Department of Mathematics(PG)

Department of Mathematics

Department Profile PG

About the Department

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:

Faculty Details

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:

Conference / Seminars / Workshops Organized / Attended:

Field Visits

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

MoUs

Publications