Mathematics
Department of Mathematical Sciences
Faculty of Science
The Department of Mathematics supports teaching and research across pure and applied mathematics. This website provides information about the department, its degree programs, curricula, faculty expertise, research areas, facilities and departmental announcements.
The
Department of Mathematics at the University of Karachi is part of the Faculty
of Science. Department of mathematics was established in 1956 under its
founding Chairman, Prof. Dr. Suleman Kerawala.
The
department’s teaching and research cover mathematical theory and applications,
including areas connected with analysis, differential equations, numerical
methods, mathematical modelling, computing and statistics.
The
department encourages students to develop mathematical reasoning, analytical
thinking and problem-solving skills that can be applied in academic,
scientific, technological and professional settings.
Introduction
Chairman: Prof. Dr. Najeeb Alam Khan.
The University of Karachi holds a unique position in the country's educational system. Its prestigious research and teaching institution meets the commitment to spreading knowledge through its programs. The research activities comprise original investigations, discussions, lectures, and teaching at various levels. We are deeply committed to supreme research in mathematics, and the scientific excellence of our faculty is well recognized.
Department of Mathematics was established in 1956, and Prof. Dr. Suleman Kerawala was the founder Chairman. It is one of the largest departments of the Faculty of Science, having a well-equipped auditorium, E-laboratory with free internet and E-Library.
We offer academic challenges and support to our students to help them succeed. We encourage them to develop problem-solving abilities to excel in mathematics. We collaborate with local community organizations, professional associations, other campus entities, and individuals. We promote the belief that mathematics holds an essential place in the history of humanity and it is valuable in the future of all disciplines.
We offer BS in pure, applied, financial, and computational mathematics. The Bachelor programs lead to the Master of Arts, Master of Science, Master and Doctor of Philosophy degrees with a major in Mathematics. In these programs, we cover a variety of subjects related to Mathematics, such as: Programming, business management, actuarial sciences, data sciences, accounting, and engineering etc.
The department is well-known for its long history, strength, and rigorous scholarships. Since its establishment, many outstanding mathematicians have served here. It has always had a leading status at home. It has been well-known abroad for its academic influences, especially in Non-Linear Mechanics, Dynamical Systems, Convex Analysis, Numerical Integration, Differential equations, Mathematical Inequalities, Mathematical and Statistical Modeling in Climate Dynamics, and Scientific and Engineering Computing.
Career Opportunities
The most common career paths of graduating students fall into some broad categories. The Department has designed the concentrations (and course requirements for each concentration) to help students prepare for a career (not limited to) in one of these main categories:
Teaching/Research related Fields at SUPARCO and Aviation.
Actuarial science.
Data science.
Business Analyst.
Information technology and computing.
Business, management, consulting.
Teaching / Research projects related to interdisciplinary fields such as: astronomy, climate related studies, robotics and other computing fields etc.
Departmental Web
Faculty
Professor
Dr. Najeeb Alam Khan
Dr. Muhammad Jamil
Associate Professors
Dr. Muhammad Ayaz Profile
Dr. Asif Raza Khan
Dr. Saqib ur Rehman
Dr. Asmat Ara
Dr. Aurangzaib
Assistant Professors
Mr. Waseem Ahmed Khan
Dr. Syeda Sadia Zia
Mr. Waseem Ahmad Ansari
Dr. Saba Naz
Dr. Tanveer Ahmed Siddiqi
Dr. Muhammad Imtiaz
Dr. Syed Inayatullah
Dr. Syed Ahmad Hassan
Dr. Fozia Hanif
Assistant Professors (T)
Dr. Hina Zaheer
Dr. Asma Rani
Dr. Noor Fatima Siddiqui
Dr. Samreen Ahmad
Lecturers
Dr. Shahid
Dr. Asif Iqbal
Ms. Hafsa Athar Jafree
Dr. Ateeq Razzak (On Leave)
Mr. Salman Safdar (Study Leave)
Dr. Sumayyah Saadi (On Leave)
Mr. Muhammad Usman Qureshi
Ms. Wajiha Riaz
Ms. Aghzia Akram
Dr. Mehwish Shafi Khan
Programs
Program Details and Eligibility Criteria
| S.No. | Program | Eligibility Criteria |
| 1 | BS Mathematics | Applied
mathematics Pure
mathematics Eligibility: pre- engineering, computer science and commerce. |
| 2 | BS Financial Mathematics | Confirm current intake, approved eligibility criteria and the latest approved scheme of studies. |
| 3 | BS Computational Mathematics | |
| 4 | BS Third Year | Eligibility: BSC, B.A with Math, B.com. |
| 5 | M.Phil. / Ph.D. | Eligibility: M.sc ,B.S in math / M.Phil., M.S in Math’s |
