Mathematics

School of Physical & Mathematical Sciences

Structure and Course Contents of M.A./M.Sc. Mathematics Programme (Batch 2024 & onwards)

[Click above to view the detailed structure and course contents]

Programme

outcome

After the completion of this programme, students shall be able;

• To apply mathematical tools and techniques in all fields of learning including research and its extension.
• To Innovate, invent and solve complex mathematical problems using the knowledge of pure and applied mathematics.
• To provide a well-rounded mathematical education that emphasizes theoretical understanding, practical application, and professional development.

Programme Specific Outcomes

Advanced Mathematical Knowledge:

• Students will develop a deep understanding of core areas of mathematics such as Algebra, Analysis, Topology, Geometry, Number Theory, and Probability.
• Students will be able to apply advanced mathematical techniques to solve complex problems in pure and applied mathematics.

Research and Analytical Skills:

• Students will acquire the ability to conduct independent research, analyze mathematical problems, and develop original solutions.
• They will be skilled in using advanced mathematical tools and techniques to formulate hypotheses, test theories, and prove conjectures.

Problem-Solving Proficiency:

• Students will develop advanced problem-solving skills, applying theoretical concepts to real-world problems.
• They will be able to approach mathematical problems systematically and solve them using logical reasoning and advanced computational methods.

Application of Mathematical Tools:

• Students will be proficient in using mathematical software and programming languages for solving mathematical problems, simulations, and data analysis.
• They will be able to apply mathematical models to problems in fields such as physics, engineering, computer science, economics, etc.

Communication and Collaboration:

• Students will be able to effectively communicate mathematical concepts, both in written and oral forms, to a variety of audiences, including peers, faculty, and professionals.
• They will be capable of working collaboratively in mathematical teams or interdisciplinary settings

Critical Thinking and Innovation:

• Students will develop critical thinking skills to assess, critique, and build upon existing mathematical theories.
• They will foster innovative approaches to solving both classical and novel problems in mathematics.

Ethical and Professional Conduct:

• Students will demonstrate professional and ethical behavior in conducting research and applying mathematical methods.
• They will appreciate the social, ethical, and cultural implications of their work and strive for responsible use of mathematical techniques.

Preparation for Higher Studies or Professional Careers:

• Students will be prepared for further study in mathematics or related fields, such as pursuing a Ph.D. or other research opportunities.
• They will also be equipped with the knowledge and skills needed for careers in education, industry, finance, data science, and other mathematics-related professions.

Learning

Outcome

The following are the learning outcomes of the programme:

• Understanding of the fundamental axioms in mathematics and capability of developing ideas based on them.
• Inculcate mathematical reasoning.
• Prepare and motivate students for research studies in mathematics and related fields.
• Provide knowledge of a wide range of mathematical techniques and application of mathematical methods/tools in other scientific and engineering domains.
• Provide advanced knowledge on topics in pure mathematics, empowering the students to pursue higher degrees at reputed academic institutions.
• Good understanding of Analysis, algebra, differential equations, discrete mathematics, mathematical biology, number theory etc..
• Nurture problem solving skills, thinking, creativity through assignments, project work.
• Assist students in preparing for competitive exams e.g. NET, SET, GATE, etc.

Board Members

Minutes of the Meeting

Date of Meeting

New Courses Added

[Committee] 

[Minutes]

October 4, 2023

• Computational Mathematics (24108DCE - 4Credits)
• Python for Mathematics (24307DCE - 4 Credits)
• Project at 4th Semester (24409DCE - 4 Credits)
• Applied Differential Equations (24004GE- 2 Credits)

[Click here for the approved Syllabus]

Course Work Syllabus for Integrated PhD Scholars (2023 & Onwards)

Programme outcome

By the end of the coursework phase:

• Students should be well-equipped with both the theoretical knowledge and practical research skills necessary for independent and original research.
• The coursework prepares them for writing a thesis, collaborating with other researchers, teaching, and contributing to the global mathematical community.
• To lay a solid foundation for students before they transition into the research phase of their PhD, where the focus will shift entirely to original research and the completion of their doctoral thesis.

