sse curriculum

8/12/2019 SSE Curriculum

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SSE Curriculum

Final Report

Dr. Shafay Shamail

May 31, 2009

Lahore University of Management Science


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Table of ContentsTable of Contents............................................................................................................................ 21 Curriculum Committees.......................................................................................................... 42 Foreword................................................................................................................................. 6

3 Revision History of Working Document ................................................................................ 74 Summary................................................................................................................................. 9

4.1 University Core Requirements...................................................................................... 104.2 SSE Core Courses ......................................................................................................... 104.3 Major Core Requirements............................................................................................. 104.4 Major Elective Requirements ....................................................................................... 114.5 Free Electives................................................................................................................ 114.6 SSE Service Courses..................................................................................................... 11

5 Codes..................................................................................................................................... 126 Graduation Requirements ..................................................................................................... 137 Structure of SSE Core........................................................................................................... 14

PART I .......................................................................................................................................... 158 University Core for SSE ....................................................................................................... 169 SSE Courses for Rest of the University................................................................................ 1710 Structure of SSE Core....................................................................................................... 18

10.1 Freshman Year .............................................................................................................. 1810.2 Sophomore Year ........................................................................................................... 1810.3 Junior and Senior Year.................................................................................................. 19

PART II......................................................................................................................................... 2011 Physics Curriculum........................................................................................................... 21

11.1 Physics Courses in SSE Core........................................................................................ 2111.2 Physics Core Courses.................................................................................................... 21

11.3 Physics Major Elective Courses.................................................................................... 2111.4 Streams.......................................................................................................................... 2211.5 Faculty Needs................................................................................................................ 2211.6 Course Descriptions...................................................................................................... 23

12 Chemistry Curriculum ...................................................................................................... 2612.1 Chemistry Courses in SSE Core ................................................................................... 2612.2 Chemistry Core Courses ............................................................................................... 2612.3 Chemistry Major Elective Courses ............................................................................... 2612.4 Chemistry Minor........................................................................................................... 2712.5 Streams.......................................................................................................................... 2812.6 Faculty Needs................................................................................................................ 28

12.7 Course Descriptions...................................................................................................... 2913 Biology Curriculum .......................................................................................................... 3213.1 Biology Courses in SSE Core ....................................................................................... 3213.2 Biology Core Courses ................................................................................................... 3213.3 Biology Major Elective Courses................................................................................... 3213.4 Streams.......................................................................................................................... 3313.5 Faculty Needs................................................................................................................ 3313.6 Course Descriptions...................................................................................................... 34

14 Mathematics Curriculum .................................................................................................. 39


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14.1 Mathematics Courses in SSE Core ............................................................................... 3914.2 Mathematics Core Courses ........................................................................................... 3914.3 Mathematics Major Elective Courses ........................................................................... 3914.4 Streams.......................................................................................................................... 4014.5 Faculty Needs................................................................................................................ 40

14.6 Sample Four Year Program .......................................................................................... 4114.7 Course Descriptions...................................................................................................... 4215 Computer Science Curriculum.......................................................................................... 59

15.1 Computer Science Courses in SSE Core ...................................................................... 5915.2 Computer Science Core Courses .................................................................................. 5915.3 Computer Science Major Elective Courses .................................................................. 5915.4 Streams.......................................................................................................................... 6015.5 Faculty Needs................................................................................................................ 6015.6 Sample Four Year Program .......................................................................................... 6115.7 Course Descriptions...................................................................................................... 62

16 Electrical Engineering Curriculum ................................................................................... 64

16.1 Electrical Engineering Courses in SSE Core ................................................................ 6416.2 Electrical Engineering Core Courses ............................................................................ 6416.3 Electrical Engineering Major Elective Courses............................................................ 6416.4 Streams.......................................................................................................................... 6516.5 Faculty Needs................................................................................................................ 6516.6 Sample Four Year Program .......................................................................................... 6616.7 Course Descriptions...................................................................................................... 67

Last Page....................................................................................................................................... 72


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1 Curriculum Committees

Physicso Dr Amer Iqbal

o Dr Asad Naqvi (Convener)o Dr Faheem Hussaino Dr Irfan Ullah Chaudhryo Dr Sabieh Anwaro Dr Tasneem Zehra

Chemistryo Dr Bilal Zuberio Dr Falak Shero Dr Hamid Zamano Dr Irshad Hussaino Dr Khalid Rasheed (Convener)

o Dr Tayyaba Asimo Dr. Usman Qazi

Biologyo Dr Fatimah Khwajao Dr Fridoon Ahmad (Convener)o Dr Hamid Zamano Dr Hassna Ramayo Dr Mohammed Tariqo Dr Shahid Khan

Mathematicso Dr. Arif Zaman

o Dr. Aslam Butt (Convener)o Dr. Faqir Bhattio Dr. Masood Hussain Shaho Dr. Naeem Qureshi

Computer Scienceo Dr. Hamid Abdul Basito Dr. Mian Muhammad Awaiso Dr. Muhammad Fareed Zaffaro Dr. Nabil Mustafao Dr. Naveed Arshad (Convener)o Dr. Shahid Masud

o Dr. Umar Saif Electrical Engineering

o Dr Abubakr Muhammad (Convener)o Dr Asad Abidio Dr Aun Abbaso Dr. Farhan Ranao Dr Jahangir Ikramo Dr Khurram Afridio Dr Nadeem Khan


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o Dr Shahab Baqaio Dr Shahid Masudo Dr Sohaib Khano Dr Tariq Jadoono Dr Zartash Uzmi

LUMS-Wide SSE Courses Committeeo Dr. Arif Zamano Dr. Sabieh Anwaro Dr. Zaeem Jafri (Convener)

SSE Curriculum Committeeo Dr. Abubakr Muhammado Dr. Ahmed Jan Durrani (Dean)o Dr. Asad Naqvio Dr. Aslam Butto Dr. Khalid Rasheedo Dr. Naveed Arshad

o Dr. Shafay Shamail (Convener)o Dr. Fridoon Ahmad (relplaced Dr. Shahid Khan)o Dr. Tariq Jadoon (Registrar)


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2 Foreword

This curriculum is the outcome of the efforts of the SSE Curriculum Committee (SSECC) forfour year programs in the areas of Physics, Chemistry, Biology, Mathematics, Computer

Science, and Electrical Engineering to be offered in the School of Science and Engineering,LUMS. Input was also sought for the University core requirements through the Registrar, Dr.Tariq Jadoon. The program is based on semester system starting from the Fall of 2009. Theoutline of the curriculum is based on the earlier work done by the Dr. Khurram Afridi and histeam. The current report is the result of the hard work done during the period starting fromFebruary 2009 to May 2009 by the members of the seven curriculum committees for therespective areas. These committees and their members are listed in Section 1.

I would like to take this opportunity to thank all of my colleagues and members of the respectivecommittees for their input in making this curriculum report possible. I hope that this report willserve as the basis for building a world class curriculum for the School of Science and

Engineering.

Shafay Shamail

May 31, 2009


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0.29 06-04-0908-04-09

University CoreBiology Curriculum UpdatedChemistry Curriculum - readjusted

Tariq JadoonFridoon AhmadKhalid Rasheed

0.30 13-04-09 Math Transition Plan Aslam Butt0.31 15-04-09 Math Updated Curriculum

Math FeedbackMath Feedback

Aslam ButtSultan SialZaeem Jafri

0.32 29-04-09 Biology Curriculum UpdatedBiology Course Descriptions

Fridoon AhmadFridoon Ahmad

0.40 29-04-09 Physics Course OutlinesPhysics Faculty Needs

Asad NaqviAsad Naqvi

0.41 30-04-0906-05-0908-05-09

MOM SSE CC 7thMeeting on (29-04-09)Phy Curriculum UpdatedBio Course Descriptions Updated

Zara QizilbashAsad NaqviFridoon Ahmad

0.50 17-05-09 Foreword and Summary Shafay Shamail1.0 18-05-09 SSE Curriculum Final Report v1.0 Shafay Shamail

0.51 24-05-09 Feedback on the SSE CC v 0.50Chemistry MinorUpdated Chemistry Curriculum

Math Updated Course DescriptionMath Credits Updated

Shafay ShamailKhalid RasheedKhalid Rasheed

Aslam ButtShafay Shamail

1.1 24-05-09 SSE Curriculum Final Report v1.1 Shafay Shamail

0.52 25-05-0926-05-0928-05-09

Physics Junior Year updateChemistry Curriculum Update (sophomore year)Math Curriculum Update (Credits adjustment)

Asad NaqviKhalid RasheedAslam Butt

1.2 31-05-09 SSE Curriculum Final Report v1.2 Shafay Shamail


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4 Summary

The philosophy of LUMS SSE curriculum is to impart essential knowledge of science andprovide them with engineering tools so that they are able to build their independent thinking and

solve problems faced by humanity. The students shall be able to grasp the concepts and applythem in their real life. LUMS SSE Graduates are expected to excel in industry and academiaalike. Their analytical skills along with their ability to perform to their best shall be at its finest.The overall objective of the SSE Curriculum is to give impetus to the inquisitive nature of thestudents so that they are able to perform independent research. The structure or the SSECurriculum is summarized below.