| 6 | M.S. Computational Mathematics / M.S. Financial Mathematics |
BS Program
|
Name of Academic
Program |
BS Mathematics |
|
Number of Seats |
100 |
|
Pre-Requisite
(Eligibility of Program) |
|
|
|
OPEN MERIT BASE |
|
|
Intermediate
(Science / Arts) with Mathematics at least 50% Marks |
|
Name of Academic
Program |
BS 3rd Year |
|
Number of Seats |
80 |
|
Pre-Requisite
(Eligibility of Program) |
|
|
|
OPEN MERIT BASE |
|
|
B. A. / B. Sc.
(with Mathematics) B. E. / B. C. S., Graduation with Diploma in Mathematics
from University of Karachi |
- Academic Program
is already approved by Board of Studies, Board of Faculty of Science and
Academic Council
|
Name of Academic
Program |
BS Financial
Mathematics |
|
Number of Seats |
50 |
|
Pre-Requisite
(Eligibility of Program) |
|
|
|
OPEN MERIT BASE |
|
|
Intermediate
(Science / Arts) with Mathematics at least 50% Marks |
|
Name of Academic
Program |
BS Computational
Mathematics (First Year) |
|
Number of Seats |
50 |
|
Pre-Requisite
(Eligibility of Program) |
|
|
|
OPEN MERIT BASE |
|
|
Intermediate
(Science / Arts) with Mathematics at least 50% Marks |
-
Recommended by Board of Studies (Minor Changes in Admission Eligibility /
Criteria for BS Financial Mathematics, BS Computational Mathematics &
Number of Seats) September 12, 2022, Approved by Board of Faculty of Science on
September 27, 2022, Approved by Academic Council on April 10, 2023
-
Subsidiary Combinations (Approved by Board of Studies) for BS Computational
Mathematics
**
01. Statistics, Physics
04.
Statistics, ISST Institute of Space Science Technology
Eligibility Criteria (Evening Program)
The following eligibility criteria were provided by the Department of Mathematics for Admission 2026 (Evening Program).
|
Information about BS Program |
BS Mathematics (First Year) |
|
Number of Seats |
100 |
|
Pre-Requisite (Eligibility of Program) |
OPEN MERIT BASE |
|
Eligibility |
Intermediate (Science / Arts) with Mathematics at least
50% Marks |
|
Additional eligibility |
Intermediate (Pre-Medical Group) at least 50% Marks, with
Certificate Course in Mathematics |
|
Approval status |
Copy of Approval of the Degree Program. This Academic
Program is already approved by Board of Studies, Board of Faculty of Science
and Academic Council. |
|
Information about BS Program |
BS Financial Mathematics (First Year) |
|
Number of Seats |
50 |
|
Pre-Requisite (Eligibility of Program) |
OPEN MERIT BASE |
|
Eligibility |
Intermediate (Science / Arts) with Mathematics at least
50% Marks |
|
Approval / recommendation |
Recommended by Board of Studies (Minor Changes in
Admission Eligibility / Criteria for BS Financial Mathematics & Number of
Seats) September 12, 2022, Approved by Board of Faculty of Science on
September 27, 2022, Approved by Academic Council on April 10, 2023. |
|
Information about BS Program |
BS Computational Mathematics (First Year) |
|
Number of Seats |
50 |
|
Pre-Requisite (Eligibility of Program) |
OPEN MERIT BASE |
|
Eligibility |
Intermediate (Science / Arts) with Mathematics at least
50% Marks |
|
Approval / recommendation |
Recommended by Board of Studies (Minor Changes in
Admission Eligibility / Criteria for BS Financial Mathematics, BS
Computational Mathematics & Number of Seats) September 12, 2022, Approved
by Board of Faculty of Science on September 27, 2022, Approved by Academic
Council on April 10, 2023. |
|
Subsidiary Combinations (Approved by Board of Studies) |
1. Statistics, Statistics 2. Statistics, ISST
Institute of Space Science Technology |
Courses
| Course Code | Course Title | Credit Hours (Theory) | Credit Hours (Practical) |
| B. Sc. (Hons) First Years | |||
| Semester - I | |||
| 300.1 (Comp.) | Pakistan Studies (Compulsory) | 3 | 0 |
