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Undergraduate Programms (Mathematics)



Bachelor of Science in Mathematics (BS-Math)


Objectives of the Program

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.


Eligibility Criteria

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


Duration

Years: 04
Semesters: 08


Course Details


Compulsory Requirements9 courses25 Credit hours
Course CodeCourse TitleCr. Hr.
ENG1101English I(Functional English)3
ENG1102English II (Communication Skills)3
ENG1103English III (Technical writing and presentation skills)3
ENG1104English IV (Oral Communication)3
ISL1101Islamic studies/ethics2
PKST1101Pakistan studies2
MATH2201Discrete Mathematics3
MATH1102Elements of Set Theory and Mathematical Logic3
CSC1101Introduction to Computers3
Total25
 
General Courses7-8 courses21-24 Cr. Hours
Course CodeCourse TitleCr. Hr.
MATH1001Statistics3
CSC1201Computer Programming3
MATH1002Software Packages3
MATH3003Latex2
 G-13
 G-23
 G-33
 G-43
Total23
 
Discipline specific Foundation Courses9-10 courses30-33 Credit hours
Course CodeCourse TitleCr. Hr.
MATH2104Algebra I3
MATH3111Algebra II3
MATH1101Calculus I4
MATH1103Calculus II3
MATH2105Calculus III4
MATH3112Complex Analysis3
MATH3202Ordinary Differential Equations3
MATH2107Linear Algebra4
MATH2106Affine & Euclidean Geometry3
Total30
 
Major Courses including research project11-13 courses36-42 Credit hours
Course CodeCourse TitleCr. Hr.
MATH4115Number Theory3
MATH3110Real Analysis I3
MATH3114Real Analysis II3
MATH4206Mathematical Methods3
MATH3108Topology3
MATH3109Differential Geometry3
MATH3203Classical Mechanics3
MATH3204Partial Differential Equations3
MATH3113Functional Analysis3
MATH4205Numerical Analysis4
MATH4207Probability Theory3
MATHT0Project6
Total40
 
Elective courses within the major6 courses12 Credit hours
Course CodeCourse TitleCr. Hr.
 Elective I3
 Elective II3
 Elective II3
 Elective IV3
 Elective V3
Total15


BS(Mathematics) Scheme of Studies Semester-Wise Breakdown



Semester-wise break down of Scheme of Studies
First Year
Course CodeSemester 1Cr. Hrs.Course CodeSemester 2Cr. Hrs.
MATH1101Calculus I4MATH1103Calculus II3
MATH1102Elements of set theory and Mathematical logic3MATH1001Statistics3
ENG 1101English I (Functional English)3MATH1002Software Packages3
ISL1101Islamic Studies2PKST1101Pakistan Studies2
CSC1101Introduction to Computers3ENG 1102English II (Readings in English Literature)3
  G13 G23
Total18Total17
 
Second Year
Course CodeSemester 3Cr. Hrs.Course CodeSemester 4Cr. Hrs.
MATH2105Calculus III4MATH2107Linear Algebra4
CSC1201Computer Programming3MATH2106Affine & Euclidean Geometry3
ENG 1103English III (Creative & Technical Writing)3 G43
 G33MATH2201Discrete Mathematics3
MATH2104Algebra I (Group Theory)3ENG 1104English IV (Oral communication)3
Total16Total16
 
Third Year
Course CodeSemester 5
(M.Sc. Mathematics)
Cr. Hrs.Course CodeSemester 6
(M.Sc. Mathematics)
Cr. Hrs.
MATH3110Real Analysis I3MATH3112Complex Analysis3
MATH3111Algebra II (Rings & Fields)3MATH3203Classical Mechanics3
MATH3108Topology3MATH3113Functional Analysis3
MATH3109Differential Geometry & Tensor Analysis3MATH3114Real Analysis II3
MATH3202Ordinary Differential Equations3MATH3204Partial Differential Equations 3
MATH3003Latex2   
Total17Total15
 
Fourth Year
Course CodeSemester 7
(M.Sc. Mathematics)
Cr. Hrs.Course CodeSemester 8
(M.Sc. Mathematics)
Cr. Hrs.
MATH4205Numerical Analysis4MATH4207Probability Theory3
MATH4115Number Theory3 Elective III3
MATH4206Mathematical Methods3 Elective IV3
 Elective I3 Elective V3
 Elective II3MATHT0Project6
Total16Total18


General Courses for BS Mathematics


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


Elective Courses


Course CodeCourse Title
MATH4116Galois Theory
MATH4117Rings and Modules
MATH4118Convex Analysis
MATH4219An Introduction to Geometric Function Theory
MATH4120Introduction to Measure Theory
MATH4121Introduction To Hilbert Spaces
MATH4122Analytical Number Theory
MATH4208Graph Theory
MATH4209Optimization
MATH4210Topics in Scientific Computing
MATH4211Approximation Theory
MATH4212Operations Research
MATH4123Integral Equations
MATH4124Riemannian Geometry
MATH4213Introduction to Combinatorics
MATH4214Special Relativity
MATH4215Quantum Mechanics
MATH4216Calculus of Variation
MATH4125Vibrational Inequalities
MATH4217Analytical Dynamics
MATH4218Fluid Mechanics
MATH4221 Financial Mathematics
MATH4220Elements of Electromagnetic Theory

Note:

• 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.


