DOCSLIB.ORG

Self-Assessment Report

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Self-Assessment Report King Fahd University of Petroleum & Minerals DEPARTMENT OF MATHEMATICAL SCIENCES Self-Assessment Undergraduate Program Volume 1 Self-Assessment Report Submitted to The Program Assessment Center Deanship of Academic Development in May 2005 (Revised Version Submitted on August 31, 2005) Note The document “Self-Assessment of BS Program in Mathematical Sciences” consists of 3 volumes: • Volume I: Self-Assessment Report • Volume II: Description of Math/Stat Courses • Volume III: Faculty Resume SAR Dept. of Math Sc. 2 Table of Contents 0. Introduction: Objectives and Self-Assessment Procedure 5-8 0.1. Introduction 6 0.2. Program Evaluation by Berkeley Team 6 0.3.Self-Assessment of BS Program 7 0.4. Assessment Objectives 7 0.5. Self-Assessment Procedure 7 1. Criterion # 1: Program Mission, Objectives and Outcomes 9-24 1.1. Introduction 10 1.2. Mission Statements 10 1.3. Program Objectives 11 1.4. Program Learning Outcomes 12 1.5. Results of Program’s Assessment 15 1.6. Periodic Assessment of the Department 22 2. Criterion # 2: Curriculum Design and Organization 25-39 2.1. Introduction 26 2.2. Consistency of Curriculum with Program Objectives 30 2.3. Characteristics of Course Contents 30 2.4. Comparative Study of Curriculum Requirements 32 2.5. Information Technology Component 35 2.6. Oral and Written Communication Skills 38 3. Criterion # 3: Computing Facilities 40-43 3.1. Introduction 41 3.2. Computer Lab Manuals 41 3.3. Technical Support 42 3.4. Computing Infrastructure & Facilities 42 4. Criterion # 4: Student Support and Guidance 44-47 4.1. Introduction 45 4.2. Course Offerings 45 4.3. Guidance for Students 46 5. Criterion # 5: Faculty 48-61 5.1. Introduction 49 5.2. Qualification and Interest of Faculty Members 50 5.3. Currency Criteria & Faculty Development Program 51 SAR Dept. of Math Sc. 3 5.4. Faculty Recruiting, Evaluation & Promotion Procedure 52 6. Criterion # 6: Process Control 62-67 6.1. Introduction 63 6.2. Admission Procedure 63 6.3. Monitoring Students’ Progress 64 6.4. Teaching & Delivery of Course Material 65 6.5. Completion of Program Requirements 66 6.6. Updating Curriculum, etc. 67 7. Criterion # 7: Institutional Facilities 68-74 7.1. Introduction 69 7.2. New Trends in Teaching 69 7.3. Library and Resource Center 69 7.4. Classrooms and Faculty Offices 73 8. Criterion # 8: Institutional Support 75-77 8.1. Introduction 76 8.2. Financial Resources 76 8.3. Graduate Students and Research Assistants 77 8.4. Computing Infrastructure & Facilities 77 9. Appendices 78-94 9.1. Appendix A: Berkeley Report 78 9.2. Appendix B: Accreditation of US Institutions 82 9.2. Appendix C: Survey Forms 86 10. Index (Observations, Comments, Recommendations) 95 SAR Dept. of Math Sc. 4 Introduction Objectives & Self-Assessment Procedure SAR Dept. of Math Sc. 5 0.1 Introduction Self-assessment in an educational set-up is a systematic process of gathering, reviewing and using important quantitative and qualitative data and information from various sources about its educational programs to evaluate whether academic and learning standards are being met. King Fahd University of Petroleum & Minerals (KFUPM) is basically a technical institution. Historically, the Department of Mathematical Sciences has been catering the needs of other disciplines at KFUPM. Very few students enter KFUPM with the objective of opting an undergraduate program in mathematics. The enrollment of math majors, therefore, remained low throughout the university history except in the mid-nineties. The Department offers BS, MS and Ph.D. programs. Compared to other departments, the math faculty is the largest in size. It is divided into several scientific groups according to an individual’s area of specialization. The Department has a separate section for the Preparatory Mathematics Program which offers two courses on Algebra & Trigonometry to newly admitted undergraduate students and monitors all the issues relevant to these courses. The Department initiated the undergraduate program in 1967. The first batch of 5 students graduated in 1972. The program underwent major revisions for the first time in 1985 and later in 1999. However, it was not evaluated formally by any external agency. 0.2 Program Evaluation by Berkeley Team Although ABET evaluates the mathematics/statistics courses required for the engineering and computer programs of the university on a regular basis, the process of assessment for the BS, MS and Ph.D. programs offered by the Department of Mathematical Sciences was carried out first time in 1995. In 1997, a team of academicians including three mathematicians from University of California, Berkeley visited all departments of the College of Sciences at KFUPM. During the visit, the team evaluated an assessment report prepared by the Department of Mathematical Sciences on various academic programs. Excerpts of the evaluation report related to BS program may be found in Appendix A. The general view of the Berkeley team was very encouraging and positive about the Revised BS program in mathematical