The first year of the SSE curriculum is highly focused on teaching fundamental concepts ofMathematics, Physics, Chemistry, Biology, Computing, and Engineering. Second year exposesthe students to fundamental courses of their respective majors while continuing with the SSEcore courses. In their third year students are able to experiment with different elective streams of

their interest in their major area of specialization. The aim is that by the fourth year the studentsare brought to a level where they are able to do independent research of exceptional quality. Thestudents are also required to take courses to meet the University requirements. These courses aredesigned to provide the SSE Graduates soft skills, impart critical thinking and inculcate socialresponsibility.

All the courses are defined in credit hours. The student load for each credit hour of a taughtcourse is defined as one hour of class room teaching accompanied by a two hour of out of classwork, where as for one credit hour of lab work a student is expected to spend three hours in lab.

A minimum of 130 credits are required to be completed for graduation. These requirements are

divided as: University Core of 28 credits, SSE Core of 40 credits, and Major requirements of 62credits. The Major requirements are further divided into Major Core requirements, MajorElectives and Free Electives.

In the proposed SSE Curriculum the number of Core and Elective credits required by each Majorare: Mathematics 55 credits, Physics 51 credits, Chemistry 56 credits, Biology 53 credits,Computer Science 57 credits, and Electrical Engineering 58 credits.

Highlight of this report include:

University Core Requirements

SSE Core Courses Major Core Requirements Major Elective Requirements Free Electives SSE Service Courses


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4.1 University Core Requirements

The University core requirements are of 28 credits. These are suggested by the UniversityUndergraduate Program Committee through the University Registrar. These required credits aredivided into three categories of courses. In the first category there are three specific courses:

Writing and Communication, Islamic Studies, and Pakistan Studies. In the second category onecourse is to be taken either from History, or from Philosophy, or from Literature satisfyingHumanities requirements. For the remaining third category at least three courses are to be takenfrom outside of the SSE group. These include courses from Economics, Accounting and Finance,Social Studies, and/or Law.

The objectives of the University-wide core requirements are manifold. Apart from fulfilling theregulatory requirements of the Undergraduate Curriculum as recommended by the Governmentof Pakistan through Higher Education Commission (HEC) the University-wide required coursesensure uniformity in imparting a breadth of knowledge in the areas of humanities and socialsciences. The objective is to develop critical thinking and impart social awareness and

responsibility among LUMS graduates.

4.2 SSE Core Courses

LUMS SSE provides an integrated education that not only gives the students a sound training intheir professional fields, but also develops their intellectual breadth, character and physical well-being. Over the course of the 4-year program, all undergraduates are required to take courses inscience, mathematics, technology, humanities and social sciences. The foundation of the SSEcurriculum is a strong science and mathematics core that is required of all majors. The SSEshares the belief that for a young person to grow into a first-rate scientist or engineer, his/her

education must be founded on a broad and thorough understanding of the workings of nature.Today, this understanding is derived from physics, chemistry, and biology with mathematics asthe common language of modeling and prediction. This core also prepares students forinterdisciplinary modern research by blurring artificial boundaries between disciplines, helpingstudents recognize and exploit connections between different branches of sciences andengineering. Thus most of the freshman (first) year courses and some of the sophomore (second)year courses are required of all majors. They offer a well-balanced mix of theory and originalstate-of-the-art laboratory experiments.

The SSE core courses are of 40 credits divided into the following: Mathematics 15 credits,Physics 13 credits, Chemistry 5 credits, Biology 4 credits, and Computing 3 credits.

4.3 Major Core Requirements

Every major within SSE is required to specify a set of courses required to complete thatrespective major. These set of courses can range from a minimum of 30 credits to a maximum of48 credits. For each SSE major these are proposed as: Mathematics 33 credits, Physics 36credits, Chemistry 47 credits, Biology 40 credits, Computer Science 45 credits, and ElectricalEngineering 41 credits.


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6 Graduation Requirements

Graduation Requirement = Min 130 credit hours (HEC Guidelines)University Core Requirements = 28 credit hours (Humanities, Social Sciences, etc)

SSE Core Requirements = 40 credit hoursMajor Requirements = Min 62 credit hours

Core Required Courses = 30 48 credit hoursMajor Electives = 9 24 credit hoursFree School Electives = 9 24 credit hours

Note:Graduation Requirement

Minimum credits to graduateUniversity Core Requirements

English Writing CoursePakistan StudiesIslamic Studies

SSE School RequirementsCourses required by the SSE

Major RequirementsCore Required Courses = courses required to do majorMajor Electives = elective courses as required by the majorFree Electives = elective courses from any area(Major Core + Major Electives = Min 50 credits)


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7 Structure of SSE Core

The major-wise structure of the SSE Curriculum is summarized in Table 1.

Table 1: Major-wise Credits Hour Distribution

Major Requirements62 Credits

Min 50 Credits

UniversityRequirement

SSERequirement

Major CoreRequirement

MajorElectives

FreeElectives

Total

Credits Credits Credits Credits Credits Credits

30-48 9-24 9-24 130Physics 28 40 36 15 12 131

Chemistry 28 40 47 9 9 133

Biology 28 40 40 13 9 130

Math 28 40 33 22 9 132

CS 28 40 45 12 9 134

EE 28 40 41 17 6 132


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PART I


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9 SSE Courses for Rest of the University

Proposed Courses:

Currently Offered Courseso CS 101 Problem Solving Using Computers (Computational Problem

Solving)o Math 132 Probability and Statistics

Basic Science Courseso SSE --- Physics 1 (Mechanics)o SSE --- Chemistry 1 (Principles of Chemistry)o SSE --- Biology 1 (Freshmen Biology)

New Courses Proposedo SSE --- History of Science


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10 Structure of SSE Core

10.1 Freshman Year

10.1.1 Fall Semester

Course Credits Load

1 Math 1 Calculus 1 (Single Variable Calculus) 3 3-0-62 Physics 1 Mechanics (including special relativity

towards end)3 3-0-6

3 Principles of Chemistry 3 3-0-64 Experimental Physics Lab 1 0-3-05 Writing Course [Univ. Core] 4 4-0-8

6 Introduction to Organic Chemistry 1 1-0-2Total 15 14-3-28 (45)

10.1.2 Spring Semester

Course Credits Load

1 Math 2 Calculus 2 (Multi-Variable Calculus) 3 3-0-62 Physics 2 Electricity and Magnetism 3 3-0-63 Modern Biology 3 3-0-64 Biology Lab 1 0-3-0

5 Introduction to Computing (CS 102) 3 2-3-66 Pakistan Studies [Univ. Core] 2 2-0-47 Experimental Chemistry Lab 1 1 0-3-0Total 16 13-9-28 (50)

10.2 Sophomore Year

10.2.1 Fall Semester

Course Credits Load1 Math 3 (Intro to Differential Equations) 3 3-0-62 Physics 3 (Modern Physics) 3 3-0-63 Islamic Studies (3) [Univ. Core] 2 2-0-44 Major Core 15 Major Core 2Total 16 16-0-32 (48)


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10.2.2 Spring Semester

Course Credits Load1 Math 4 (Linear Algebra - I) 3 3-0-62 Physics 4 Heat and Thermodynamics 3 3-0-6

3 Major Core 34 Major Core 45 Humanities/Social Science/etc course 4 3-0-6Total 16 16-0-32 (48)

10.3 Junior and Senior Year

10.3.1 Fall Semester Junior Year

Course Credits Load

1 Probability 3 3-0-6

All courses, other than the Humanities/Social Science/etc courses needed to meet theUniversity-wide core requirements (average 1 per semester), are determined by the major.


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PART II


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11 Physics Curriculum

11.1 Physics Courses in SSE Core

Course Credits Load Semester Year

1 Physics I Mechanics 3 3-0-6 Fall Freshmen2 Experimental Physics Lab 1 0-3-0 Fall Freshmen

3 Physics II - Electricity and Magnetism 3 3-0-6 Spring Sophomore

4 Physics III - Modern Physics 3 3-0-6 Fall Sophomore

5 Physics IV - Heat and Thermodynamics 3 3-0-6 Spring Sophomore

TOTAL 13 12-3-24

11.2 Physics Core Courses


1 Waves and Optics 3 3-0-6 Fall Sophomore

2 Quantum Mechanics I 3 3-0-6 Spring Sophomore

3

Mathematical Methods in Physics andEngineering - I

3 3-0-6 Spring Sophomore

4 Quantum Mechanics II 3 3-0-6 Fall Junior

5 Statistical Mechanics 3 3-0-6 Fall Junior

6 Experimental Physics II 3 3-0-6 Fall Junior

7 Atomic, Molecular and Laser Physics (*) 3 3-0-6 Fall Junior

8 Classical Mechanics 3 3-0-6 Spring Junior

9 Condensed Matter Physics (*) 3 3-0-6 Spring Junior

10 Electromagnetic Theory 3 3-0-6 Fall Senior

11 Astrophysics (*) 3 3-0-6 Fall Senior

12 Senior Project-I 3 0-0-12 Fall Senior

13 Particle and Nuclear Physics (*) 3 3-0-6 Spring Senior

14 Senior Project-II (3) 3 0-0-12 Spring SeniorTOTAL 36 (*) 30-0-84

(*) Students will only be required to take two courses out of Atomic, Molecular and LaserPhysics, Condensed Matter Physics, Astrophysics, Particle and Nuclear Physics.