Download:

Course Contents of BS Foundation and Major Courses













M.Sc. Matehmatics


Objectives of Program:

• 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

Eligibility Criteria:

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

Duration:

• 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-wise breakdown of scheme of studies:


Semester 1
Course CodeCourse TitleCredit Hours
MATH3110Real Analysis I03
MATH3108Topology03
MATH3112Complex Analysis03
MATH3202Ordinary Differential Equations03
MATH2104Algebra I03
MATH3003Latex02
Semester 2
Course CodeCourse TitleCredit Hours
MATH3109Differential Geometry and Tensor Analysis03
MATH4115Number Theory03
MATH3113Functional Analysis03
MATH4205Numerical Analysis03
MATH3114Real Analysis II03
Semester 3
Course CodeCourse TitleCredit Hours
MATH4206Mathematical Methods03
MATH3203Classical Mechanics03
MATH***Elective I 03
MATH Elective II03
MATH***Elective III03
Semester 4
Course CodeCourse TitleCredit Hours
MATH***Elective IV03
MATH***Elective V03
MATH***Elective VI03
MATH***Elective VII03
MATH***Elective VIII03

Elective Courses


Course CodeCourse Title
MATH4116Galois Theory
MATH4117Rings and Modules
MATH4118Convex Analysis
MATH4219An Introduction to Geometric Function Theory
MATH4120Introduction to Measure Theory
MATH4121Introduction To Hilbert Spaces
MATH4122Analytical Number Theory
MATH4208Graph Theory
MATH3204Partial differential equations
MATH4209Optimization
MATH4210Topics in Scientific Computing
MATH4211Approximation Theory
MATH4212Operations Research
MATH4123Integral Equations
MATH4124Riemannian Geometry
MATH4213Introduction to Combinatorics
MATH4214Special Relativity
MATH4215Quantum Mechanics
MATH4216Calculus of Variation
MATH4125Variational Inequalities
MATH4217Analytical Dynamics
MATH4218Fluid Mechanics
MATH4220Elements of Electromagnetic Theory
MATH4221Mathematical Statistics

Note:

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.


Download:

Course Outlines of Courses of M.Sc.













M.Phil. Mathematics


Objectives of Program:

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.


Eligibility Criteria:

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


Duration:

• 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.


List of courses


Pure Mathematics
Course CodeCourse Title
MATH 5101Advanced Group Theory
MATH 5102Rings and modules
MATH 5103Commutative Algebra
MATH 5104Homological Algebra
MATH 5105Combinatorial Commutative Algebra
MATH 5106Advanced Functional Analysis
MATH 5107Advanced Measure Theory
MATH 5108Advanced Convex Analysis
MATH 5109Fixed Point Theory and Applications
MATH 5110Approximation Theory and Applications
MATH 5111Variational Inequalities and Applications
MATH 6101Algebraic Geometry
MATH 6102Algebraic Number Theory
MATH 6103Field Extension and Galois Theory
MATH 6104Algebraic Topology
MATH 6105Representation Theory of Finite Groups
MATH 6106Special Topics in Pure Mathematics
MATH 6107Interpolation spaces for Operators

Applied Mathematics
Course CodeCourse Title
MATH 5201Advanced Numerical Analysis
MATH 5202Advanced Differential Equations
MATH 5203Advanced Partial Differential Equations
MATH 5204Numerical Solution of Ordinary Differential Equations
MATH 5205Numerical Solution of Partial Differential Equations
MATH 5206Advanced Mathematical Statistics
MATH 5207Advanced Mathematical Modeling
MATH 5208Advanced Optimization Theory
MATH 5209Integral Inequalities
MATH 5210Approximation Theory and Applications
MATH 5211Perturbation Methods
MATH 5212Nonlinear Analysis and Fixed Point Theory
MATH 5213Special Topics in Numerical Methods
MATH 5214Advanced Graph Theory
MATH 6201Numerical Linear Algebra
MATH 6202Special Topics in Applied Mathematics
MATH 6203Advanced Analytical Dynamics
MATH 6204Control Theory
MATH 6205Iterative Methods for Solving Nonlinear Equations
MATH 6206Computational Electrodynamics

Download:

Course Outlines of Courses of MS/M.Phil