PhD Mathematics

PhD Optional Courses

S.#

Course Code

Title

Pre-requisite

Cr. Hrs

1

MATH 633

Non-linear Programming

MATH 532

(3 3 4)

2

MATH 711

Representation Theory of Finite Dimensional Algebras

MATH 612

(3 0 3)

3

MATH 731

Constraint Satisfaction for Decision Making

None

(3 3 4)

4

MATH 741

Multivariate Analysis–I

MATH 542

(3 0 3)

5

MATH 742

Multivariate Analysis–I

MATH 741

(3 0 3)

6

MATH 771

q-Special Functions

MATH 572

(3 0 3)

7

MATH 831

Evolutionary  Computation

None

(3 3 4)

8

MATH 832

Evolutionary Computation and Genetic Programming

MATH 831

(3 3 4)

9

MATH 833

Combinatorial Optimization

None

(3 3 4)

Thesis

10

MATH 999

PhD Thesis

None

(0 18 6)

MPhil Mathematics

Core Courses

S.#

Course Code

Title

Pre-requisite

Cr. Hrs

1

MATH 511

Advanced Linear Algebra

None

(3 0 3)

2

MATH 521

Complex Variables and Applications

None

(3 0 3)

 

M.Phil Optional Courses

S.#

Course Code

Title

Pre-requisite

Cr. Hrs

1

MATH 501

Departmental Seminars

None

(0 0 0)

2

MATH 512

Commutative Rings-I

None

(3 0 3)

3

MATH 513

Commutative Rings-II

MATH 512

(3 0 3)

4

MATH 514

Theory of Semigroups

None

(3 0 3)

5

MATH 522

Fixed Point Theory

MATH 521

(3 0 3)

6

MATH 531

Unconstrained Optimization

None

(3 3 4)

7

MATH 532

Constrained Optimization

MATH 531

(3 3 4)

8

MATH 541

Probability Distributions

None

(3 0 3)

9

MATH 542

Statistical Inference

MATH 541

(3 0 3)

10

MATH 543

Linear Models

MATH 541

(3 0 3)

11

MATH 571

Special Functions-I

None

(3 0 3)

12

MATH 572

Special Functions -II

MATH 571

(3 0 3)

13

MATH 611

Theory of Semirings

None

(3 0 3)

14

MATH 612

Homological Algebra

None

(3 0 3)

15

MATH 631

Advanced Numerical Analysis-I

None

(3 3 4)

16

MATH 632

Advanced Numerical Analysis-II

MATH 631

(3 3 4)

17

MATH 671

Non-linear Ordinary Differential Equations -I

None

(3 0 3)

18

MATH 672

Non-linear Ordinary Differential Equations -II

MATH 671

(3 0 3)

Thesis

19

MATH 699

M.Phil Thesis 

None

(0 18 6)

MSc Mathematics

First Year

First Semester

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH321

Real Analysis-I

None

(3 0 3)

2

MATH211

Group Theory

None

(3 0 3)

3

MATH302

Set Theory and Mathematical Logic

None

(3 0 3)

4

MATH351

General Topology

None

(3 0 3)

5

MATH271

Ordinary Differential Equations

None

(3 0 3)

6

ENG101

Functional English

None

(3 0 3)

Total Credit Hrs.

18

 

Second Semester

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH322

Real Analysis-II

MATH321

(3 0 3)

2

MATH311

Linear Algebra

None

(3 0 3)

3

MATH312

Advanced Group Theory

MATH211

(3 0 3)

4

MATH323

Complex Analysis

MATH321

(3 0 3)

5

MATH301

Programming with MATLAB

None

(2 3 3)

6

ENG134

Communication Skills

 

(3 0 3)

Total Credit Hrs.

18

 Second Year

Third Semester

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH331

Numerical Analysis-I

MATH321

(3 3 4)

2

MATH324

Functional Analysis-I

MATH311

(3 0 3)

3

MATH241

Mathematical Statistics-I

None

(3 0 3)

4

MATH481

Differential Geometry

None

(3 0 3)

5

MATH4XX

Elective

MATHXXX

(3 0 3)/ (3 3 4)

6

MATH4XX

Elective

MATHXXX

(3 0 3)

Total Credit Hrs.

19-20

 

Fourth Semester

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH431

 Numerical Analysis-II

MATH331

(3 3 4)

2

MATH422

Functional Analysis-II

MATH324

(3 0 3)

3

MATH341

Mathematical Statistics-II

MATH241

(3 0 3)

4

MATH4XX

Elective

MATHXXX

(3 0 3)/ (3 3 4)

5

MATH4XX

Elective

MATHXXX

(3 0 3)

6

MATH491

Viva Voce

None

(3 0 3)

Total Credit Hrs.