11.3 Physics Major Elective CoursesCourse Credits Load Semester Year

1

Mathematical Methods for Physics andEngineering II

3 3-0-6 Spring Junior

2 Experimental Physics III 3 3-0-6 Spring Junior

3 Advanced Quantum Mechanics 3 3-0-6 Fall Senior

4 General Relativity and Cosmology 3 3-0-6 Spring Senior


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11.4 Streams

Physics streams are yet to be defined.

11.5 Faculty Needs

Academic Year 2009-2010 6-7 Faculty MembersAcademic Year 2010-2011 9-10 Faculty MembersAcademic Year 2011-2012 12-13 Faculty MembersAcademic Year 2012-2013 15-16 Faculty Members


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11.6 Course Descriptions

Classical Mechanics

Introduces the principles of classical mechanics. Straight-line kinematics; motion in a plane;relative inertial frames and relative velocity; forces; particle dynamics with force; simpleharmonic motion; work, conservative forces, potential energy and conservation of energy;conservation of momentum, center of mass and the center of mass frame of reference; rigidbodies and rotational dynamics; conservation of angular momentum; central force motions; fluidmechanics.

Experimental Physics 1

This is an inter-disciplinary core laboratory that will expose students to the experimental culturethrough a set of carefully selected experiments from different branches of physics. Theexperiments will train students in computational programming, error analysis, concepts of

accuracy and precision, measurement units and dimensions. Students will learn how to analyze,store, process and display data with special emphasis on curve fitting, plotting and regression.Students will be exposed to safety, kinds and types of materials and important test andmeasurement apparatus, technical report writing, mathematical modelling of natural phenomenaand design of simple experiments to test hypotheses. Furthermore, they learn about thecorrelation between equations, text and illustrations. All experiments will be supervised andguided.

Electromagnetism

Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, ElectricField; Gausss law; Electrostatic Potential; Capacitors; conductors and dielectrics. Electrostatic

energy. Electric currents, and electric circuits; Kirchoff laws; Magnetic fields, Biot-Savart lawand Ampere's law. Magnetic materials. Time-varying fields and Faraday's law of induction;Displacement Current and Maxwell's equations; Electromagnetic Waves; Poynting Vector.

Waves and Optics

Mechanical oscillations and waves; simple harmonic motion, principle of superposition, dampedand forced vibrations and resonance; coupled oscillations, and normal modes; vibrations ofcontinuous systems; reflection and refraction; phase and group velocity. Optics; wave solutionsto Maxwell's equations; polarization; Snell's Law, interference, Huygens's principle, Fraunhoferdiffraction, and gratings.

Modern PhysicsExperimental basis of quantum physics: photoelectric effect, Compton scattering, photons,Franck-Hertz experiment, the Bohr atom, deBroglie waves, and wave-particle duality.Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states,the Heisenberg uncertainty principle. Solutions to Schroedinger's equation in one dimension:transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonicoscillator. Schroedinger's equation in three dimensions: central potentials and introduction tohydrogenic systems.


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Thermodynamics and Statistical Physics

Introduction to Thermodynamic concepts, conservation of energy and the first law ofthermodynamics. Reversibility, Entropy, heat engines and the second law. Concepts ofmacroscopic variables and thermodynamic equilibrium. Fundamental assumption of statisticalmechanics, microcanonical and canonical ensembles. Numerous examples illustrating a wide

variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electronsin solids, and noise in electronic devices.

Quantum Physics 2

Formal sturcture of quantum mechanics: states, operators, representations, and the Diracnotation. Elements of measurement theory. Harmonic oscillator: operator algebra, states.Quantum mechanics in three-dimensions: central potentials and the radial equation, bound andscattering states. Angular momentum: operators, algebra of commutators, eigenvalues andeigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclearmagnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan seriesand coefficients, spin systems, and allotropic forms of hydrogen.

Quantum Physics 3

Continuation of Quantum Physics 2. Time-independent approximation methods: degenerate andnondegenerate perturbation theory, variational method, Born-Oppenheimer approximation,applications to atomic and molecular systems. The structure of one- and two-electron atoms:overview, spin-orbit and relativistic corrections, fine structure, variational approximation,screening, Zeeman and Stark effects. Charged particles in a magnetic field: Landau levels andinteger quantum hall effect. Scattering: general principles, partial waves, review of one-dimension, low-energy approximations, resonance, Born approximation. Time-dependentperturbation theory.

Statistical Mechanics

Review of Probability distributions for classical and quantum systems. Microcanonical,canonical, and grand canonical partition-functions and associated thermodynamic potentials.Conditions of thermodynamic equilibrium for homogenous and heterogenous systems.Applications: non-interacting Bose and Fermi gases; magnetic systems, polymer solutions; phaseand reaction equilibria, critical phenomena. Fluctuations, correlation functions andsusceptibilities, and Kubo formulae.


This an experimental lab based course in which the students will be expected to design andperform advanced physics experiments. These experiments will test the students' understandingof basic physics and will revolve around the themes of atomic physics, lasers, fluid mechanics,heat and thermodynamics, nuclear physics, medical physics, condensed matter physics,computation and simulation, microscopy and spectroscopy, optics and quantum optics, wavephenomena, low temperature physics, materials science climatology and atmospheric physics.The students are expected to write and submit technical reports of the experiments. Students willbe exposed to sophisticated physical instruments.


In this advanced physics lab, students will be allowed to choose research based experimentalprojects centering around different areas of physics, both fundamental and applied. The course


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will be supervised by various Faculty members and will involve focused research. Emphasis willbe on the creation and design of new experimental setups and their subsequent employment totest a physical principle, demonstrate a natural occurence, measure a property or to achieve anengineering task. Research reports will be submitted at the end of the project.

Condensed Matter PhysicsStructure and properties of materials from classical and quantum mechanical perspectives.Topics covered include crystal structure and lattices; crystal imperfections; diffusion; atomicvibrations; thermal properties of materials; electronic properties of materials with discussions ofFermi-Dirac statistics, the band theory, Fermi surface and Brillouin zone; description ofsemiconductors; dielectric and magnetic properties of materials Introduction tosuperconductivity and superfluidity; semi-solid and amorphous materials; surface physics andexperimental techniques to probe materials such as X-ray and electron diffraction, surface probemicroscopy.

Atomic and Laser Physics

Electronic structure of one-electron atoms and their interaction with electromagnetic radiationand external electric and magnetic fields; fine and hyperfine structure, Zeeman, Lamb and Starkshifts. Building up of atoms to construct molecules, their electronic, rotational and vibrationalstructure and the role of electron and nuclear spin. Different kinds of atomic and molecularspectroscopy with emphasis on experimental techiques. Lasers, their mechanics, kinds andproperties. Introduction to Bose-Einsten condensation; atom optics and atomic clocks; magneticresonance; ion traps and optical cavities.

Classical Mechanics 2

Formal introduction to framework of classical mechanics, generalized coordinates, Lagrangianand Hamiltonian formulations, canonical transformations, and Poisson brackets. Euler-Lagrangeequations, Hamilton's equations of motion used to describe central force motion, scattering,perturbation theory and Noether's theroem.

Electromagnetism 2

Electrostatics, magnetostatics; electromagnetic properties of matter. Time-dependentelectromagnetic fields and Maxwell's equations. Maxwells Equations in Matter.Electromagnetic waves, emission, absorption, and scattering of radiation. Relativisticelectrodynamics and mechanics.

Mathematical Methods for Physics I

Complex analysis. Integral transforms. Ordinary and partial differential equations withapplications to physical problems. Perturbation theory.


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12 Chemistry Curriculum

12.1 Chemistry Courses in SSE Core


1 Principles of Chemistry 3 3-0-6 Fall Freshmen2 Experimental Chemistry Lab 1 0-3-0 Fall Freshmen

3 Experimental Chemistry Lab 1 0-3-0 Spring FreshmenTOTAL 5 3-6-6

12.2 Chemistry Core Courses


1 Organic Chemistry 3 3-0-6 Fall Sophomore

2 Genetics 3 3-0-6 Fall Sophomore

3 Physiology 2 2-0-4 Fall Sophomore

4 Biochemistry 3 3-0-6 Spring Sophomore

5 Physical Chemistry I 3 3-0-6 Spring Sophomore

6 Organic Lab. I 1 0-3-0 Spring Sophomore

7 Inorganic Chemistry I 3 3-0-6 Fall Junior

8 Analytical Chemistry 3 3-0-6 Fall Junior

9 Inorganic Chem. Lab. I 1 0-3-0 Fall Junior

10 Physical Chem. Lab. I 1 0-3-0 Fall Junior

11 Spectroscopic Techniques 3 3-0-6 Fall Junior

12 Organic Chemistry II 3 3-0-6 Spring Junior13 Inorganic Chemistry II 3 3-0-6 Spring Junior

14 Physical Chemistry II 3 3-0-6 Spring Junior

15 Organic Lab. II 1 0-3-0 Spring Junior

16 Inorganic Lab. II 1 0-3-0 Spring Junior

17

Organic/Inorganic/PhysicalChemistry III

3 3-0-6 Fall Senior

18

Research Project I for physical,organic and inorganic majors (3)

3 0-0-12 Fall Senior

19 Physical Chem. Lab. II (1) 1 0-3-0 Fall Senior

20

Research Project II for physical,organic and inorganic majors (3)

3 0-0-12 Spring Senior

TOTAL 47 35-15-94

12.3 Chemist ry Major Elective Courses


1 Green chemistry 3 3-0-62 Atmospheric chemistry & climate 3 3-0-6


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change3 Chemistry of Nanomaterials 3 3-0-64 Nanobiotechnology 3 3-0-65 Colloid science 3 3-0-66 Electronic and magnetic materials 3 3-0-6

7 Materials chemistry 3 3-0-68 Soild electrolytes 3 3-0-69 Electronic structures in the condensed

state3 3-0-6

10 Organometallic chemistry 3 3-0-611 Bio-organic chemistry 3 3-0-612 Organic and Inorganic polymers 3 3-0-613 Computer simulations /molecular

dynamics3 3-0-6

14 Group theory and elements ofsymmetry

3 3-0-6

15 Biological Chemistry II 3 3-0-616 Physical Inorganic Chemistry 3 3-0-617 Crystal structure analysis 3 3-0-618 Chemistry of Biomolecules and

Natural Product Pathways3 3-0-6

19 Protein Folding and Human Disease 3 3-0-620 Enzymes: Structure and Function 3 3-0-621 Bioinorganic Chemistry 3 3-0-622 Organometallic Chemistry 3 3-0-623 Inorganic Ring Chemistry 3 3-0-624 Modern diffraction techniques 3 3-0-625 Reactive Intermediates 3 3-0-626 Liquids and Solutions 3 3-0-6

NOTE: Electives courses can be offered if there is sufficient interest and that a minimum numberof students register for the course to be offered.

