020 | PVN Balram Murthy, Assistant Professor, Neilgogtey Institute of Technology, Hyderabad | International |

3. | 18-21 June 2020 | Prof Alex Ryba, Professor, Department of Computer Science, Queens College, City University, New York, USA | International |

4. | 18-21 June 2020 | Dr B Mallikarjun, Assistant Professor, BMS College of Engineering, Bangalore, Karnataka | International |

5. | 13-16 July 2020 | Mr Devraj, Director, Master Trainer, Alappuzha, Kerala | International |

6. | 13-16 July 2020 | Mr James Glover, Chairperson, IAVM, Academic Director and Editor for IAVM Conferences and Courses, London, UK | International |

7. | 13-16 July 2020 | Mr Naveen Bhargava, Director, Aryan Vedic Mathematics, Jaipur, Rajasthan | International |

8. | 15 July 2021 | Mrs P Sarada, HOD Mathematics – “A Strong She is A Strong We” | National |

9. | 18 December 2021 | Mrs P Sarada – National Mathematics Day Celebrations on “Life and Works of Sri Srinivasa Ramanujan” | National |

10. | 30 June 2022 | Mrs K Arun Jyothi – “Solutions of System of Linear Equations on Geometrical and Vector Methods” | National |

11. | 28 February 2022 | National Science Day conducted by AMSASCW in collaboration with Telangana Citizens Council | State |

12. | 28 February 2023 | National Science Day conducted by all Science departments in collaboration with LEE Shreyus Foundation | State |

##### MoUs

S.No | MoU with | Date of Signing MoU | Activities Taken Up | Date of Activity |
---|---|---|---|---|

1. | Siksha Sanskruthi Uthanyas | 10-01-2018 (renewed on 26-07-2024 for 5 years) | Vedic Mathematics as a value-added course | Every year certificate course in semester-I |

2. | Siksha Sanskruthi Uthanyas | 10-01-2018 (renewed on 26-07-2024 for 5 years) | Conducted One Day Seminar on “New Trends and Advances of Mathematics and Statistics in Technology” | 15-03-2019 |

### Publications

S.No | Year | Paper Title | Journal | ISSN/ISBN No | Impact Factor |
---|---|---|---|---|---|

1. | 2019 | Natural Language Processing and Recent Development in NLP | Pramana Research Journal Volume-9 Issue-6 | ISSN NO: 2249-2976 | Impact factor: 6.2 |

2. | 2019 | Natural Language Processing and Recent Development in NLP | Pramana Research Journal Volume-9 Issue-6 | ISSN NO: 2249-2976 | Impact factor: 6.2 |

3. | 2020 | An Analysis on Key Problems of Software Risk Management | IWR Aug 2022 to Jan 2023 | 2349-1027 | |

4. | 2021 | An Algorithm for Sniffer Detection Using Mobile Agents in Network Security | Universal Research Analysis Sept 2021 to Feb 2022 edition | 2229-4406 | IF: 6.10 |

5. | 2022 | Boundary Value Problems for Nonlinear Fourth Order Differential Equations | Universal Research Analysis March 2022 to August 2022 | 2229-4406 | |

6. | 2022 | Artificial Intelligence Role in Higher Education | Three Day International Conference on Higher Education and Sustainable Development Volume-1 | ISBN No: 978-93-95944-56-4 | |

7. | 2022 | Artificial Intelligence Role in Higher Education | Three Day International Conference on Higher Education and Sustainable Development Volume-1 | ISBN No: 978-93-95944-56-4 | |

8. | 2022 | Advances in Biometrics: Towards Secure World | Journal of Management and Entrepreneurship | 2348-7976 | Impact factor: 6.30 |

9. | 2021 | Srinivasa Ramanujan as an Indian Mathematician | Universal Research Analysis Sept 2021-Feb 2022 | 2229-4406 | IF: 6.10 |