**Lahore Leads University**

The BS in Mathematics are primarily intended for students wishing to pursue graduate work in mathematics. However, it is becoming more and more apparent that the need for mathematicians in our economy is shifting away from the academically oriented (i.e. trained to do basic research in mathematically related fields) to those equipped to aid in solving applied problems in business and the emerging high-tech industries. The program is designed to give students flavor of a theoretical as well as applied dimension of Mathematics. Application of a subject is unsatisfactory unless strong theoretical base is present. Keeping this fact in mind, the Department of Mathematics at Lahore Leads University aims to train its students with all the crucial theoretical background, one may need, to not only excel in the application of theory but also to help the students pursue the higher studies with ease structure, semester-wise breakdown and the contents of each course for the 4-year BS Mathematics curriculum are given below.

F.Sc. (pre-engineering) / F.A. with Mathematics / A-Level with Mathematics or equivalent with at least 2^{nd} division.

**Years: 04
Semesters: 08
**

Compulsory Requirements | 9 courses | 25 Credit hours |
---|---|---|

Course Code | Course Title | Cr. Hr. |

ENG1101 | English I(Functional English) | 3 |

ENG1102 | English II (Communication Skills) | 3 |

ENG1103 | English III (Technical writing and presentation skills) | 3 |

ENG1104 | English IV (Oral Communication) | 3 |

ISL1101 | Islamic studies/ethics | 2 |

PKST1101 | Pakistan studies | 2 |

MATH2201 | Discrete Mathematics | 3 |

MATH1102 | Elements of Set Theory and Mathematical Logic | 3 |

CSC1101 | Introduction to Computers | 3 |

Total | 25 | |

General Courses | 7-8 courses | 21-24 Cr. Hours |

Course Code | Course Title | Cr. Hr. |

MATH1001 | Statistics | 3 |

CSC1201 | Computer Programming | 3 |

MATH1002 | Software Packages | 3 |

MATH3003 | Latex | 2 |

G-1 | 3 | |

G-2 | 3 | |

G-3 | 3 | |

G-4 | 3 | |

Total | 23 | |

Discipline specific Foundation Courses | 9-10 courses | 30-33 Credit hours |

Course Code | Course Title | Cr. Hr. |

MATH2104 | Algebra I | 3 |

MATH3111 | Algebra II | 3 |

MATH1101 | Calculus I | 4 |

MATH1103 | Calculus II | 3 |

MATH2105 | Calculus III | 4 |

MATH3112 | Complex Analysis | 3 |

MATH3202 | Ordinary Differential Equations | 3 |

MATH2107 | Linear Algebra | 4 |

MATH2106 | Affine & Euclidean Geometry | 3 |

Total | 30 | |

Major Courses including research project | 11-13 courses | 36-42 Credit hours |

Course Code | Course Title | Cr. Hr. |

MATH4115 | Number Theory | 3 |

MATH3110 | Real Analysis I | 3 |

MATH3114 | Real Analysis II | 3 |

MATH4206 | Mathematical Methods | 3 |

MATH3108 | Topology | 3 |

MATH3109 | Differential Geometry | 3 |

MATH3203 | Classical Mechanics | 3 |

MATH3204 | Partial Differential Equations | 3 |

MATH3113 | Functional Analysis | 3 |

MATH4205 | Numerical Analysis | 4 |

MATH4207 | Probability Theory | 3 |

MATHT0 | Project | 6 |

Total | 40 | |

Elective courses within the major | 6 courses | 12 Credit hours |

Course Code | Course Title | Cr. Hr. |

Elective I | 3 | |

Elective II | 3 | |

Elective II | 3 | |

Elective IV | 3 | |

Elective V | 3 | |

Total | 15 |

Semester-wise break down of Scheme of Studies | |||||
---|---|---|---|---|---|

First Year | |||||

Course Code | Semester 1 | Cr. Hrs. | Course Code | Semester 2 | Cr. Hrs. |

MATH1101 | Calculus I | 4 | MATH1103 | Calculus II | 3 |

MATH1102 | Elements of set theory and Mathematical logic | 3 | MATH1001 | Statistics | 3 |

ENG 1101 | English I (Functional English) | 3 | MATH1002 | Software Packages | 3 |

ISL1101 | Islamic Studies | 2 | PKST1101 | Pakistan Studies | 2 |

CSC1101 | Introduction to Computers | 3 | ENG 1102 | English II (Readings in English Literature) | 3 |

G1 | 3 | G2 | 3 | ||

Total | 18 | Total | 17 | ||

Second Year | |||||

Course Code | Semester 3 | Cr. Hrs. | Course Code | Semester 4 | Cr. Hrs. |

MATH2105 | Calculus III | 4 | MATH2107 | Linear Algebra | 4 |

CSC1201 | Computer Programming | 3 | MATH2106 | Affine & Euclidean Geometry | 3 |