| 301 (H) | Algebra | 3 | 0 |
| Semester - II | |||
| 300.2 (Comp.) | English (Compulsory) | 3 | 0 |
| 302 (H) | Calculus | 3 | 0 |
| Semester - III | |||
| 400.1 (Comp.) | Islamic Studies (Compulsory) | 3 | 0 |
| 401 (H) | Geometry | 3 | 0 |
| 403 (H) | Data Processing & Programming-I | 2 | 1 |
| Semester - IV | |||
| 400.2 (Comp.) | Urdu (Compulsory) | 3 | 0 |
| 402 (H) | Mechanics | 3 | 0 |
| 404 (H) | Data Processing & Programming-II | 2 | 1 |
| Semester - V | |||
| 501 | Analysis - I | 3 | 0 |
| 503 | Algebra - I | 3 | 0 |
| 505 | Numerical Analysis - I | 2 | 1 |
| 507 | Applicable Differential Geometry - I | 3 | 0 |
| 509 | Methods of Mathematical Physics - I | 3 | 0 |
| Semester - VI | |||
| 502 | Analysis - II | 3 | 0 |
| 504 | Algebra - II | 3 | 0 |
| 506 | Numerical Analysis - II | 2 | 1 |
| 508 | Applicable Differential Geometry - II | 3 | 0 |
| 510 | Methods of Mathematical Physics - II | 3 | 0 |
| Semester - VII | |||
| 601 | Abstract Algebra | 3 | 0 |
| 603 | Commutative Rings | 3 | 0 |
| 605 | Measure Theory – I | 3 | 0 |
| 609 | Bio Mathematics – I | 3 | 0 |
| 611 | Functional Analysis – I | 3 | 0 |
| 615 | Summability Theory – I | 3 | 0 |
| 621 | Algebraic Topology – I | 3 | 0 |
| 631 | Numerical Analysis – I | 2 | 1 |
| 633 | Mathematical Statistics – I | 3 | 0 |
| 637 | Applied Algebra – I | 2 | 1 |
| 643 | Complex Analysis – I | 3 | 0 |
| 645 | Operations Research – I | 2 | 1 |
| 647 | Projective Geometry – I | 3 | 0 |
| 649 | Stochastic Processes | 3 | 0 |
| 651 | Classical Mechanics – I | 3 | 0 |
| 653 | Integral Equations | 3 | 0 |
| 655 | Fluid Dynamics – I | 2 | 1 |
| 657 | Nonlinear Systems – I | 3 | 0 |
| 661 | Electromagnetics - I | 3 | 0 |
| 663 | Software Engineering | 2 | 1 |
| 665 | Quantum Mechanics - I | 3 | 0 |
| 671 | Relativity - I | 3 | 0 |
| 685 | Astronomy - I | 3 | 0 |
| Semester - VIII | |||
| 602 | Glaois Theory and Its Applications | 3 | 0 |
| 604 | Field Theory | 3 | 0 |
| 606 | Measure Theory – II | 3 | 0 |
| 610 | Bio Mathematics – II | 3 | 0 |
| 612 | Functional Analysis – II | 3 | 0 |
| 616 | Summability Theory – II | 3 | 0 |
| 622 | Algebraic Topology – II | 3 | 0 |
| 632 | Numerical Analysis – II | 2 | 1 |
| 634 | Mathematical Statistics – II | 3 | 0 |
| 638 | Applied Algebra – II | 2 | 1 |
| 644 | Complex Variable – II | 3 | 0 |
| 646 | Operations Research – II | 2 | 1 |
| 648 | Projective Geometry – II | 3 | 0 |
| 650 | Renewal Processes & Theory of Queues | 3 | 0 |
| 652 | Classical Mechanics – II | 3 | 0 |
| 654 | Partial Differential Equations | 3 | 0 |
| 656 | Fluid Dynamics – II | 2 | 1 |
| 658 | Nonlinear Systems – II | 3 | 0 |
| 662 | Electromagnetics – II | 3 | 0 |
| 664 | Software Programming & Analysis | 2 | 1 |
| 666 | Quantum Mechanics - II | 3 | 0 |
| 672 | Relativity - II | 3 | 0 |
| 686 | Astronomy - II | 3 | 0 |
| Four Year Degree Program BS (Financial Mathematics) | |||
| Semester - I | |||
| FM-300.1 | Pakistan Studies (Compulsory) | 3 | 0 |
| FM-301 | Pre-Calculus | 3 | 0 |
| FM-303 | Introductory Statistics for Business | 2 | 1 |
| FM-305 | Microeconomics | 3 | 0 |
| FM-307 | Business Mathematics | 3 | 0 |
| Semester - II | |||
| FM-300.2 | English (Compulsory) | 3 | 0 |
| FM-302 | Calculus with Applications | 3 | 0 |
| FM-304 | Multivariate Statistical Analysis | 2 | 1 |
| FM-306 | Macroeconomics | 3 | 0 |
| FM-308 | Introduction to Business Finance | 3 | 0 |
| Semester - III | |||
| FM-400.1 | Islamic Studies (Compulsory) | 3 | 0 |
| FM-401 | Mathematical Methods | 3 | 0 |
| FM-403 | Inferential Statistics for Business | 2 | 1 |
| FM-405 | Money, Banking and Trade | 3 | 0 |
| FM-407 | Financial Accounting-I | 3 | 0 |
| FM-409 | Programming Language-I | 2 | 1 |
| Semester - IV | |||