sciences. Nevertheless, they did recommend some measures for further improvement of the program. One such measure was related to the creation of areas of concentration from different groups of courses. The Department adopted this viewpoint and accordingly subdivided the Math electives into three groups (see Table 21). Another crucial recommendation made by the team concerned MATH 201 & 202 which states: It is our view that the same considerations that led KFUPM to go from 3 to 4 credits for Math 101-102 apply to Math 201 and 202 as well. The topics in Math 201-202 include concepts of crucial importance for the application of calculus to engineering and SAR Dept. of Math Sc. 6 sciences. These notions, ranging from power series and functions of several variables to differential equations, are the ‘bread and butter’ of many classes that follow. In order to master these powerful tools, the students need to devote more time to this material than they presently do. We recommend that both Math 201 and 202 should be made into classes with 4 credits. The Department put forward the recommendation to the University. But it could not get any positive response due to constraints from the engineering departments in spite of the fact that the courses similar to MATH 201-202 are appended with at least 1 additional hour of problem solving session in US institutions. 0.3 Self-Assessment of BS Program In May 2001, the Deanship of Academic Development (DAD) introduced a set of procedures and standards for self-assessment of academic programs at KFUPM which was revised in June 2002 and later in April 2004. The revised document contains 8 criteria each of which is comprised of several standards. Based on the DAD document, the Department of Mathematical Sciences initiated the process of self-assessment for its undergraduate program in September 2004. In this regard, the Department set up a program team (PT), which consisted of the following faculty members: • Dr. Muhammad A. Bokhari (Chairman) • Dr. Anwar Joarder (Member) • Dr. Salim Messaoudi (Member) • Dr. Ibrahim Al-Rasasi (Member) • Dr. Mahmoud Sarhan (Member) • Mr. Hussam Sharqawi (Member). 0.4 Assessment Objectives The PT took up the task of self-assessment in accordance with the following guidelines as provided in the DAD document: 1. Improve and maintain academic standards 2. Enhance students’ learning 3. Verify that the existing programs meet their objectives and institutional goals 4. Provide feedback for quality assurance of academic programs. 0.5 Self-Assessment Procedure In September 2004, DAD organized a workshop on “Outcome-Based Program Assessment” which addressed several topics and issues related to the process of self-assessment. The PT attended all sessions of the workshop. SAR Dept. of Math Sc. 7 The faculty members of the Department were informed about the self-assessment process and its objectives on different occasions. The need for their involvement in the process was emphasized throughout this exercise. The PT held several meetings to develop measurable objectives and learning outcomes of the BS program. The opinion of the Department Planning & Advisory Committee was also sought on this matter. The PT met with the Scientific Groups of the Department to review the format of undergraduate courses and identify their objectives and learning outcomes that support the program objectives. The Scientific Groups set up various committees, which took charge of furnishing the information for each course in a specific format. This exercise involved almost every faculty member of the Department. Different questionnaires (see Appendix C) were used to seek feedback from graduating students, alumni, employers and faculty about the undergraduate program. The qualitative data received from these sources were analyzed. The PT also received the resume of the faculty members, which included their teaching assignments and research activities for the past five years. This information identifies the areas of strength of the Department. While going through the process of self-assessment, it was emphasized that this process was neither an exercise in data collection nor an effort of creating a positive image for the Department. It was to identify the areas where improvements can be made. SAR Dept. of Math Sc. 8 Criterion 1 Program Mission, Objectives and Outcomes SAR Dept. of Math Sc. 9 1.1 Introduction This chapter describes • The mission statement of the Department, • Measurable objectives and outcomes of the BS program in Mathematics, • Results of program’s assessment and suggested improvements, • Overall performance of the Department. The Department of Mathematical Sciences offers a 4-year B.S. program as well as a graduate program leading to MS and Ph. D. degrees. Besides, the department is heavily involved in the teaching of mathematics and statistics courses in the colleges of Sciences, Engineering, Computer Science & Computer Engineering, Industrial Management and Environmental Design. The faculty of the department are quite productive in various areas of research and have maintained a good record of publications in journals of international repute.