12.4 Chemistry Minor

A minor in chemistry can be earned by taking the following courses:1. Physical Chemistry I: (3 credit hours)2. Inorganic Chemistry I: (3 credit hours)3. Physical/Inorganic Chemistry Laboratory: (1 credit hour)

4. Organic Chemistry I: (3 credit hours)5. Organic Chemistry Laboratory I: (1 credit hour)6. Organic/Inorganic/Physical Chemistry Laboratory II: (1 credit hour)Choose any two of the followings:

7. Organic Chemistry II: (3 credit hours)8. Physical Chemistry II: (3 credit hours)9. Inorganic chemistry II: (3 credit hours)10. Analytical Chemistry: (3 credit hours)11. Bioinorganic Chemistry: (3 credit hours)


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12.5 Streams

Physical Chemistry Organic Chemistry Inorganic Chemistry

12.6 Faculty NeedsAcademic year 2009-2010: 4 5 Faculty.Academic year 2010 2011: 7 8 Faculty.Academic year 2011 2012: 10 11 FacultyAcademic year 2012 2013 : 12 13 Faculty


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Principles of Chemistry (3)

This is an introductory course providing a common background for students with a wide range ofhigh school experiences. It also serves as a foundation course for students who will go on tomajor in chemistry. This introduction ensures that students understand basic chemical conceptssuch as stoichiometry, states of matter, atomic structure and bonding, thermodynamics, equilibriaand kinetics.

Chemistry Lab CH 110 (1)

This is designed to be a semester long lab that exposes students to basic laboratory skills such assafe lab practices, keeping a lab notebook, use of electronic balances, volumetric glassware,preparation of solutions, chemical measurements using pH and conductivity meters andspectrophotometers. Emphasis is placed on data analysis and report writing.

Physical Chemistry I (3) (Pre-Req: Calculus I & 2)

Thermodynamics, chemical equilibria and kinetics. This is a foundation level course whichbuilds on the introductory course experience. It provides breadth and lays the groundwork forfurther in-depth course work.

Organic Chemistry I (3) (Pre-req: CH 101 and 102)

Basic organic chemistry. This includes a description of major classes of organic compounds,their structures, and reactivities. Emphasis will be placed on correlating reactivity and function.

Inorganic Chemistry I (3) (Pre-Req: CH 101 and 102)

Will include the electronic structures of the elements and how this impacts their properties andpositions in the periodic table. Bonding theories will be discussed as well as how symmetry canbe used to analyze bonding in a variety of molecules from all branches of chemistry.

Organic Chemistry II (3) (Pre-Req: Organic I)

This is an extension of organic I that treats the reactions of various functional groupsmechanistically and introduces UV-visible and IR spectroscopy.

Organic Lab. I (1)

This introductory organic lab. Will involve synthetic and analytical procedures to introducestudents to basic laboratory instrumentation and processes.

Physical Chemistry II (3) (Pre-Req: Calculus 1 &2)

This will introduce the fundamental ideas of Quantum Mechanics, Schrodinger wave equationand its application to hydrogen atom, helium atom, hydrogen molecule and diatomic molecules.In the second part we will show how the thermodynamic properties of a macroscopic sample ofmatter can be expressed in terms of the energy levels of individual molecules and the interactionsbetween them.


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Inorganic Chemistry II (3) (Pre-req: Inorganic I)

Coordination/complexes of transition metals and the related chemistry of organometallics, anarea that has contributed to catalyst science and remains of central importance to both academicand industrial research. Brief introduction to bioinorganic chemistry.

Analytical Chemistry (3)An integrated view of chemical, biological methods and instrumental techniques that provides atheoretical basis of solving real chemical problems.

Inorganic Chem. Lab. I (1) (Pre-req: CH 110)

The goal is to give students experience with a range of techniques used in the synthesis andcharacterization of inorganic compounds (coordination, organometallic, main groupcompounds).

Physical Chem. lab. I (1)

Determination of heats of combustion, enthalpies of reaction, phase changes, thermal

conductivity and viscosity of gases.

Biological Chemistry I (3) (Pre-req: Organic I & II)

Structure of DNA double helix, hydrogen bonding, van der Waals interactions, the hydrophobiceffect, the role of proteins as structural units, and as catalysts and receptors. Also discussed willbe basic principles of metabolism and various metabolic pathways.

Organic Lab. II (1)

Multistep syntheses including isolation and purification of products. Deducing structures usingspectroscopic and computational data.

Inorganic Lab. II (1)

Students use synthetic methods making use of dry boxes, Schlenk tubes, high temperaturefurnace/heated tube, vacuum lines, high pressure autoclaves and electrochemical apparatus.

Organic/Inorganic/Physical Chemistry III (3)

Advanced Organic chemistry will include treatment of reaction mechanisms involvingkinetic isotope effects, concerted reactions based on frontier orbitals, structures of transitionstates, calculation of activation energies and a modern treatment of synthetic strategies suchas retrosynthetic analyses.

Inorganic chemistry will explore the chemistry of s and p block elements. The chemistry ofLanthanides and Actinides will be discussed, highlighting their differences to transition metal

chemistry. Physical chemistry will include molecular spectrcoscopy dealing with rotational spectra ofmolecules and determination of bond lengths. Also discussed will be vibrationalspectroscopy using harmonic and Morse oscillator models. Electron spectroscopy of atomsand simple molecules will be introduced.

Spectroscopic Techniques (3)

Basic techniques for organic structure determinations will be discussed. This will include UV-VIS and IR spectroscopy. Basic principles and applications of 1-D & 2-D proton and C13 NMR


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spectroscopy to organic structure determination . Fundamentals of mass spectroscopy to structuredetermination will also be discussed.

Physical Chemistry Lab II (1)

First order kinetic relaxation study using laser, enzyme kinetics and analysis of vibrational

spectra of simple molecules and conjugated polyene dyes.

Research Project for Organic, Inorganic and Physical Chemistry Majors (3)

Semester long research projects. Exceptional students might undertake year long projectsreported as a thesis for graduation with honors.


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13 Biology Curriculum

13.1 Biology Courses in SSE Core


1 Freshmen Biology 3 3-0-6 Spring Freshmen2 Freshmen Biology Laboratory 1 0-3-0 Spring Freshmen

TOTAL 4 3-3-6

13.2 Biology Core Courses


1 Organic Chemistry 3 3-0-6 Fall Sophomore

2 Genetics 3 3-0-6 Fall Sophomore

3 Physiology 2 2-0-4 Fall Sophomore

4 Biochemistry 3 3-0-6 Spring Sophomore

5 Physical Chemistry I 3 3-0-6 Spring Sophomore

6 Organic Lab. I 1 0-3-0 Spring Sophomore

7 Developmental Biology 3 3-0-6 Fall Junior

8 Cell Biology 3 3-0-6 Fall Junior

9 Computational Biology* 3 3-0-6 Fall Junior

10 Virology & Microbiology+ 3 3-0-6 Fall Junior

11 Junior Biology Laboratory 2 0-6-0 Fall Junior

12 Human Pathobiology# 3 3-0-6 Spring Junior

13 Systems Biology~ 3 3-0-6 Spring Junior14 Environmental Sciences 3 3-0-6 Spring Junior

15 Plant sciences 2 2-0-4 Spring Junior

16 Senior Project-I 3 0-0-12 Fall Senior

17 Senior Project-II 3 0-0-12 Spring SeniorTOTAL 40 (+) 31-9-86

*/~ Students will be required to take either Computational Biology or Systems Biology+/# Students will be required to take either Virology & Microbiology or Human Pathobiology+ two sets of courses have options

13.3 Biology Major Elective Courses


1 Population Biology 2 2-0-4

2 Immunology 2 2-0-4

3 Bioengineering 2 2-0-4

4 Nutrition 2 2-0-4

5 Physical Biochemisrty 3 3-0-6

6 Neuroscience 3 3-0-6


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7

Topics in Systems & ComputationalBiology

3 3-0-6

8 Nanobiology 3 3-0-6

9 Seminar course 1 1-0-2

10 Pharmacology & Toxicology 3 3-0-6

11 Epidemiology & Biostatistics 3 3-0-612 Structural Biology 3 3-0-6

13 Neuroscience II 3 3-0-6

14 Epigenetics & Evolution 3 3-0-6

15 Comparative Anatomy 3 3-0-6

16 Food Science and Technology 3 3

17 Seminar course 1 1-0-2

13.4 Streams

Molecular and Cellular Biology

GeneticsPharmacology & ToxicologyFood Science and TechnologyBioinformatics and Computational BiologyEnvironmental Sciences

13.5 Faculty Needs


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BI 101 Freshmen Biology: (Prerequisites: None)

Organized into six modules (1) Genetics (2) Biochemistry (3) Cell Biology (4) DevelopmentalBiology (5) Ecology (6) Mathematical Biology. Modules will develop from preceding modules;the systems being studied increasing in complexity from single molecules (hemoglobin) toecosystems (salt marsh). As far as possible ideas will be developed from first principles andquantitative analysis encouraged.