| FM-400.2 | Urdu (Compulsory) | 3 | 0 |
| FM-402 | Multivariate Calculus and Geometry | 3 | 0 |
| FM-404 | Quantitative Methods in Business | 2 | 1 |
| FM-406 | Pakistan Economics | 3 | 0 |
| FM-408 | Financial Accounting-II | 3 | 0 |
| FM-410 | Programming Language-II | 2 | 1 |
| Semester - V | |||
| FM-501 | Real and Complex Analysis | 3 | 0 |
| FM-503 | Linear Algebra with Applications | 3 | 0 |
| FM-505 | Numerical Analysis - I | 3 | 0 |
| FM-507 | Differential Equations-I | 3 | 0 |
| FM-509 | Cost and Management Accounting-I | 3 | 0 |
| Semester - VI | |||
| FM-502 | Actuarial Mathematics | 3 | 0 |
| FM-504 | Discrete Mathematics | 3 | 0 |
| FM-506 | Numerical Analysis – II | 3 | 0 |
| FM-508 | Differential Equations-II | 3 | 0 |
| FM-510 | Cost and Management Accounting-II | 3 | 0 |
| Semester - VII | |||
| FM-601 | Operations Research | 2 | 1 |
| FM-603 | Financial Derivatives | 3 | 0 |
| FM-605 | Stochastic Processes | 3 | 0 |
| Optional-I | |||
| Optional-I | |||
| Optional Courses For Semester - VII | |||
| FM-607 | Corporate Finance | 3 | 0 |
| FM-609 | Management Information System | 3 | 0 |
| FM-611 | Discrete time Modelling and Derivative Security | 3 | 0 |
| FM-613 | Principles of Risk | 3 | 0 |
| FM-615 | Equities Foreign Exchange and Commodities Modelling | 3 | 0 |
| FM-617 | Financial Computer Simulation-I | 2 | 1 |
| FM-619 | Analysis of Financial Time Series | 3 | 0 |
| Semester - VIII | |||
| FM-602 | Analysis of Financial Report Writing | 3 | 0 |
| FM-604 | Portfolio theory and Management | 3 | 0 |
| FM-606 | Stochastic Calculus | 3 | 0 |
| Optional-II | |||
| Optional-II | |||
| Optional Courses For Semester - VIII | |||
| FM-608 | Games, Markets and Information | 3 | 0 |
| FM-610 | Financial Modelling and Simulation | 3 | 0 |
| FM-612 | Life Insurance and Institutional Investment | 3 | 0 |
| FM-614 | Global Financial Market | 3 | 0 |
| FM-616 | Interest Rate and Credit Modelling | 3 | 0 |
| FM-618 | Financial Computer Simulation-II | 2 | 1 |
| Four Year Degree Program BS (Computational Mathematics) | |||
| Semester - I | |||
| CM-300.1 | Pakistan Studies (Compulsory) | 3 | 0 |
| CM-301 | Algebra | 3 | 0 |
| CM-303 | Number Theory | 3 | 0 |
| STA 301 | Subsidiary-I (Statistics) | 2 | 1 |
| Phy 301 / SST 301 | Subsidiary-II (Physics / ISST) | 2 | 1 |
| Semester - II | |||
| CM-300.2 | English (Compulsory) | 3 | 0 |
| CM-302 | Calculus | 3 | 0 |
| CM-304 | Discrete Mathematics | 3 | 0 |
| STA 302 | Subsidiary-I (Statistics) | 2 | 1 |
| Phy 302 / SST 302 | Subsidiary-II (Physics / ISST) | 2 | 1 |
| Semester - III | |||
| CM-400.1 | Islamic Studies (Compulsory) | 3 | 0 |
| CM-401 | Multivariable Calculus and Geometry | 3 | 0 |
| CM-403 | Tensors and Fourier Analysis | 3 | 0 |
| CM-405 | Functional Biology-I | 3 | 0 |
| STA 401 | Subsidiary-I (Statistics) | 2 | 1 |
| Phy 401 / SST 401 | Subsidiary-II (Physics / ISST) | 2 | 1 |
| Semester - IV | |||
| CM-400.2 | Urdu (Compulsory) | 3 | 0 |
| CM-402 | Mechanics | 3 | 0 |
| CM-404 | Set Topology | 3 | 0 |
| CM-406 | Functional Biology-II | 3 | 0 |
| STA 402 | Subsidiary-I (Statistics) | 2 | 1 |
| Phy 402 / SST 402 | Subsidiary-II (Physics / ISST) | 2 | 1 |
| Semester - V | |||
| CM-501 | Mathematical Analysis | 3 | 0 |
| CM-503 | Linear Algebra | 3 | 0 |
| CM-505 | Differential Equations | 3 | 0 |
| CM-507 | Fluid Dynamics-I | 3 | 0 |
| CM-509 | Programming Language-I | 2 | 1 |
| Semester - VI | |||
| CM-502 | Functional Analysis | 3 | 0 |
| CM-504 | Probability & Statistics | 3 | 0 |
| CM-506 | Numerical Analysis | 3 | 0 |
| CM-508 | Fluid Dynamics-II | 3 | 0 |
| CM-510 | Programming Language-II | 2 | 1 |
| Semester - VII | |||
| CM-601 | Advanced Partial Differential Equations | 3 | 0 |
| CM-603 | Advanced Numerical Analysis | 3 | 0 |