19-20

BS/M.Sc. Elective Courses

BS/M.Sc. Elective Courses

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH434

Numerical Solution of PDEs

MATH431

(3 3 4)

2

MATH324

Functions Analysis-I

MATH311

(3 0 3)

3

MATH422

Functional Analysis-II

MATH324

(3 0 3)

4

MATH431

Numerical Analysis-II

MATH331

(3 3 4)

5

MATH332

Operation Research

MATH301

(3 3 4)

6

MATH411

Rings and Fields

MATH312

(3 0 3)

7

MATH423

Measure Theory & Integration

MATH321

(3 0 3)

8

MATH461

Analytical  Dynamics

None

(3 0 3)

9

MATH361

Fluid Mechanics

MATH371

(3 0 3)

10

MATH412

Galois Theory

MATH411

(3 0 3)

11

MATH432

Optimization Theory-I

MATH301

(3 3 4)

12

MATH433

Optimization Theory-II

MATH432

(3 3 4)

13

MATH371

Partial Differential Equations

MATH271

(3 0 3)

14

MATH413

Theory of Modules

MATH411

(3 0 3)

 

BS Mathematics

First year

Semester-I

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH101

Calculus-I

None

(3 0 3)

2

ENG112

English (Study Skills)

None

(3 0 3)

3

CS101

Introduction to Computing

None

(3 3 4)

4

PHY101

Introductory Mechanics

None

(3 3 4)

5

RS101

Islamic Study/Theology

None

(3 0 3)

Total Credit Hrs.

17

 

Semester-II

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH102

Calculus-II

MATH101

(3 0 3)

2

MATH103

Discrete Mathematics

None

(3 0 3)

3

PS101

Pak Studies

None

(3 0 3)

4

PHY102

Introductory Electricity and Magnetism

None

(3 3 4)

5

ENG134

English (Communication Skills)

None

(3 0 3)

Total Credit Hrs

16 

Second Year

Semester-III

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH201

Calculus-III

MATH102

(3 0 3)

2

MATH221

Vector and Tensor Analysis

MATH102

(3 0 3)

3

MATH202

Number Theory

None

(3 0 3)

4

IMS141

Principles of Management

None

(3 0 3)

5

PHY211

Classical Mechanics

None

(3 0 3)

Total Credit Hrs

15

 

Semester-IV

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH211

Group Theory

None

(3 0 3)

2

MATH271

Ordinary Differential Equations

MATH101

(3 0 3)

3

MATH241

Mathematical Statistics-I

MATH101

(3 0 3)

4

PHY212

Quantum Mechanics

None

(3 0 3)

5

SWS201

Sociology and Social Work

None

(3 0 3)

Total Credit Hrs

15

Third Year

Semester-V

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH311

Linear Algebra

MATH211

(3 0 3)

2

MATH321

Real Analysis-I

MATH101

(3 0 3)

3

MATH351

General Topology

MATH102

(3 0 3)

4

MATH371

Partial Differential Equations

MATH271

(3 0 3)

5

MATH341

Mathematical Statistics-II

MATH241

(3 0 3)

6

MATH301

Programming with MATLAB

None

(2 3 3)

Total Credit Hrs.

18

 

Semester-VI

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH312

Advanced Group Theory

MATH211

(3 0 3)

2

MATH322

Real Analysis-II

MATH321

(3 0 3)

3

MATH331

Numerical Analysis-I

MATH321

(3 3 4)

4

MATH323

Complex Analysis

MATH321

(3 0 3)

5

MATH3XX

Elective

MATHXXX

(3 0 3)

Total Credit Hrs

16

Fourth Year

Semester-VII

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH471

Mathematical Modeling

MATH371

(3 0 3)

2

MATH481

Differential Geometry

MATH271

(3 0 3)

3

MATH3XX

Elective

MATHXXX

(3 0 3)

4

MATH3XX

Elective

MATHXXX

(3 0 3)

5

MATH4XX

Elective

MATHXXX

(3 0 3)

6

MATH4XX

Elective/Project

MATHXXX

(3 0 3)/

(3 3 4)

Total Credit Hrs

(18+0)/

(18+1)

 

Semester-VIII

S.#

Course Code

Title

Pre-requisite

Cr. Hrs.

1

MATH472

Integral Equations

MATH271

(3 0 3)

2

MATH4XX

Elective

MATHXXX

(3 0 3)

3

MATH4XX

Elective

MATHXXX

(3 0 3)

4

MATH4XX

Elective

MATHXXX

(3 0 3)

5

MATH4XX

Elective

MATHXXX

(3 0 3)/

(3 3 4)

6

MATH491

Elective/ Project

None

(3 0 3)

Total Credit Hrs

18-19

 

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