BI 110 Freshmen Biology Laboratory: (Prerequisites: None)

This introductory biology laboratory course will introduce students to experimental techniques inmicrobiology, biochemistry, molecular cell biology and developmental biology. Emphasis willbe placed on understanding of the design of the experiments and data analysis and interpretationin order to prepare the students for future research projects.

Organic Chemistry: (Prerequisites: CH101)

This course will be an introduction to organic chemical structures, nomenclature, bonding,chemical reactivity and stereochemistry. These concepts would then be used to study thechemistry of hydrocarbons, alkyl halides, alcohols, carbonyl compounds, carboxylic acids (withemphasis on amino acids) and aromatic compounds and ultimately relating these concepts tobiomolecules.

Genetics: (Prerequisites: 1 year biology experience at SSE)

This course will focus on principles of genetics with major emphasis on epigenetic mechanismsinvolved in gene regulation and development. The basic principles of genetics will be described

with an application to the study of biological functions at the level of molecules, cells andmulticellular organisms. Specific topics will include structure and function of genes,chromosome dynamics and genomes, gene regulation, use of genetic/epigenetic methods toanalyze the protein function and inherited diseases. In addition, biological variation resultingfrom recombination, mutation and selection will also be discussed. Students will also set upgenetic crosses to analyze effects of different mutations and resultant phenotypes.

Physiology: (Prerequisite: Freshman Biology).

Development of the principles of physiology from processes that have evolved from single cellsand developed into integrated control processes of cell and organ systems. Focus areas: cellphysiology, intercellular communication and coordination, homeostasis and the regulation of

physiological systems, and integration of physiological systems.

Biochemistry: (Prerequisites: Organic Chemistry).

Nucleic acids chemistry and structure. Metabolic pathways and enzymes. Vitamins and co-factors. Protein-protein interactions in signal transduction circuits. Feedback and control.Photobiology and spectroscopy. Macromolecular assemblies and small viruses.


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Physical Chemistry I: (Prerequisites: Calculus I & 2).

Thermodynamics, chemical equilibria and kinetics. This is a foundation level course whichbuilds on the introductory course experience. It provides breadth and lays the groundwork forfurther in-depth course work.

Organic Lab. I: ((Prerequisites: Organic Chemistry)An introductory organic chemistry course to learn and practice basic laboratory skills such asdistillation, crystallization, filtration, separation techniques and proceeding towards the synthesisand characterization of simple organic compounds.

Developmental Biology: (Prerequisites: for advance undergraduate students, 2 years

biology at SSE)

This course will teach how a fertilized egg develops into a complex organism with different celltypes yet containing same genetic information. The lecture series will focus on our currentunderstanding of the molecular mechanisms that regulate eukaryotic development. Vertebrateand invertebrate models will be discussed with major emphasis on Drosophila melanogaster.

Specific topics include formation of early body plan, cell fate determination, organogenesis,cellular memory, stem cells and nuclear reprogramming, cloning and issues in humandevelopment and diseases. The practical training will cover molecular methods used indevelopmental genetics using Drosophila melanogaster.

Cell Biology: (Prerequisites: two semesters of biology, and on semester of biochemistry)

This course is designed to give students a detailed perception of how cellular machinery works atthe molecular level. The students will learn about the mechanisms that govern the cell responseto both external and internal signals.

Computational Biology: (Prerequisites: Genetics, Biochemistry. Physical Chemistry I).

This course will cover sequence alignments, phylogeny, motif recognition, structure prediction(homology modeling, protein threading), maximum parsimony, Hidden Markov models, neuralnetwork algorithms, Perl programming basics. It will introduce 3D in silico simulation of cellarchitecture, metabolic network analysis, stochastic and molecular dynamics.

Virology & Microbiology (Prerequisites: one semester of biochemistry, genetics and cell

biology).

This course acquaints students with microorganisms and their activities. Topics includemicrobial cell structure and function, metabolism, microbial genetics, and the role ofmicroorganisms in disease, immunity. Furthermore biology of viruses, virus-host relationshipsand the molecular mechanisms of viral gene expression and regulation will be covered.

Junior Biology Laboratory. (Prerequisites: Freshmen Biology Laboratory, one semester of

biochemistry, genetics and cell biology).

This biology laboratory based course will cover problem based training of students wherestudents will learn how molecular biology, biochemistry and genetics can be efficiently used todissect gene function. Students will design and carry out experiments to address specificquestions about genes involved in the regulation of transcriptional regulation, cellulardevelopment, cell fate determination and cell death etc.


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Human Pathobiology: (Prerequisites: one semester of biochemistry and cell biology)

The course focuses on the basic cellular and molecular mechanisms some of the more prevalentof human diseases. Some of diseases that will be discussed in this course are as follows,inflammation, diseases of immunity, neoplasia, infectious diseases and aging.

Systems Biology: (Prerequisites: Genetics, Biochemistry. Physical Chemistry I).

The course will focus will on quantitative studies of cellular and developmental systems inbiology. It will examine the architecture of specific genetic circuits controlling microbialbehaviors and multicellular development in model organisms. The course will approach mosttopics from both experimental and theoretical/computational perspectives. Specific topicsinclude chemotaxis, multistability and differentiation, biological oscillations, stochastic effects incircuit operation, as well as higher-level circuit properties such as robustness. The course willalso consider the organization of transcriptional and protein-protein interaction networks at thegenomic scale.

Environmental Sciences: (Prerequisites: one semester of biology and chemistry each).The course will cover scientific principals, concepts and methodologies required to understandthe interrelationships of natural world to identify and analyze environmental problems bothnatural and human-made. Furthermore this course will allow students to evaluate the relativerisks associated with the above mentioned problems, and to examine alternative solutions forresolving or preventing them.

Plant sciences: (Prerequisites: one semester of biology)

This is an introductory course designed to introduce students to the basic plant taxonomy,anatomy, physiology. Additionally this course will also discuss plant responses to environmentalchallenges.

Population Biology (Prerequisites: Genetics)

Population biology course focuses on processes influencing population size and structure such asreproduction, survival, migration, and regulation of population growth. Population biology hasbeen used to establish sustainable harvest levels, recover populations, and evaluate projectimpacts.

Immunology: (Prerequisites: one semester of biochemistry and cell biology)

This course designed to familiarize students with cellular, molecular and biochemical aspects ofthe development of the immune system and the immune response. The course focuses on thedevelopment of the immune system and the function of its major components.

Bioengineering: (Prerequisites: Cell Biology, Physiology).

Students will be introduced to materials used in biomedical applications with focus on tissueengineering. Topics: material selection and processing, degradation mechanisms, cell-materialinteractions; optimising construct architecture; and transport through engineered tissues.Examples will include replacements for musculoskeletal elements as well as skin and liver.

Nutrition: (Prerequisites: one semester of biology and chemistry each).

Introduction, the physiology of taste, digestion and absorption, starches and cereals,carbohydrate nutrition, diabetes and dental health, pastry, quick breads, fiber and alcohol, yeast


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breads, water, fruits and vegetable, phytochemicals, protein nutrition, cheese, eggs, vegetariandiet, food allergies, minerals, supplements and what FDA approves, meat and meat ID, gelatin,fats and oils, emulsions, energy balance, obesity, solutions, sugars and syrups, nutrition andcoronary heart disease, nutrition and cancer, frozen desserts, nutrition, fitness and performance,nutrition in pregnancy and lactation, nutrition and the lifestyle, food safety.

Physical Biochemisrty: (Prerequisites: Biochemistry. Physical Chemistry I).

Enzyme mechanisms and energetics; transient-state kinetic analysis with associatedmethodologies {e.g. biological spectroscopy (fluorescence energy transfer, depolarizationlifetimes), analytical ultracentrifugation, hydrogen-deuterium exchange} and numerical methods.Reading and presentation of research literature will be a compulsory part of this advancedcourse.

Neuroscience IMolecular and Cellular Neuroscience: (Prerequisites: Genetics,

Biochemistry. Physical Chemistry I)

Ion channel structure and function, the action potential and electrical recordings. Synaptic

transmission and excitation-contraction coupling. Neurotransmitters structure, pharmacology(extracellular reception and intracellular signaling cascades). Gap junctions and chemicalcommunication. Visual, auditory and olfactory receptors.

Topics in Systems & Computational Biology: (Prerequisites: Computational Biology or

Systems Biology).