| CM-605 | Modelling & Simulation | 3 | 0 |
| CM-607 | Software Applications-I | 2 | 1 |
| Optional-I Courses For Semester - VII | |||
| CM-609 | Perturbation Methods-I | 3 | 0 |
| CM-611 | Fractional Calculus-I | 3 | 0 |
| CM-613 | Boundary Layer Theory-I | 3 | 0 |
| CM-615 | Fuzzy Mathematics-I | 3 | 0 |
| CM-617 | Graph Theory & Applications-I | 2 | 1 |
| CM-619 | Bioinformatics | 2 | 1 |
| CM-621 | Computational Finance | 2 | 1 |
| CM-623 | Operations Research-I | 2 | 1 |
| CM-625 | Computational Fluid Dynamics-I | 2 | 1 |
| CM-627 | Numerical Linear Algebra-I | 2 | 1 |
| Semester- VIII | |||
| CM-602 | Integral Equations | 3 | 0 |
| CM-604 | Stochastic Process | 3 | 0 |
| CM-606 | Wavelets | 3 | 0 |
| CM-608 | Software Applications-II | 2 | 1 |
| Optional-II Courses For Semester - VII | |||
| CM-610 | Perturbation Methods-II | 3 | 0 |
| CM-612 | Fractional Calculus-II | 3 | 0 |
| CM-614 | Boundary Layer Theory-II | 3 | 0 |
| CM-616 | Fuzzy Mathematics-II | 3 | 0 |
| CM-618 | Graph Theory & Applications-I | 2 | 1 |
| CM-620 | Cryptography | 2 | 1 |
| CM-622 | Data Mining | 2 | 1 |
| CM-624 | Operations Research-II | 2 | 1 |
| CM-626 | Computational Fluid Dynamics-II | 2 | 1 |
| CM-628 | Numerical Linear Algebra-I | 2 | 1 |
| Four Year BS Degree Program | |||
| Semester - I | |||
| M-301 | Algebra | 3 | 0 |
| M-303 | Mathematical Logic and Number Theory | 3 | 0 |
| Semester - II | |||
| M-302 | Calculus | 3 | 0 |
| M-304 | Introduction to Computer Programming | 2 | 1 |
| Semester - III | |||
| M-401 | Multivariable Calculus and Geometry | 3 | 0 |
| M-403 | Discrete Mathematics and Graphs Theory | 3 | 0 |
| Semester - III | |||
| M-402 | Mechanics | 3 | 0 |
| M-404 | Topology | 3 | 0 |
| Semester - VI | |||
| M-501 | Real Analysis | 3 | 0 |
| M-503 | Linear Algebra | 3 | 0 |
| M-505 | Numerical Analysis-I | 2 | 1 |
| M-507 | Differential Geometry | 3 | 0 |
| M-509 | Methods of Mathematical Physics | 3 | 0 |
| Semester - VI | |||
| M-502 | Complex Analysis | 3 | 0 |
| M-504 | Abstract Algebra | 3 | 0 |
| M-506 | Numerical Analysis-II | 2 | 1 |
| M-508 | Functional Analysis-I | 3 | 0 |
| M-510 | Integral Transforms and Special Functions | 3 | 0 |
| Semester - VII (Pure Mathematics Courses) | |||
| M-601 | Theory of Rings & Modules | 3 | 0 |
| M-605 | Measure Theory-I | 3 | 0 |
| M-611 | Functional Analysis-II | 3 | 0 |
| Optional - I | |||
| Optional - II | |||
| Semester - VIII (Pure Mathematics Courses) | |||
| M-602 | Galois Theory and its Applications | 3 | 0 |
| M-606 | Measure Theory-II | 3 | 0 |
| M-612 | Algebraic Topology | 3 | 0 |
| Optional - I | |||
| Optional - II | |||
| Semester - VII (Applied Mathematics Courses) | |||
| M-651 | Classical Mechanics-I | 3 | 0 |
| M-655 | Fluid Dynamics-I | 3 | 0 |
| M-653 | Tensor Analysis | 3 | 0 |
| Optional - I | |||
| Optional - II | |||
| Semester - VIII (Applied Mathematics Courses) | |||
| M-651 | Classical Mechanics-II | 3 | 0 |
| M-655 | Fluid Dynamics-II | 3 | 0 |
| M-653 | Partial Differential Equations | 3 | 0 |
| Optional - I | |||
| Optional - II | |||
| Semester - VII (Optional Courses)(Only for Pure Mathematics Students) | |||
| M-615 | Summability Theory-I | 3 | 0 |
| M-647 | Projective Geometry-I | 3 | 0 |
| Semester - VII (Optional Courses)(Only for Applied Mathematics Students) | |||
| M-661 | Electromagnetics-I | 3 | 0 |
| M-671 | Relativity-I | 3 | 0 |
| M-685 | Astronomy-I | 3 | 0 |
| Semester - VII (Optional Courses)(Only for Applied & Pure Mathematics Students) | |||
| M-631 | Numerical Methods | 3 | 0 |
| M-633 | Mathematical Statistics-I | 3 | 0 |
| M-637 | Applied Algebra-I | 2 | 1 |
| M-645 | Operations Research-I | 3 | 0 |
| M-649 | Stochastic Processes | 3 | 0 |
