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SYLLABUS FOR 4 YEAR B.S. MATHEMATICS

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1SYLLABUS FOR 4 YEAR B.S. MATHEMATICS (SEMESTER SYSTEM PROGRAMME) Combination I MATHEMATICS-A, MATHEMATICS-B, PHYSICS Duration of Programme: 4Years (Eight Semesters) Requirement: F.Sc./ICS/General Science (with Maths and Stats.) F.Sc./ICS (with Maths and Physics.) Medium of instructions: English Credit Hours: 76+66=142 B.S. Mathematics Semester I ISE-111 Islamiat / Ethics 2 cr. ENG-111 English-I (Language in Use) 3 cr. COMP-111 Computer (Introduction and Applications) 3 cr. MATH-101 Mathematics A-I [Calculus (I)] 4 cr. MATH-102 Mathematics B-I [ Vectors & Mechanics (I)] 4 cr. PHY-111 Physics-I 3 cr. PHY -112 Physics Lab-I 1 cr. Total= 20 cr. B.S. Mathematics Semester II PST-111 Pakistan Studies 2 cr. ENG-112 English-II (Academic Reading and Writing) 3 cr. PHY -113 Physics -II 3 cr. PHY -114 Physics Lab-II 1 cr. MATH-103 Mathematics A-II [ Plane Curves & Analytic Geometry ] 4 cr. MATH-104 Mathematics B-II [ Mechanics (II) ] 4 cr. MATH-105 Discrete Mathematics 2 cr. Total= 19 cr. B.S. Mathematics Semester III ENG-211 English-III (Communication Skills) 3 cr. PHY -211 Physics -III 3 cr. PHY -212 Physics Lab-III 1 cr. MATH-201 Mathematics A-III [ Linear Algebra] 4 cr. MATH-202 Mathematics B-III [ Calculus (II)] 4 cr. MATH-205 Graph Theory 2 cr. Total= 17 cr. B.S. Mathematics Semester IV ENG-212 English-IV (English for Practical Aims) 3 cr. PHY -213 Physics -IV 3 cr. PHY -214 Physics Lab-IV 1 cr. MATH-203 Mathematics A-IV [ Ordinary Differential Equations] 4 cr. MATH-204 Mathematics B-IV [ Metric Spaces & Group Theory] 4 cr. SOC-211 Introduction to Sociology 3 cr. MATH-206 Elementary Number Theory 2 cr. Total= 20 cr.2 Combination II MATHEMATICS-A, MATHEMATICS-B, STATISTICS Duration of Programme: 4 Years (Eight Semesters) Requirement: F.Sc./ICS/General Science (with Maths and Stats.) F.Sc./ICS (with Maths and Physics.) Medium of instructions: English Credit Hours: 76+66=142 B.S. Mathematics Semester I ISE-111 Islamiat / Ethics 2 cr. ENG-111 English-I (Language in Use) 3 cr. COMP-111 Computer (Introduction and Applications) 3 cr. MATH-101 Mathematics A-I [ Calculus (I)] 4 cr. MATH-102 Mathematics B-I [ Vectors & Mechanics (I)] 4 cr. STAT-101 Statistics-I 3 cr. STAT-102 Statistics Lab-I 1 cr. Total= 20 cr. B.S. Mathematics Semester II PST-111 Pakistan Studies 2 cr. ENG-112 English-II (Academic Reading and Writing) 3 cr. STAT-103 Statistics-II 3 cr. STAT-104 Statistics Lab-II 1 cr. MATH-103 Mathematics A-II [Plane Curves & Analytic Geometry ] 4 cr. MATH-104 Mathematics B-II [ Mechanics (II) ] 4 cr. MATH-105 Discrete Mathematics 2 cr. Total= 19 cr. B.S. Mathematics Semester III ENG-211 English-III (Communication Skills) 3 cr. STAT-201 Statistics-III 3 cr. STAT-202 Statistics Lab-III 1 cr. MATH-201 Mathematics A-III [ Linear Algebra] 4 cr. MATH-202 Mathematics B-III [ Calculus (II)] 4 cr. MATH-205 Graph Theory 2 cr. Total= 17 cr. B.S. Mathematics Semester IV ENG-212 English-IV (English for Practical Aims) 3 cr. STAT-203 Statistics-IV 3 cr. STAT-204 Statistics Lab-IV 1 cr. MATH-203 