Students will research a selected topic under the guidance of a faculty member. The research willinvolve literature search, critique, presentation and a short study to address gaps in currentknowledge either by analysis of available databases or algorithm development. Evaluations willbe based on seminar presentations and a final project report.

Nanobiology: (Prerequisites: Anyone majoring in chemistry or biology can take this

course).

This multidisciplinary course is designed for students who are interested to work at the interfaceof nanoscale chemistry and biological systems to synthesize and explore the applications ofnanomaterials in biotechnology. It introduces basic and advanced concepts in nanomaterials(metal nanoparticles, quantum dots and carbon nanostructures) synthesis, characterization,properties and applications with specific reference to disease diagnostics and treatment, genemanipulation, environment and drug delivery etc. The major objective of this course is to enablestudents of different backgrounds (chemistry, biology, physics and engineering) to communicatewith each other and enable them to design research projects of multidisciplinary nature.

Pharmacology & Toxicology: (Prerequisites: one semester of biochemistry and cell

biology).

This course covers pharmacodynamics and toxicity of diagnostic and therapeutic agents.Principles of drug absorption, distribution, biotransformation and elimination. Consideration isgiven to antimicrobials, cancer chemotherapeutics, autonomic pharmacology, andneuropharmacology agents.


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Epidemiology & Biostatistics: (Prerequisite: None).

Data types, basic probability concepts, survey sampling, parametric and non-parametricinference, analysis of contingency tables, statistical models, experimental design, generalizedlinear models and survival data analysis.

Structural Biology: (Prerequisites: Biochemistry. Physical Chemistry I).Principles underlying current techniques for probing structures of macromolecules, includingstatic and dynamic light scattering, X-ray crystallography, NMR spectroscopy, electron and lightmicroscopy, atomic force microscopy and single molecule techniques.

Neuroscience IIDevelopmental and Organismal Neuroscience: (Prerequisites: Genetics,

Developmental Biology)

Evolutionary origins of excitability; neuronal cell differentiation and plasticity; neuro-genetics inmodel systems (worms, flies and zebrafish); neuroanatomy of the brain; information processingin the central nervous system.

Epigenetics & Evolution: (Prerequisites: 3 years biology)This advance undergraduate elective course will describe genotype-phenotype relationship withmajor emphasis on contribution of epigenetics as a decisive factor in genotype-phenotypecorrelation and how epigenetics may contribute to biological diversity, phenotypic variation andthe process of evolution. Potential link between macro/micro environment, epigenetics andprocess of development will be explored to explain not only the process of evolution but alsodisease like cancer. This course will also include seminar presentations by students based onresearch articles and review literature given to them.

Comparative Anatomy: (Prerequisites: Developmental Biology).

This course will examine the similarities of anatomy and phylogenetic relationships of majorvertebrate groups. Specifically phylogeny, ontogeny (development) and morphology in groupsranging from protochordates to highly derived vertebrates will be compared. Special emphasiswill be paid to the structure of anatomical features, emphasizing how anatomy relates to function(including comparisons of specialized features in organisms adapted to different conditions).

Food Science and Technology: (Prerequisites: Nutrition and biochemistry).

Introduction, food chemistry, food analysis, food biochemistry, food laws, nutrition labeling andfood regulation, food processing theory and methods, mixing and forming, separation andconcentration of food components, microbiology, fermentation and enzyme technology,irradiation, pasteurization and heat sterilization, evaporation and distillation, baking and roasting,frying, chilling, packaging, freezing, coating, food handling and safety, food contamination andtoxicology, food engineering principles, biotechnology, sensory evaluation, food businessmanagement and marketing.


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14 Mathematics Curriculum

14.1 Mathematics Courses in SSE Core


1 Math 1 Calculus - I 3 3-0-6 Fall Freshmen

2 Math 2 Calculus - II 3 3-0-6 Spring Freshmen

3 Math 3 (Linear Algebra - I) 3 3-0-6 Fall Sophomore

4 Probability 3 3-0-6 Fall Sophomore

5

Math 4 (Introduction to DifferentialEquations)

3 3-0-6 Spring Sophomore

TOTAL 15 15-0-30

14.2 Mathematics Core CoursesCourse Credits Load Semester Year

1 Advanced Calculus 3 3-0-6 Fall Sophomore

2 Set Theory 3 3-0-6 Spring Sophomore

3 Linear Algebra II 3 3-0-6 Spring Sophomore

4 Real Analysis 4 4-0-8 Fall Junior

5 Algebra - I 4 4-0-8 Fall Junior

6 Ordinary Differential Equations 3 3-0-6 Fall Junior

7 General Topology 3 3-0-6 Fall Junior

8 Complex Variables 4 4-0-8 Spring Junior

9 Numerical Analysis 3 3-0-6 Spring Junior

10 Honours Project I 3 3-0-6 Fall SeniorTOTAL 33 33-0-66

14.3 Mathematics Major Elective Courses



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14.4 Streams

Real, Complex & Functional Analysis Differential Equations & Boundary Value Problems Algebra Probability & Statistics Tools & Applications of Mathematics Number Theory, Discrete & Concrete Mathematics Mathematical Physics

14.5 Faculty Needs

Faculty = 13 (Two sections for each faculty member over the course of oneacademic year)

Teaching Assistant = 50 approximately (One TA for every 25 students over thecourse of one academic year)


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14.6 Sample Four Year Program

Credits Fall Credits SpringFreshman

3 Math 1 Calculus 1 3 Math 2 - Calculus 23 Physics 1 Mechanics 3 Physics 2 Electricity & Magnetism3 Principles of Chemistry 3 Bio Modern Biology1 Experimental Physics Lab 1 Bio Freshmen Bio Lab1 Introduction to Organic Chemistry 1 Experimental Chemistry Lab I

3 CS Computational Problem Solving4 Writing and Communication 2 Pakistan Studies

Sophomore3 Math Linear Algebra I 3 Math Intro to Differential Equations

4 Math Probability 3 Phys Heat and Thermodynamics3 Phys Modern Physics3 Advanced Calculus 3 Set Theory

3 Linear Algebra II2 Islamic Studies 4 Humanities/Social Science/etc course

Junior3 Real Analysis I 4 Complex Variables4 Algebra - I 3 Numerical Analysis3 ODE 3-4 Math Elective-300 level or above3 General Topology 3-4 Math Elective-300 level or above

3 Non SSE Elective3 Humanities/SS 3 Humanities/SS

Senior3 Honours Project - I 3 Honours Project - II3-4 Math Elective-300 level or above 3-4 Math Elective-300 level or above3-4 Math Elective-300 level or above 3-4 Math Elective-300 level or above3-4 Math Elective-300 level or above 3-4 Math Elective-300 level or above3 Non SSE Elective 3 Non SSE Elective3 Humanities/SS 3 Humanities/SS

Regular SSE CoreUnderline University CoreBold Major Core

Italic Electives


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MATH 101 Calculus-I (3)

Functions, limits, continuity, derivatives, implicit differentiation, rate problems, maxima andminima, elementary transcendental functions, Riemann Sums and the definite integral,techniques of integration, area and volumes of revolution, polar coordinated and parametricequations.Course Offering Period

Fall

Lead Instructor

Ismat Beg

Pre-requisites

One year each of high school algebra-I, algebra-II, geometry, pre-calculus or equivalent.

Designation

School Core

MATH 102 Calculus-II (3)

Infinite sequences and series, vector functions and curves in space, analytic geometry in threedimensions, vectors, functions of several variables, and partial derivatives, multiple integrals,theorems of Green, Gauss and Stokes.Course Offering Period

Spring

Lead Instructor

Ismat Beg

Pre-requisitesMATH 101- Calculus-I

Designation

School Core

MATH 201 Set Theory (3)

Axioms of set theory. Development of the systems of natural numbers and the real numbers.Axiom of choice, Zorn's lemma, well-ordering. The Schrder-Bernstein theorem, cardinalnumbers, ordinal numbers, transfinite induction, cardinal and ordinal arithmetics. This course isproof-based.Course Offering Period

Spring

Lead Instructor

Ismat Beg


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Pre-requisitesMATH 101 Calculus-I

Designation

Math Major

MATH 202 Advanced Calculus (3)

Differentiation of Vector function of one Variables, Arc length, Line integral, Differentiable

Functions (from Rnto Rm), Chain rule, Parametric representation of surface in space, Explicit /Implicit representation, Normals to surfaces given parametrically, Normals to surface givenexplicitly, Plane polar Co-ordinates, Spherical Polar Co-ordinates, Cylinderical Polar Co-ordinates, Linear Transformation & Matrices, Continuity of transformations, Properties ofdifferentiable transformations, Inverse Function Theorem, Implicit Function Theorem.Course Offering Period

Fall

Lead Instructor

Ismat Beg

Pre-requisitesMATH 102 Calculus-II

Designation

Math Major

MATH 211 Introduction to Differential Equations (3)

First order differential equations; Modeling; second order linear equations; Damped motion inmechanical and electrical systems; Power series solution, eigen-values and eigen- vectors;system of first order linear equations; stability and qualitative properties of nonlinearautonomous systems in the plane; Fourier series; Separation of variables and Partial DifferentialEquations.Course Offering Period

Spring

Lead Instructor

TBA


Designation

School Core

MATH 221 Linear Algebra-I (3)

Systems of linear equations. Matrix algebra. Determinants. Complex numbers. Eigenvalues.Diagonalization and applications.