| M-657 | Nonlinear Systems-I | 3 | 0 |
| M-687 | Advance Statistics-I | 3 | 0 |
| M-689 | Mathematical Finance-I | 3 | 0 |
| M-691 | Biological Modeling | 3 | 0 |
| M-693 | Optimization Theory | 3 | 0 |
| M-695 | Computational Number Theory | 3 | 0 |
| M-697 | Actuarial Mathematics-I | 3 | 0 |
| Semester - VIII (Optional Courses)(Only for Pure Mathematics Students) | |||
| M-616 | Summability Theory-II | 3 | 0 |
| M-648 | Projective Geometry-II | 3 | 0 |
| Semester - VIII (Optional Courses)(Only for Applied Mathematics Students) | |||
| M-662 | Electromagnetics-II | 3 | 0 |
| M-672 | Relativity-II | 3 | 0 |
| M-686 | Astronomy-II | 3 | 0 |
| Semester - VIII (Optional Courses)(Only for Applied & Pure Mathematics Students) | |||
| M-632 | Integral Equations | 3 | 0 |
| M-634 | Mathematical Statistics-II | 3 | 0 |
| M-638 | Applied Algebra-II | 2 | 1 |
| M-646 | Operations Research-II | 3 | 0 |
| M-650 | Stochastic Processes | 3 | 0 |
| M-658 | Nonlinear Systems-II | 3 | 0 |
| M-688 | Advance Statistics-II | 3 | 0 |
| M-690 | Mathematical Finance-II | 3 | 0 |
| M-692 | Discrete Maps | 3 | 0 |
| M-694 | Machine Learning & Data Science | 2 | 1 |
| M-696 | Scientific Computing | 2 | 1 |
| M-698 | Actuarial Mathematics-II | 3 | 0 |
| Note: 01.Courses M-301, M-302, M-401, M-402 for Subsidiary Students. | |||
| 02. Courses M-633 may be opted by those students who studied B.A./B. Sc. Without minor Statistics, however M-687, M-688 be opted by those students who studied B.A./B. Sc. With minor Statistics. | |||
| 03. The Optional Course M-691 to M-696 are independent Courses. | |||
| 04. A Student who transfer from any department to MathematicsDepartment (as a Major Subject) must Pass the courses M-303 and m-304 in second / third year. | |||
| Applied Mathematics M. Phil Program | |||
| Semester – I | |||
| MTHN-701 | Differential Geometric Techniques-I | 3 | 0 |
| MTHN-703 | Differential Equations-I | 3 | 0 |
| MTHN-705 | Group Theory & Symmetries | 3 | 0 |
| MTHN-707 | Lie Algebra-I | 3 | 0 |
| MTHN-709 | Topics in Fluid Dynamics-I | 3 | 0 |
| MTHN-711 | Classical Electrodynamics-I | 3 | 0 |
| MTHN-713 | Topics in Relativity-I | 3 | 0 |
| MTHN-715 | Some Exact Solutions Of Einstein’s Vacuum Field Equations | 3 | 0 |
| MTHN-717 | Continuum Mechanics-I | 3 | 0 |
| MTHN-719 | Classical Field Theory-I | 3 | 0 |
| MTHN-721 | Topics in Quantum Mechanics-I | 3 | 0 |
| MTHN-723 | Quantum Field Theory-I | 3 | 0 |
| MTHN-725 | Representation Theory-I | 3 | 0 |
| MTHN-727 | Gauge Theory Of Gravitation-I | 3 | 0 |
| MTHN-729 | Topics in Numerical Analysis-I | 3 | 0 |
| MTHN-731 | Plasma Dynamics-I | 3 | 0 |
| MTHN-733 | Atmospheric Study-I | 3 | 0 |
| MTHN-735 | Solar-System Astrophysics | 3 | 0 |
| MTHN-737 | Extra-Galactic Astronomy | 3 | 0 |
| MTHN-747 | Operations Research-I | 3 | 0 |
| MTHN-751 | General Topology-I | 3 | 0 |
| MTHN-753 | Topological-Dimension Theory | 3 | 0 |
| MTHN-755 | Topological Groups-I | 3 | 0 |
| MTHN-757 | Functional Analysis-I | 3 | 0 |
| MTHN-759 | Combina Rorics & Measure Theory-I | 3 | 0 |
| MTHN-761 | Summability Theory-I | 3 | 0 |
| MTHN-763 | Fouries Series-I | 3 | 0 |
| MTHN-765 | Almost Periodic Functions-I | 3 | 0 |
| MTHN-767 | Homological Algebra-I | 3 | 0 |
| MTHN-769 | Abelian Groups | 3 | 0 |
| MTHN-771 | Theory of Rings-I | 3 | 0 |
| MTHN-773 | Special Classes of Rings-I | 3 | 0 |
| MTHN-775 | Near Rings | 3 | 0 |
| MTHN-777 | Galois Theory & Applications-I | 3 | 0 |
| Semester – II | |||
| MTHN-702 | Differential Geometric Techniques-II | 3 | 0 |
| MTHN-704 | Differential Equations-II | 3 | 0 |
| MTHN-708 | Lie Algebra-II | 3 | 0 |
| MTHN-710 | Topics in Fluid Dynamics-II | 3 | 0 |
| MTHN-712 | Classical Electrodynamics-II | 3 | 0 |