Programme Specific Outcomes

Advanced Knowledge of Core Mathematical Areas:

• Students will gain an in-depth understanding of advanced topics in pure and applied mathematics, including but not limited to Algebra, Analysis, Topology, Geometry, Functional Analysis, and Mathematical Logic.
• They will develop expertise in specialized areas of mathematics that align with their research interests, ensuring a strong foundation for their dissertation work.

Research Methodology and Techniques:

• Students will become proficient in various mathematical research methodologies, including rigorous proofs, model formulation, and problem-solving strategies.
• They will be familiar with modern research tools, mathematical software, and computational techniques, allowing them to tackle complex research problems effectively.

Independent Research Skills:

• Students will develop the ability to work independently on advanced mathematical problems and generate original research questions.
• They will be equipped to formulate hypotheses, structure mathematical arguments, and develop research papers or articles for publication.

Critical Analysis of Mathematical Literature:

• Students will be trained in critically analyzing and interpreting existing research in mathematics, identifying gaps, and proposing new avenues for exploration.
• They will demonstrate the ability to conduct comprehensive literature reviews, synthesizing information from various sources to advance their research.

Advanced Problem Solving and Application:

• Students will develop advanced problem-solving abilities, applying theoretical mathematics to practical problems in various fields, such as physics, computer science, engineering, and finance.
• They will be able to devise novel solutions to complex mathematical problems and contribute to the development of new mathematical models or methods.

Communication and Presentation Skills:

• Students will be skilled in effectively communicating complex mathematical ideas and research findings to a range of audiences, including academic peers, researchers, and students.
• They will develop strong writing and presentation skills, ensuring that their research is published in reputable journals and presented at national/international conferences.

Collaboration and Interdisciplinary Work:

• Students will be capable of collaborating with other researchers in interdisciplinary teams, applying mathematical principles to solve real-world problems.
• They will also be prepared to engage with mathematicians from different subfields, encouraging cross-pollination of ideas and approaches.

Ethics in Research:

• Students will be aware of the ethical considerations in mathematical research, including the importance of integrity, avoiding plagiarism, and giving proper credit to others' work.
• They will adhere to ethical guidelines in conducting and presenting their research.

Teaching and Mentoring Skills:

• Students will be trained to teach and mentor undergraduate or graduate students in mathematics, helping to communicate complex concepts in accessible ways.
• They will be prepared to take on academic roles, fostering future generations of mathematicians.

Preparation for Thesis Work:

• The coursework phase will equip students with the necessary skills and knowledge to undertake independent dissertation research. They will be ready to develop an original, significant, and well-documented thesis that contributes to the advancement of mathematical knowledge.

Innovation and Development in Mathematical Theories:

• Students will be encouraged to develop new theories, methods, or models that can push the boundaries of existing mathematical knowledge.
• They will contribute to the innovation of mathematical thought and be ready to engage with the global mathematical community to address open problems.

Learning 

Outcome

The learning outcomes of the programme are:

• The scholars shall be able to understand research design, research ethics, plagrism and can identify their research problems.
• The scholars shall be able to develop a confidence in themselves and can work indepently.
• To get updated through literature survey and can understand emerging areas of research of their fields.
• Can prepare research synopsis, research proposal, learn scientific documentation and software’s that can be used to analyze and simulate theirresearch work.

Board Members

Minutes of the Meeting

Date of Meeting

New Courses Added

[DRC Members]

[Minutes]

September 9, 2023

• New topics like C programming and MATLAB Software were incorporated.
• Scientific Documentation like LaTeX has been added to the syllabus.
• Research ethics and emerging topics of mathematics.

[Click below for the approved syllabi]

Course Work Syllabus of Integrated PhD (Paper-1)]

&

[Approved DRC Minutes]

Paper - II and Paper III Syllabus, (Mr. Naveed Ahmad Rather & Mr. Zuhaib Mushtaq) -Batch 2024

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Paper - II and Paper III Syllabus, (Ms. Ulfat Bashir) - Batch 2024

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Recent Advances & Recent Topics (Graph theory & Mathematical Biology, Papers-II & III), Batch 2023