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Course Offering Period

Fall

Lead Instructor

TBA


Designation

School Core

MATH 222 Linear Algebra-II (3)

Vector Spaces, Linear Independence, Bases, Dimension, Linear Transformations, Matrices,Change of Bases, Linear Functionals, System of Linear Equations, Eigenvalues and Eignvectors,Diagonalization, Inner Products, Orthonormalization and QR Factorization, Quadratic Forms,

Jordan Canonical Form and Applications.Course Offering PeriodSpring

Lead Instructor

TBA

Pre-requisitesMATH 221 Linear Algebra - I

Designation

Math Major

MATH 231 Probability (4)

Counting, Basic Axioms, Independence, conditional probability, random variables, moments,some discrete and continuous distributions, jointly distributed random variables, conditionalexpectation, limit theorems, simulation of random variables.Course Offering Period

Fall

Lead InstructorArif Zaman

Pre-requisitesMATH 102 Calculus-IIDesignation

School Core

MATH 232 Statistics (4)

Basic Probability, Expected value, Random Variables, Binomial and Poisson distribution andtheir fitting. Concept of Statistics, Basic Terminology, Experiment control experiment, Single


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blind and double blind, Descriptive and Analytical study, Cross Sectional and Cohort study,Variable, Independent and Dependent Variable, Collection and classification of dataSummarization of data, graphical representation of qualitative and quantitative data, Histogramfor equal and unequal interval, Descriptive statistics (measures of Location and Dispersion)Coefficient of Variation and Application of Chebyshevs inequality Fitting of straight line

Method of Least square Linear Regression, Fitting and interpretation the coefficients,2

R ,standard error of estimate etc. Continue Linear Regression, Simple and Rank Correlation, Surveysampling and different sample design, Estimation of sample size, Sampling distribution of meanand idea of central limit theorem and standard error. Confident interval for mean, proportion andvariance for single and two samples. Hypothesis tests for mean for single and two samples F-

Test and Analysis of variance (One way Classification) Chi square distribution, 2 Goodness of

fit test 2 Independence test, Contingency Tables.


Fall / spring

Lead Instructor

TBA

Pre-requisitesMATH 231 - Probability

Designation

Elective

MATH 261 Foundations of physics-I

This calculus-based course covers mechanics, gravitation, oscillations, and thermodynamics.Course Offering Period

Fall

Lead Instructor

Zaeem Jafri

Pre-requisitesMATH 102 Calculus- II

Designation

ElectiveMATH 262 Foundations of physics-II

Electricity, magnetism, wave motion.Course Offering Period

Spring

Lead Instructor

Zaeem Jafri



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Designation

Elective

MATH 301 Real Analysis-I (3)

The real number system, sequences and series, limit of functions, continuous and uniformcontinuous functions, monotone functions, differentiable function, Taylor theoremCourse Offering Period

Fall

Lead Instructor

Mujahid Abbas


DesignationMath Major

MATH 302 Complex Variables (4)

Analytic functions, contour integration, residue calculus, conformal mapping.Course Offering Period

Spring

Lead Instructor

Mujahid Abbas

Pre-requisitesMATH 102 Calculus-II, MATH 221 Linear Algebra-I

Designation

Math Major

MATH 303 Complex Analysis (4)

The Algebra and Geometry of complex numbers, Complex Functions and Linear Mappings, the

Mappings nzw = and nzw1

= , Limits and Continuity of complex valued functions, Branches ofMulti-valued Functions, the Reciprocal Transformation, Differentiable and Analytic Functions,the Cauchy - Riemann equations, Harmonic functions, Geometric Series and Convergence tests,

Power series functions, Complex logarithm and complex exponents, Trigonometric, hyperbolic,inverse trigonometric and hyperbolic functions, Complex Integrals, Contours and Contourintegrals, Cauchy - Goursat theorem, Fundamental theorems of integration, Cauchys integralformula, Taylors series representations, Laurent Series Representation, Singularities, Zeros andPoles, Residue Theorem and Calculation of Residues, Trigonometric integrals, ImproperIntegrals.Course Offering Period

Fall


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Lead Instructor

Ismat Beg


Designation

Elective

MATH 304 General Topology (3)

Metric spaces, Topological spaces, Continuity and Homeomorphisms, Product spaces,Introduction to Separation Axioms, Introduction to Compactness, Introduction to Connectedness.Course Offering Period

Fall

Lead Instructor

Masood Hussain Shah

Pre-requisitesMATH 301 Real Analysis

Designation

Math Major

MATH 311 Ordinary Differential Equations (3)

Modeling with linear equations; Population dynamics and related problems; Lipschitz continuity;

existence and uniqueness of solutions; first-order difference equations and equilibrium solutions;reduction of order of a second order homogeneous equation; mechanical and electricalvibrations; solution of 3rdand higher order linear equations with constant coefficients; variationof parameters; series solutions near regular singular point ( Frobenius method);Bessel ,Legendreand Hermite equations; Laplace transform with application to initial-value and boundary-valueproblems; competing species; predator-prey equations; Liapunovs second method and Liapunovfunctions; numerical solutions by Euler, Taylor and Runge-Kutta methods; local truncationerrors.Course Offering PeriodFall

Lead InstructorTBA

Pre-requisitesMATH 211 Introduction to Differential Equations

Designation

Math Major


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MATH 312 Numerical Solutions of Initial Value and Boundary Value Problems for

Ordinary Differential Equations (NSBVP) (3)

Round-off errors and normalization of variables ; Methods of Euler and Taylor; Lipschitzcontinuity and uniqueness of solutions; Local and global truncation errors; Derivation and use ofRuge-Kutta methods; Variable-step RK methods; Multi-step methods like Adams-Bashforth and

Moulton; Predictor-corrector techniques; Introduction to Difference equations; Intervals ofStability; ODE solvers for stiff differential equations; Solution of linear second-order BVPs bylinear shooting method; non-linear shooting method; solution of higher order BVPs by Newton-Raphson approach ; Calculus of finite differences and solution of BVPs.Course Offering Period

TBA

Pre-requisites

MATH102 Calculus-II

Lead Instructor

TBA

Designation

Elective

MATH 321 Algebra-I (4)

Sets Induction, Some number theory, Binary operations, Groups, subgroups, cyclic groups andgenerators. Symmetric Groups, Cosets Langrage Theorem .Normal Subgroups, Factor groups.Homomorphisms, Isomorphism Theorems, Cayleys Theorem. Direct Products and finiteAbelian groups. Sylow Theorems.Course Offering Period

FallLead Instructor

TBA

Pre-requisitesMATH 201 Set Theory

Designation

Math Major

MATH 322 Algebra-II (3)

Continuation of Math 321. Ring Theory, Ideal, Polynomials, Homomorphism, Field Theory ,Unique Factorization Domains. Euclidean Domains, Extension of fields. Construction withStraight edge and compass.Course Offering Period

Spring

Lead Instructor

TBAPre-requisitesMATH 321 Algebra-I


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Designation

Elective

MATH 331 Biostatistics (4)

Introduction to BioStatistics,Types of medical data, Cross sectional and Cohort studies, basicdescriptive measures for biological data, the Measures of Location and Dispersion, descriptivemeasures for qualitative data, Basic probability concepts, types of events and computingprobabilities, simple and conditional probabilities, Bayes theorem and its use, some commonprobability distributions: Binomial, Negative Binomial, Poisson, Normal, Exponential, and theiruse in Biological Sciences, Survey Sampling, Basic sampling concepts, some commonly usedsampling designs and estimation of sample size, Types of Statistical Inference; IntervalEstimation and Hypothesis testing, Inference for single and two population Means and

population Proportions, Inference based upon c2 distribution, Analysis of Contingency Table,The Contingency table and its use in Biological Sciences, Odds Ratios and Relative Risks and

inference about them, The Stratified Contingency Tables, Marginal and Adjusted measures forStratified tables, Cochran-Mental Haenszel Test for Stratified tables, The Analysis of MatchedData. Meta Analysis, Sensitivity , Specificity and Kappa- Statistic, Statistical Models, StatisticalModels for Biological Sciences, Classical simple and multiple regression Models and thereapplications in biological sciences, Simple, partial and multiple correlations, Models for BinaryResponses; the Logistic and Probit models, The Designed Experiments, Single Factor and MultiFactor Experiments.. Repeated Measure design and Nested experiments with applications, TheGeneralized Linear Models, Introduction to Generalized Linear Models, Special cases ofGeneralized Linear Models, Models of Multinomial and Ordinal Responses, Models for CountData; the Poisson and Gamma Regression Models, Survival Data Analysis, Nature andcharacteristic of Survival Data, Survival Function and Hazard Function with application, Non

parametric estimation of various survival functions, Models for Survival Data; the TimetoEvent models & Cox Proportional Hazard Models, Weibull Models for Survival data.


TBA

Lead Instructor

TBA

Pre-requisitesMATH 231 - Probability

Designation

Elective

MATH 341 Operations Research-I (4)

Intro to OR, Linear Programming, Graphical Solutions, Simplex Alogrithm, Big M Method, TwoPhase Method, Use of Computer to solve LP Models(LINDO, MS Excel), Post-optimalityAnalysis, Duality, Interior Point Alogrithm, The Transportation Problem, Generating BFSolutions, North West Rule, Vogel Approximation Method, The Trasshipment Problem, The


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Assignment Problem, Hungarian Method, Goal Programming Problems, Network Models,Alogrithms for Solving Minimum Spanning Tree, Shortest Path Problems, Alogrithms forSolving Maximum Flow Problems, Minimum Cost Flow Problem, Upper Bound Technique,Network Simplex Method, Project Management, Critical Path Method, Program Evaluation andReview Technique, Activity Crashing, Cost Time Trade-Off Analysis.