| MTHN-714 | Topics in Relativity-II | 3 | 0 |
| MTHN-718 | Continuum Mechanics-II | 3 | 0 |
| MTHN-720 | Classical Field Theory-II | 3 | 0 |
| MTHN-722 | Topics in Quantum Mechanics-II | 3 | 0 |
| MTHN-724 | Quantum Field Theory-II | 3 | 0 |
| MTHN-726 | Representation Theory-II | 3 | 0 |
| MTHN-728 | Gauge Theory of Gravitation-II | 3 | 0 |
| MTHN-730 | Topics in Numerical Analysis-II | 3 | 0 |
| MTHN-732 | Plasma Dynamics-II | 3 | 0 |
| MTHN-734 | Atmospheric Study-II | 3 | 0 |
| MTHN-736 | Stellar & Galactic Astronomy | 3 | 0 |
| MTHN-738 | Cosmology | 3 | 0 |
| MTHN-748 | Operations Research-II | 3 | 0 |
| MTHN-752 | General Topology-II | 3 | 0 |
| MTHN-754 | Differential Topology | 3 | 0 |
| MTHN-756 | Topological Groups-II | 3 | 0 |
| MTHN-758 | Functional Analysis-II | 3 | 0 |
| MTHN-760 | Combina Torics & Measure Theory-II | 3 | 0 |
| MTHN-762 | Summability Theory-II | 3 | 0 |
| MTHN-764 | Fouries Series-II | 3 | 0 |
| MTHN-766 | Almost Periodic Functions-II | 3 | 0 |
| MTHN-768 | Homological Algebra-II | 3 | 0 |
| MTHN-770 | Soluble & Nilpotent Groups | 3 | 0 |
| MTHN-772 | Theory of Rings-II | 3 | 0 |
| MTHN-774 | Special Classes of Rings-II | 3 | 0 |
| MTHN-776 | Special Classes of Near Rings | 3 | 0 |
| MTHN-778 | Galois Theory & Applications-II | 3 | 0 |
| New M. Phil Program | |||
| Semester - I | |||
| ASR 701 | Research Methodology-I | 3 | 0 |
| MATH-703 | Compressible Flow-I | 2 | 1 |
| MATH-705 | Fourier Series-I | 3 | 0 |
| MATH-707 | Homological Algebra-I | 3 | 0 |
| MATH-709 | Abelian Groups | 3 | 0 |
| MATH-711 | Theory of Rings-I | 3 | 0 |
| MATH-713 | Near Rings | 3 | 0 |
| MATH-715 | Galois Theory and Applications-I | 3 | 0 |
| MATH-717 | Astrodynamics-I | 3 | 0 |
| MATH-719 | Abelian Groups-I | 3 | 0 |
| MATH-721 | Integral Equation | 3 | 0 |
| MATH-723 | Non-linear System-I | 3 | 0 |
| MATH-749 | Convex Analysis-I | 3 | 0 |
| MTHN-779 | Geometry-I | 3 | 0 |
| MTHN-781 | Number Theory-I | 3 | 0 |
| MTHN-783 | Coding Theory-I | 3 | 0 |
| Semester - II | |||
| ASR 702 | Research Methodology-II | 3 | 0 |
| MATH-704 | Compressible Flow-II | 2 | 1 |
| MATH-706 | Fourier Series-II | 3 | 0 |
| MATH-708 | Homological Algebra-II | 3 | 0 |
| MATH-710 | Soluble and Nilpotent Groups | 3 | 0 |
| MATH-712 | Theory of Rings-II | 3 | 0 |
| MATH-714 | Special Classes of Rings | 3 | 0 |
| MATH-716 | Galois Theory and Applications-II | 3 | 0 |
| MATH-718 | Astrodynamics-II | 3 | 0 |
| MATH-720 | Abelian groups-II | 3 | 0 |
| MATH-722 | Partial Differential Equation | 3 | 0 |
| MATH-724 | Non-linear System-II | 3 | 0 |
| MATH-750 | Convex Analysis-II | 3 | 0 |
| MATH-780 | Geometry-II | 3 | 0 |
| MATH-782 | Number Theory-II | 3 | 0 |
| MATH-784 | Coding Theory-II | 3 | 0 |
| Ph. D. Program | |||
| Semester - I | |||
| MATH-801 | Computational Methods for Fluid Flow-I | 3 | 0 |
| MATH-803 | Modelling and Simulation of Biological Systems-I | 3 | 0 |
| MATH-805 | Special Classes of Rings-I | 3 | 0 |
| MATH-807 | Stochastic Processes | 3 | 0 |
| MATH-809 | Theory of Mathematical Inequalities and Applications-I | 3 | 0 |
| MATH-813 | Theory of Matrix Rings and Matrix Near Rings-I | 3 | 0 |
| MATH-815 | Mathematical Biosciences | 3 | 0 |
| MATH-817 | Optimization Algorithms | 3 | 0 |
| Semester - II | |||
| MATH-802 | Computational Methods for Fluid Flow-II | 3 | 0 |
| MATH-804 | Modelling and Simulation of Biological Systems-II | 3 | 0 |
| MATH-806 | Special Classes of Rings-II | 3 | 0 |
| MATH-808 | Renewal Processes and Queuing Theory | 3 | 0 |
| MATH-810 | Theory of Mathematical Inequalities and Applications-II | 3 | 0 |
| MATH-814 | Theory of Matrix Rings and Matrix Near Rings-II | 3 | 0 |
| MATH-816 | Mathematical Epidemiology | 3 | 0 |
Syllabus
Aims and Objectives
