Page | 1 Page | 2 Academic Programs Offered 1. BS Mathematics 2. M. Sc. Mathematics 3. M. Phil. Mathematics 4. Ph. D. Mathematics BS Mathematics Eligibility: Intermediate or equivalent with Mathematics (at least 45% marks in Intermediate & 50% marks in Mathematics). Duration: 04 Years Program (08 Semesters) Degree Requirements: Minimum 124 Credit Hours Semester-1 Course Code Course Title Credit Hours MATH-5101 Calculus-I 3(3+0) MATH-5102 Elements of Set Theory and Mathematical Logic 3(3+0) PHYS-5161 Physics-I 4(3+1) URCE-5101 Grammar 3(3+0) URCP-5106 Pakistan Studies 2(2+0) URCI -5109 Introduction to Information and Communication Technologies 3( 3+0) Semester-2 MATH-5103 Calculus-II 3(3+0) MATH-5104 Statistics 3(3+0) PHYS-5162 Physics-II 4(3+1) URCE-5102 Language Comprehension & Presentation Skills 3(3+0) URCI-5105 Islamic Studies 2(2+0) MATH-5105 Programming Languages for Mathematicains 3(2+1) No-Credit Course URCC-5110 Citizenship Education and Community Engagement 3(1+2) Semester-3 MATH-5106 Calculus-III 3(3+0) MATH-5107 Algebra-I 3(3+0) PHYS-5163 Physics-III 4(3+1) URCE-5103 Academic Writing 3(3+0) MATH-5108 Probability Theory 3(3+0) Semester-4 MATH-5109 Vector Analysis & Mechanics 3(3+0) MATH-5110 Linear Algebra 3(3+0) PHYS-5164 Physics-IV 4(3+1) MATH-5111 Discrete Mathematics 3(3+0) Page | 3 MATH-5112/ Spanish/French/Mathematical Economics 3(3+0) MATH-5113/ ECON-5118 Semester-5 MATH-6112 Topology 3(3+0) MATH-6113 Differential Geometry 3(3+0) MATH-6114 Ordinary Differential Equations 3(3+0) MATH-6115 Real Analysis-I 3(3+0) MATH-6116 Algebra-II 3(3+0) Semester-6 MATH-6117 Classical Mechanics 3(3+0) MATH-6118 Mathematical Methods 3(3+0) MATH-6119 Complex Analysis 3(3+0) MATH-6120 Functional Analysis 3(3+0) MATH-6121 Real Analysis-II 3(3+0) Semester-7 MATH-6122 Numerical Analysis-I 3(3+0) MATH-6123 Number Theory 3(3+0) MATH-6124 Partial Differential Equations 3(3+0) MATH-61xx Elective-I* 3(3+0) MATH-61xx Elective-II* 3(3+0) Semester-8 MATH-6125 Numerical Analysis-II 3(3+0) MATH-6126 Integral Equations 3(3+0) MATH-61xx Project / Course** 3(3+0) MATH-61xx Elective-III* 3(3+0) MATH-61xx Elective-IV* 3(3+0) Total Numbers of Credit Hours=128 * These four courses are optional & can be selected either from list A or B but cannot be mixed from both or any two courses can be selected from list C. ** In lieu of dissertation a course can be selected from list C. *** Any other language can be added according to availability of resources. Note: These courses will be offered by the department from the lists of concentration elective courses & free elective courses as per availability of the resources. List of Concentration Elective Courses A student must satisfactorily complete 12 credit hours of any one of the following concentration groups of Elective Courses namely, Pure or Applied Mathematics. MATH-6127 Advanced Group Theory-I 3(3+0) Page | 4 MATH-6128 Advanced