Course Offering PeriodFall

Lead Instructor

TBA

Pre-requisitesMATH 221 Linear Algebra-I

Designation

Elective

MATH 343 Optimization Techniques (3)

The present course is designed to give students an exposure to solving non-linear optimizationproblems by various techniques, with due emphasis on their mathematical rigor in terms of theirderivation / justification. The course work is supported by some carry-home assignments onmathematical modeling / investigating optimal solutions to a variety of daily life problemsthrough Matlab / any other suitable software.The course contents include : positive definitematrices, convexity of regions and functions, quadratic function and Hessian matrix, uniquenessof minimum; single search techniques such as bracketing method, quadratic and cubicinterpolation; Fibonacci search; golden-section; gradient / conjugate- gradient methods ofNewton ,steepest descent; Davidon-Fletcher-Powell ( DFP ), Fletcher- Reeves ; pattern search

techniques of simplex and by Hooke and Jeeves ;constrained minimization by Lagrangemultipliers ,handling of various types of constraints, use of slack variables, Kuhn-Tuckerconditions; methods of feasible directions by Zoutendijk and by Rosen; penalty-functionapproach to constrained optimization, interior and exterior penalty functions, equality ,inequalityand mixed constraints; Boxs simplex method; introduction to Calculus of variations; derivationof Eulers equation with fixed and moving boundaries; functionals dependent on higher-orderderivatives and on functions of several independent variables; direct variational methods of Ritzand Galerkin with applications.


Fall

Lead Instructor

Aslam Butt

Pre-requisitesMATH 102 Calculus-II, MATH 221 Linear Algebra-I

Designation

Math Elective


51/72

MATH 344 Numerical Analysis (3)

Fixed and floating point arithmetic; round-off and truncation errors; real roots of non-linearequations( single variable) by iterative methods like fixed-point,, regula-falsi, bisection andNewtons methods; roots of a system of nonlinear equations ( in 2 and 3 variables);decomposition of matrices by Doolitle and Choleskys procedures;band-matrices and Crouts

method; solution of systems of linear algebraic equations by Gauss, Jacobi and Seidel methods;curve fitting ; calculus of finite differences; various techniques of interpolation based on equallyand non-equally spaced data; numerical differentiation ( total and partial) based on 1st,2nd and4thorder errors; numerical integration in single and several variables with error analysis; eigen-values of a matrix and Girschgorins theorem; dominant eigen-values by Power and Inverse-power methods, deflation techniques for symmetric and non-symmetric matrices.Course Offering Period

Spring

Lead Instructor

Aslam Butt

Pre-requisites

MATH 102 Calculus-II, MATH 221- Linear Algebra-I, Computing

Designation

Math Major

MATH 345 Introduction to Mathematical Biology (4)

The course will introduce students to developing mathematical models in biology and techniquesused to study such models. Populations Dynamics, Epidemic Modeling, Tumor Modeling,Population Genetics, Biological Motion, Reaction Kinetics.Course Offering Period

TBA

Lead Instructor

Adnan Khan

Pre-requisitesMATH 211 Introduction to Differential Equations, MATH 221 Linear Algebra-I

Designation

Elective

MATH 351 Theory of Numbers (4)

Mathematical induction, divisibility, representation of integers. Primes, Greatest commondivisor. Euclidean Algorithm. Congruences. The Chinese remainder theorem. Fermats andWilson theorems. Eulers function. Perfect numbers. Primitive roots. Quadratic residues.

Quadratic reciprocity Law. Some nonlinear Diophantine Equalions. Sums of squares.Course Offering Period

FallLead Instructor

TBA


52/72

Pre-requisitesMATH 201 Set Theory

Designation

Elective

MATH 355 Combinatorics (3)Permutation and Combination, Injection and Bijection Principles Pigeonhole Principle,Arrangements and selection with repetitions Pascal Formula, Binomial Coefficients, BinomialIdentities, Multinomial Coefficients and Multinomial Theorem, Generating Functions, Ordinaryand exponential generating functions, products of generating functions, Partition of Integers,Ferrers Diagram and their Applications, Eulers pentagonal number theorem, Durfee Squares,Inclusion-Exclusion Principle, Derangements, Generalized Inclusion-Exclusion Principle. RookPolynomials, Recurrence Relations, Linear Homogeneous Recurrence Relations, NonlinearRecurrence Relation and Catalan Numbers Basic concepts of Young tableaux, Bumping and

Sliding, Schur Polynomials, Robinson-Schensted-Knuth(RSK) Correspondence, Matrix BallConstruction, Applications of RSK Correspondence, Hook length formula.Course Offering Period

Fall

Lead InstructorFaqir Muhammad Bhatti

Pre-requisitesMATH 252 Discrete Mathematics

DesignationElective

MATH 362 Electromagnetic Theory-I

Electrostatic field and magnetostatics. Examples involving Laplace's and Poisson's equations;vector potential; Faraday's laws of induction; Maxwell's equations, waves invacuum and dielectric media, guided waves.Course Offering PeriodFall

Lead Instructor

Zaeem Jafri

Pre-requisitesMATH 102 Calculus-II, MATH 211 Introduction to Differential Equations

Designation

Elective


53/72

MATH 401 Functional Analysis (3)

Banach spaces and bounded linear operators, Hahn-Banach extension and separation, dualspaces, bounded inverse theorems, uniform boundedness principle, applications. Compactoperators.Course Offering Period

TBA

Lead Instructor

Mujahid Abbas

Pre-requisitesMATH 301 Real Analysis

DesignationElective

MATH 402 Real Analysis-II (3)The Riemann Integrable functions, Fundamental theorems, Approximate integration,generalized Riemann integral, Point wise and Uniform Convergence; Interchange of limits,infinite series and the real line topology.Course Offering Period

Spring

Lead Instructor

Mujahid Abbas

Pre-requisitesMATH 301 Real Analysis - I

Designation

Elective

MATH 403 Introduction to Algebraic Topology

Review of the important topics from the pointset topology. Homotopy, Homotopy Type andRetractions, Paths, the Fundamental Group, Fundamental Group of the Circle, Covering Spaces.Course Offering PeriodSpring

Lead Instructor

Masood Hussain Shah

Pre-requisitesMATH 304 General Topology, MATH 221 Linear Algebra-I

Designation

Elective


54/72

MATH 412 Partial Differential Equations and Boundry Value Problems (PDEs) (4)

Normalization of variables; Modeling of heat ,wave and Laplace equations in one, two and threedimensions in Cartesian ,polar , cylindrical and spherical coordinates ;Classification of second-order linear partial differential equations; Canonical forms; Method of D-operators; Separationof variables; DAlemberts solution; Sturm Louville problem; Bessel and Legendre functions and

their properties; Bessel Fourier and Legendre Fourier series; Double and triple Fourier series;Curvilinear Coordinates; Solution of diffusion ,wave and Laplace equations in one ,two andthree dimensionswith various types of boundaries and conditions ; Use of Laplace Transformand Fourier Integral to solve BVPs.Course Offering Period

TBA

Lead Instructor

TBA

Pre-requisites

MATH 211 Introduction to Differential Equations

DesignationElective

MATH 431 Advanced Statistical Analysis (4)

Univarite Analysis, Descriptive statistics, exploratory data analysis, probability (only concepts)basic idea of sampling, sampling designs, estimation of sample size, Bivariate Analysis, Tests ofsignificance such as comparing of groups (one, two), Simple linear correlation and regression,Analysis of Variance, contingency tables, Mantel Haenszel test for linear association, MetaAnalysis, Multivariate Analysis, ANOVA (TWO-WAYS), MANOVA, Repeated measure

design, Simple factorial design, multiple regression models, Principle component analysis,Factor analysis, Canonical Correlation, Simple and Multiple logistic regressions, log linearmodels.


TBA

Lead InstructorTBA

Pre-requisitesMATH 232 - Statistics

Designation

Elective

MATH 432 Stochastic Processes

Review of basic probability, finite Markov chains, branching processes, renewal theory,Markov processes, Brownian motion.Course Offering Period

TBA


55/72

Lead Instructor

Arif Zaman

Pre-requisites

MATH 231 - Probability

Designation

Elective

MATH 441 Mathematical Modeling with Applications (3)

Mathematical formulation of models in physical, biological and behavioral sciences and finance,dimensional analysis, scaling, linear and non linear systems of differential equations andqualitative methods, introduction to regular and singular perturbation theory, stochastic modelsin continuous time, first order partial differential equations and traffic flow, elementary fluidmechanics.

Course Offering PeriodSpring

Lead Instructor

Adnan Khan

Pre-requisitesMATH 211 Introduction to differential Equations, MATH 221 Linear Algebra-I

Designation

Elective

MATH 442 Introduction to Non Linear Dynamics (4)

The course emphasizes qualitative methods for studying differential equations and theirapplications in physical and biological sciences. One dimensional flows, two dimensional flows,existence and uniqueness results, linearization and phase plane analysis, bifurcation theory, Limitcycles, higher dimensional systems and chaos

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