- To inculcate habits of creative thinking, critical analysis and rigorousness, so that the students start enjoying mathematics.
- To make the student appreciate the uniqueness of mathematics as tool of the tools, having the power of generalization and the power of application.
- To develop ability in students to formulate a problem using the language of mathematics.
- To equip students with the tools required and the mathematical techniques applied in the industrial, the business, the financial and the health-care organizations.
- To propose mathematical solutions to indigenous problems arising in the industrial, the business, the financial and the health-care sectors.
- To strengthen academia-professional-world bonding by tailoring the courses and the trainings offered according to needs of the end-user.
Facilities
Facilities
The department offers an environment conducive
to learning The department offers an environment conducive to learning and
provides all modern facilities to students. This is the second and provides all
modern facilities to students. This is the second largest department of the
Faculty of Science, with a building largest department of the Faculty of
Science, with a building consisting of many class rooms, a computer laboratory
with consisting of many class rooms, a computer laboratory with internet
facility and a seminar library having three thousand internet facility and a
seminar library having three thousand books. To keep the students informed and
updated with the lat-books. To keep the students informed and updated with the
latest developments in the modern era, the department organizes est
developments in the modern era, the department organizes seminars and workshops
for faculty members and students who seminars and workshops for faculty members
and students who actively participate in local, national and international math
e-actively participate in local, national and international mathematical
activities and conferences.
Activities
- To keep the students informed and updated with the latest developments in the modern era, department organizes seminars and workshops for faculty members/students and also allow them to participate in such events both within and outside the university.
- Bimonthly Seminars, Invited Lectures by renowned Mathematicians, and Workshop on latest technologies and techniques help students in achieving their goals.
- One of the prominent features of the department is its strong International/National linkages. It provides ample opportunity to work on mutual projects, exchange research data, invite experts to hold lectures, seminars and special courses. In addition, collaboration with Universities also provides research facilities for the faculty members to improve their education.
- First National Conference on Mathematics on 22nd March 2010 to celebrate Golden Jubilee of Department of Mathematics. Brochure
- Future programs include a workshop on Use of technology in Math-Education and the First International Video Conference on Mathematics.
Arfa Karim Memorial Workshop Use of technology in Math Education (Program)
Research
The department website identifies
research interests including Non-Linear Mechanics, Dynamical Systems, Convex
Analysis, Numerical Integration, Differential Equations, Mathematical
Inequalities, climate-related mathematical and statistical modelling, and
scientific and engineering computing.
Contact
For further information please contact:
DEPARTMENT OF MATHEMATICS
UNIVERSITY OF KARACHI, KARACHI-75270
Telephone: (9221) 9926 1300–7; extensions 2293 / 2584
Email: mathematics@uok.edu.pk
Departmental website: https://www.uok.edu.pk/department-mathematics
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