ENG 1103 | English III (Creative & Technical Writing) | 3 | G4 | 3 | |

G3 | 3 | MATH2201 | Discrete Mathematics | 3 | |

MATH2104 | Algebra I (Group Theory) | 3 | ENG 1104 | English IV (Oral communication) | 3 |

Total | 16 | Total | 16 | ||

Third Year | |||||

Course Code | Semester 5 (M.Sc. Mathematics) | Cr. Hrs. | Course Code | Semester 6 (M.Sc. Mathematics) | Cr. Hrs. |

MATH3110 | Real Analysis I | 3 | MATH3112 | Complex Analysis | 3 |

MATH3111 | Algebra II (Rings & Fields) | 3 | MATH3203 | Classical Mechanics | 3 |

MATH3108 | Topology | 3 | MATH3113 | Functional Analysis | 3 |

MATH3109 | Differential Geometry & Tensor Analysis | 3 | MATH3114 | Real Analysis II | 3 |

MATH3202 | Ordinary Differential Equations | 3 | MATH3204 | Partial Differential Equations | 3 |

MATH3003 | Latex | 2 | |||

Total | 17 | Total | 15 | ||

Fourth Year | |||||

Course Code | Semester 7 (M.Sc. Mathematics) | Cr. Hrs. | Course Code | Semester 8 (M.Sc. Mathematics) | Cr. Hrs. |

MATH4205 | Numerical Analysis | 4 | MATH4207 | Probability Theory | 3 |

MATH4115 | Number Theory | 3 | Elective III | 3 | |

MATH4206 | Mathematical Methods | 3 | Elective IV | 3 | |

Elective I | 3 | Elective V | 3 | ||

Elective II | 3 | MATHT0 | Project | 6 | |

Total | 16 | Total | 18 |

The courses G-1, G-2, G-3 and G-4 may be chosen from following titles. This list may be extended with consent of Board of Studies keeping in view the availability of expertise in the University.

● Physics-I

● Physics-II

● Biology

●Economics

● Chemistry

● Accounting

● Psychology

● Sociology

● Philosophy

● Environmental
Sciences

Course Code | Course Title |
---|---|

MATH4116 | Galois Theory |

MATH4117 | Rings and Modules |

MATH4118 | Convex Analysis |

MATH4219 | An Introduction to Geometric Function Theory |

MATH4120 | Introduction to Measure Theory |

MATH4121 | Introduction To Hilbert Spaces |

MATH4122 | Analytical Number Theory |

MATH4208 | Graph Theory |

MATH4209 | Optimization |

MATH4210 | Topics in Scientific Computing |

MATH4211 | Approximation Theory |

MATH4212 | Operations Research |

MATH4123 | Integral Equations |

MATH4124 | Riemannian Geometry |

MATH4213 | Introduction to Combinatorics |

MATH4214 | Special Relativity |

MATH4215 | Quantum Mechanics |

MATH4216 | Calculus of Variation |

MATH4125 | Vibrational Inequalities |

MATH4217 | Analytical Dynamics |

MATH4218 | Fluid Mechanics |

MATH4221 | Financial Mathematics |

MATH4220 | Elements of Electromagnetic Theory |

• Course contents and recommended books of the elective courses are given below. Contents and recommended books of few elective will be prepared by the teacher concerned.

• Electives may be chosen for one of the following areas of specialization keeping in view the availability of expertise in the university with consent of Board of Studies.
**(1)** Pure Mathematics
**(2)** Applied Mathematics
**(3)** Computational Mathematics
**(4)** Financial Mathematics

Etc.

• Produce trained manpower in mathematics for institution of higher learning in the country

• Initiate, promote and foster research in the various disciplines of mathematics

• Produce trained man power that can work as researcher in industries/ or research institutions

B.Sc. (Mathematics) or equivalent with at least 2^{nd} division.

• Years: 02

• Semesters: 04

• Total Credit Hours: 62

The duration of studies for the M.Sc. Degree shall normally be not less than one and half year and not more than three years. The M.Sc. in Mathematics Program consists of 60 credit hours (courses with three credit hours each). The students have to take courses from the following list with the prior approval of Department.