Group Theory-II 3(3+0) MATH-6129 Modern Algebra-I 3(3+0) MATH-6130 Modern Algebra-II 3(3+0) MATH-6131 Algebraic Topology-I 3(3+0) MATH-6132 Algebraic Topology-II 3(3+0) MATH-6133 Advanced Functional Analysis 3(3+0) MATH-6134 Theory of Modules 3(3+0) List A: Concentration Elective Courses in Pure Mathematics List B: Concentration Elective Courses in Applied Mathematics MATH-6135 Astronomy-I 3(3+0) MATH-6136 Astronomy-II 3(3+0) MATH-6137 Electromagnetism-I 3(3+0) MATH-6138 Electromagnetism-II 3(3+0) MATH-6139 Fluid Mechanics-I 3(3+0) MATH-6140 Fluid Mechanics-II 3(3+0) MATH-6141 Operations Research-I 3(3+0) MATH-6142 Operations Research-II 3(3+0) MATH-6143 Quantum Mechanics-I 3(3+0) MATH-6144 Quantum Mechanics-II 3(3+0) MATH-6145 Analytical Dynamics 3(3+0) MATH-6146 Special Relativity 3(3+0) List C: List of Free Elective Courses A student must also satisfactorily complete 06 credits of any one of the following free Elective courses in Applied & Pure Mathematics. MATH-6147 Numerical Solution of Partial differential equations 3(3+0) MATH-6148 Elasticity Theory 3(3+0) MATH-6149 History of Mathematics 3(3+0) MATH-6150 Heat Transfer 3(3+0) MATH-6151 Bio-Mathematics 3(3+0) MATH-6152 Theory of Automata 3(3+0) MATH-6153 Measure Theory 3(3+0) MATH-6154 Special Functions 3(3+0) MATH-6155 Theory of Splines-I 3(3+0) MATH-6156 Theory of Splines-II 3(3+0) MATH-6157 Methods of Optimization-I 3(3+0) MATH-6158 Methods of Optimization-II 3(3+0) MATH-6159 Control Theory 3(3+0) MATH-6160 Applied Matrix Theory 3(3+0) Note: Other elective courses can be offered according to availability of resources. Page | 5 M. Sc. Mathematics Eligibility: At least 45% marks in B.Sc. with Mathematics A & B courses & 50% marks in Mathematics A & B courses. Duration: 02 Years Program (04 Semesters) Degree Requirements: Minimum 66 credit hours Semester-1 MATH-6201 Real Analysis-I 3 (3+0) MATH-6202 Abstract Algebra 3 (3+0) MATH-6203 Topology 3 (3+0) MATH-6204 Vector & Tensor Analysis 3 (3+0) MATH-6205 Set Theory and ODEs 3 (3+0) URCI-5109 Introduction to Information and Communication Technologies 3 (2+1) Semester-2 MATH-6206 Real Analysis-II 3 (3+0) MATH-6207 Linear Algebra 3 (3+0) MATH-6208 Functional Analysis 3 (3+0) MATH-6209 Mechanics 3 (3+0) MATH-6210 Complex Analysis 3 (3+0) MATH-6211 Computer Programming with C++ 3 (2+1) No-Credit Course URCC-5110 Citizenship Education and Community Engagement 3(1+2) Semester-3 MATH-6212 Differential Geometry 3 (3+0) MATH-6213 Partial Differential Equations 3 (3+0) MATH-6214 Numerical Analysis-I 3 (3+0) Pure Mathematics Group MATH-62XX Elective-I* 3 (3+0) MATH- 62XX Elective-II* 3 (3+0) Applied Mathematics Group MATH- 62XX Elective-I** 3 (3+0) MATH- 62XX Elective-II** 3 (3+0) Computational Mathematics Group MATH- 62XX Elective-I*** 3 (3+0) MATH- 62XX Elective-II*** 3 (3+0) Semester-4 MATH-6215 Probability Theory 3 (3+0) MATH-6216 Integral Equations 3 (3+0) MATH-6217 Numerical Analysis-II 3 (3+0) MATH-6218 History of Mathematics 2 (2+0) Pure Mathematics Group MATH-62XX Elective-I* 3 (3+0) Page | 6 MATH- 62XX Elective-II* 3 (3+0) Applied Mathematics Group MATH- 62XX Elective-I** 3 (3+0) MATH- 62XX Elective-II** 3 (3+0) Computational Mathematics Group MATH- 62XX Elective-I*** 3 (3+0) MATH- 62XX Elective-II*** 3 (3+0) Common Elective Courses MATH-6219 Special Functions 3 (3+0) MATH-6220 Algorithms and Computer Programming 3 (2+1) MATH-6221 Advanced Programming for Scientific Computing 3 (2+1) List A: Courses of Pure Mathematics MATH-6222 Analytic Number Theory 3 (3+0) MATH-6223 Algebraic Number Theory 3 (3+0) MATH-6224 Advanced Group Theory –I 3 (3+0) MATH-6225 Advanced Group Theory –II 3 (3+0) MATH-6226 Algebraic Topology-I 3 (3+0) MATH-6227 Algebraic Topology-II 3 (3+0) MATH-6228 Category Theory –I 3 (3+0) MATH-6229 Category Theory–II 3 (3+0) MATH-6230 Rings & Fields 3 (3+0) MATH-6231 Theory of Modules 3 (3+0) MATH-6232 Lie Algebra 3 (3+0) MATH-6233 Advanced Functional Analysis 3 (3+0) MATH-6234 Galois Theory 3 (3+0) MATH-6235 Measure Theory 3 (3+0) List B: Courses of Applied Mathematics MATH-6236 Fluid Mechanics-I 3 (3+0) MATH-6237 Fluid Mechanics-II 3 (3+0) MATH-6238 Quantum Mechanics-I 3 (3+0) MATH-6239 Quantum Mechanics-II 3 (3+0) MATH-6240 Electromagnetic Theory –I 3 (3+0) MATH-6241 Electromagnetic Theory –II 3 (3+0) MATH-6242 Special Relativity 3 (3+0) MATH-6243 Elasticity Theory 3 (3+0) MATH-6244 Analytical Dynamics 3 (3+0) MATH-6245 Astronomy-I 3 (3+0) MATH-6246 Astronomy-II 3 (3+0) List C: Courses of Computational Mathematics MATH-6247 Operations Research-I 3 (3+0) MATH-6248 Operations Research-II 3 (3+0) Page | 7 MATH-6249 Methods of Optimization-I 3 (3+0) MATH-6250 Methods of Optimization-II 3 (3+0) MATH-6251 Theory of Splines-I 3 (3+0) MATH-6252 Theory of Splines-II 3 (3+0) MATH-6253 Graph Theory 3 (3+0) MATH-6254 Theory of Automata 3 (3+0) MATH-6255 Control Theory 3 (3+0) MATH-6256 Applied Matrix Theory 3 (3+0) MATH-6257 Finite Element Analysis 3 (3+0) Cumulative Credits= 68 * These courses are optional & can be selected from list A or common electives. ** These courses are optional & can be selected from list B or common electives. ***These courses are optional & can be selected from list C or common electives. Page | 8 M. Phil. Mathematics Eligibility: M. Sc./BS 4-Year or equivalent (16 years of Education) in the relevant field or equivalent degree from HEC recognized institution with at least second Division or CGPA 2.00 out of 4.00. Duration: 02 Years Program (04 Semesters) Degree Requirements: Minimum 30 Credit Hours Semester-1 MATH-71xx Elective-I 3(3+0) MATH-71xx Elective-II 3(3+0) MATH-71xx Elective-III 3(3+0) MATH-71xx Elective-IV 3(3+0) Semester-2 MATH-71xx Elective-I 3(3+0) MATH-71xx Elective-II 3(3+0) MATH-71xx Elective-III 3(3+0) MATH-71xx Elective-IV 3(3+0) Semester 3-4 M.