Mathematics A-IV [ Ordinary Differential Equations] 4 cr. MATH-204 Mathematics B-IV [ Metric Spaces & Group Theory] 4 cr. SOC-211 Introduction to Sociology 3 cr. MATH-206 Elementary Number Theory 2 cr. Total= 20 cr.3 B.S. Mathematics Semester V MATH-301 Real Analysis –I 3 cr. MATH-302 Group Theory-I 3 cr. MATH-303 Complex Analysis-I 3 cr. MATH-304 Vector and Tensor Analysis 3 cr. MATH-305 Topology 3 cr. MATH-306 Differential Geometry 3 cr. Total = 18 cr. B.S. Mathematics Semester VI MATH-307 Real Analysis –II 3 cr. MATH-308 Rings and Vector Spaces 3 cr. MATH-309 Complex Analysis – II 3 cr. MATH-310 Mechanics 3 cr. MATH-311 Functional Analysis-I 3 cr. MATH-312 Ordinary Differential Equations 3 cr. Total = 18 cr. B.S. Mathematics Semester VII MATH-401 Set Theory 3 cr. MATH-402 Partial Differential Equations 3 cr. MATH-403 Numerical Analysis-I 3 cr. Any Two of the following: MATH-404 Mathematical Statistics-I 3 cr. MATH-405 Fortran Programming 3 cr. MATH-406 Group Theory-II 3 cr. MATH-407 Ring Theory 3 cr. MATH-408 Number Theory-I 3 cr. MATH-409 Quantum Mechanics-I 3 cr. MATH-410 Analytical Dynamics 3 cr. MATH-411 Electromagnetic Theory-I 3 cr. MATH-412 Operations Research-I 3 cr. MATH-413 Theory of Approximation and Splines-I 3 cr. MATH-414 Functional Analysis- II 3 cr. MATH-415 Fluid Mechanics-I 3 cr. Total = 15 cr.4 B.S. Mathematics Semester VIII MATH-416 Measure Theory and Lebesgue Integration 3 cr. MATH-417 Methods of Mathematical Physics 3 cr. MATH-418 Numerical Analysis-II 3 cr. Any Two of the following: MATH-419 Mathematical Statistics-II 3 cr. MATH-420 Computer Applications 3 cr. MATH-421 Group Theory-III 3 cr. MATH-422 Theory of Modules 3 cr. MATH-423 Number Theory-II 3 cr. MATH-424 Quantum Mechanics-II 3 cr. MATH-425 Special Theory of Relativity 3 cr. MATH-426 Electromagnetic Theory-II 3 cr. MATH-427 Operations Research-II 3 cr. MATH-428 Theory of Approximation and Splines-II 3 cr. MATH-429 Functional Analysis- III 3 cr. MATH-430 Fluid Mechanics-II 3 cr. Total = 15 cr.5Semester I Module Code: MATH-101 Module Title: Mathematics A-I [ Calculus (I)] Module Rating: 4 Cr. Hours Preliminaries - Real numbers and the real line - Functions and their graphs - Shifting and scaling graphs - Solution of equations involving absolute values - Inequalities - Complex numbers system. Polar form of complex numbers, De Moivr’s theorem - Circular function, hyperbolic functions, logarithmic Limit and Continuity - Limit of a function, left hand and right hand limits, Theorems of limits - Continuity, Continuous functions Derivatives and its Applications - Differentiable functions - Differentiation of polynomial, rational and transcendental functions - Mean value theorems and applications - Higher derivatives, Leibniz’s theorem - L’Hospitals Rule - Intermediate value theorem, Rolle’s theorem - Taylor’s and Maclaurin’s theorem with their remainders Integration and Definite Integrals - Techniques of evaluating indefinite integrals - Integration by substitutions, Integration by parts - Change of variable in indefinite integrals - Definite integrals, Fundamental theorem of calculus -


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