Semester 1 | ||
---|---|---|

Course Code | Course Title | Credit Hours |

MATH3110 | Real Analysis I | 03 |

MATH3108 | Topology | 03 |

MATH3112 | Complex Analysis | 03 |

MATH3202 | Ordinary Differential Equations | 03 |

MATH2104 | Algebra I | 03 |

MATH3003 | Latex | 02 |

Semester 2 | ||

Course Code | Course Title | Credit Hours |

MATH3109 | Differential Geometry and Tensor Analysis | 03 |

MATH4115 | Number Theory | 03 |

MATH3113 | Functional Analysis | 03 |

MATH4205 | Numerical Analysis | 03 |

MATH3114 | Real Analysis II | 03 |

Semester 3 | ||

Course Code | Course Title | Credit Hours |

MATH4206 | Mathematical Methods | 03 |

MATH3203 | Classical Mechanics | 03 |

MATH*** | Elective I | 03 |

MATH | Elective II | 03 |

MATH*** | Elective III | 03 |

Semester 4 | ||

Course Code | Course Title | Credit Hours |

MATH*** | Elective IV | 03 |

MATH*** | Elective V | 03 |

MATH*** | Elective VI | 03 |

MATH*** | Elective VII | 03 |

MATH*** | Elective VIII | 03 |

Course Code | Course Title |
---|---|

MATH4116 | Galois Theory |

MATH4117 | Rings and Modules |

MATH4118 | Convex Analysis |

MATH4219 | An Introduction to Geometric Function Theory |

MATH4120 | Introduction to Measure Theory |

MATH4121 | Introduction To Hilbert Spaces |

MATH4122 | Analytical Number Theory |

MATH4208 | Graph Theory |

MATH3204 | Partial differential equations |

MATH4209 | Optimization |

MATH4210 | Topics in Scientific Computing |

MATH4211 | Approximation Theory |

MATH4212 | Operations Research |

MATH4123 | Integral Equations |

MATH4124 | Riemannian Geometry |

MATH4213 | Introduction to Combinatorics |

MATH4214 | Special Relativity |

MATH4215 | Quantum Mechanics |

MATH4216 | Calculus of Variation |

MATH4125 | Variational Inequalities |

MATH4217 | Analytical Dynamics |

MATH4218 | Fluid Mechanics |

MATH4220 | Elements of Electromagnetic Theory |

MATH4221 | Mathematical Statistics |

Course contents and recommended books of the elective courses are given below. Contents and recommended books of few elective will be prepared by the teacher concerned.

The purpose of MS program in Mathematics is to offer students who hold a BS or M.Sc. degree with a major in mathematics or a neighboring field:

• an opportunity to expand their knowledge in the several fields of mathematics and its applications by providing courses at graduate level

• a unique academic experience via a high-quality international program

• preparation for a professional career in education, or in business, industry and research institutions

• for those wishing to continue their studies in the PhD track, comprehensive knowledge in mathematics and its applications, as well as an opportunity to decide whether they are willing to become mathematicians.

BS (Mathematics) or equivalent; GAT (General) Score: Minimum 50%

• Years: 02

• Semesters: 04

• Total Credit Hours: 30

The duration of studies for the MS Degree shall normally be not less than one and half year and not more than three years. The MS in Mathematics Program consists of 24 credit hours (courses with three credit hours each) and 6 credit hours of thesis. The students have to take courses from the following list with the prior approval of Department.

Pure Mathematics | |
---|---|

Course Code | Course Title |

MATH 5101 | Advanced Group Theory |

MATH 5102 | Rings and modules |

MATH 5103 | Commutative Algebra |

MATH 5104 | Homological Algebra |

MATH 5105 | Combinatorial Commutative Algebra |

MATH 5106 | Advanced Functional Analysis |

MATH 5107 | Advanced Measure Theory |

MATH 5108 | Advanced Convex Analysis |

MATH 5109 | Fixed Point Theory and Applications |

MATH 5110 | Approximation Theory and Applications |

MATH 5111 | Variational Inequalities and Applications |

MATH 6101 | Algebraic Geometry |

MATH 6102 | Algebraic Number Theory |

MATH 6103 | Field Extension and Galois Theory |

MATH 6104 | Algebraic Topology |

MATH 6105 | Representation Theory of Finite Groups |

MATH 6106 | Special Topics in Pure Mathematics |

MATH 6107 | Interpolation spaces for Operators |

Applied Mathematics | |
---|---|

Course Code | Course Title |

MATH 5201 | Advanced Numerical Analysis |

MATH 5202 | Advanced Differential Equations |

MATH 5203 | Advanced Partial Differential Equations |

MATH 5204 | Numerical Solution of Ordinary Differential Equations |

MATH 5205 | Numerical Solution of Partial Differential Equations |

MATH 5206 | Advanced Mathematical Statistics |

MATH 5207 | Advanced Mathematical Modeling |

MATH 5208 | Advanced Optimization Theory |

MATH 5209 | Integral Inequalities |

MATH 5210 | Approximation Theory and Applications |

MATH 5211 | Perturbation Methods |

MATH 5212 | Nonlinear Analysis and Fixed Point Theory |

MATH 5213 | Special Topics in Numerical Methods |

MATH 5214 | Advanced Graph Theory |

MATH 6201 | Numerical Linear Algebra |

MATH 6202 | Special Topics in Applied Mathematics |

MATH 6203 | Advanced Analytical Dynamics |

MATH 6204 | Control Theory |

MATH 6205 | Iterative Methods for Solving Nonlinear Equations |

MATH 6206 | Computational Electrodynamics |