Load more

Recommended publications
  • High-Level Nuclear Wastes and the Environment: Analyses of Challenges and Engineering Strategies
    World Journal of Nuclear Science and Technology, 2012, 2, 89-105 http://dx.doi.org/10.4236/wjnst.2012.23015 Published Online July 2012 (http://www.SciRP.org/journal/wjnst) High-Level Nuclear Wastes and the Environment: Analyses of Challenges and Engineering Strategies Mukhtar Ahmed Rana Physics Division, Directorate of Science, PINSTECH, Islamabad, Pakistan Email: [email protected], [email protected] Received February 11, 2012; revised April 2, 2012; accepted April 19, 2012 ABSTRACT The main objective of this paper is to analyze the current status of high-level nuclear waste disposal along with presen- tation of practical perspectives about the environmental issues involved. Present disposal designs and concepts are ana- lyzed on a scientific basis and modifications to existing designs are proposed from the perspective of environmental safety. A new concept of a chemical heat sink is introduced for the removal of heat emitted due to radioactive decay in the spent nuclear fuel or high-level radioactive waste, and thermal spikes produced by radiation in containment materi- als. Mainly, UO2 and metallic U are used as fuels in nuclear reactors. Spent nuclear fuel contains fission products and transuranium elements which would remain radioactive for 104 to 108 years. Essential concepts and engineering strate- gies for spent nuclear fuel disposal are described. Conceptual designs are described and discussed considering the long-term radiation and thermal activity of spent nuclear fuel. Notions of physical and chemical barriers to contain nu- clear waste are highlighted. A timeframe for nuclear waste disposal is proposed and time-line nuclear waste disposal plan or policy is described and discussed.
    [Show full text]
  • Mathematics for ASSESSMENT and ACCREDITATION Submitted To
    Track ID: UPUNGN11440 Volume-6 EVALUATIVE REPORT Department of Mathematics for ASSESSMENT AND ACCREDITATION Submitted to NATIONAL ASSESSMENT AND ACCREDITATION COUNCIL BANGALORE JAYPEE INSTITUTE OF INFORMATION TECHNOLOGY NOIDA 17 September, 2015 Evaluative Report of the Department 1. Name of the Department Mathematics 2. Year of establishment 2001 3. Is the Department part of a School/Faculty of the university? JIIT is a unitary university. It has departments that include Department of Mathematics, and also a Business School. 4. Names of programmes offered (UG, PG, M.Phil., Ph.D., Integrated Masters; Integrated Ph.D., D.Sc., D.Litt., etc.) (a) Ph. D. (b) M. Tech. (Applied and Computational Mathematics) 5. Interdisciplinary programmes and departments involved None. However, curriculum of the M. Tech (ACM) programme contains courses of other disciplines like Electronics and Communication Engineering (ECE) and Humanities and Social Sciences (HSS). 6. Courses in collaboration with other universities, industries, foreign institutions, etc. None 7. Details of programmes discontinued, if any, with reasons None in the last four years 8. Examination System: Annual/Semester/Trimester/Choice Based Credit System Semester, along with choice based credit system 9. Participation of the department in the courses offered by other departments Department offers courses in UG and PG Programs of other departments: (a) Courses offered in B. Tech programmes: 1 | P a g e Beneficiary S. No. Course Title Department CSE, ECE, IT, 1 Mathematics-I Biotech 2 Basic Mathematics-I Biotech CSE, ECE, IT, 3 Mathematics-II Biotech 4 Probability and Statistics Biotech Probability Theory and Random 5 CSE, ECE, IT Processes 6 Discrete Mathematics CSE, ECE, IT 7 Basic Mathematics –II Biotech CSE, ECE, IT, 8 Applied Linear Algebra Biotech CSE, ECE, IT, 9 Applied Numerical Methods Biotech CSE, ECE, IT, 10 Operations Research Biotech CSE, ECE, IT, 11 Advanced Matrix Computations Biotech (b) Courses offered in M.
    [Show full text]
  • Quaid-I-Azam University Department of Mathematics M
    QUAID-I-AZAM UNIVERSITY DEPARTMENT OF MATHEMATICS M. Phil. Produced (1967 to 2018) Year of Name of Supervisor S# Name of Student Award of Dissertation Title/Approved on Approved on Degree Muhammad Idrees 1 1967 Dr. Q.K. Ghori On the Second Method of Liapunov & its applications to the steady motion of gyroscope Ch. 2 Miss Kulsoom Aijaz 1967 DR. S.A. Haq Ivestigation in the category of graded algebras Muhammad Abdur 3 1967 Dr. Q.K. Ghori Stability in the Large of the two differential Equations Rahim Muhammad Aslam 4 1967 Dr. A.H. Baloch Linear regression with auto correlated errors. Noor 5 M. Siddique Ansari 1967 Dr. A.H. Baloch Specification errors in Linear Model 6 Munawar Hussain 1967 Dr. Q.K. Ghori Absolute stability of Non-Linear control systems 7 Muhammad Nazir 1968 Dr. Q.K. Ghori The Problem of centre and focus 8 Miss Khalida Inayat 1968 Dr. Q.K. Ghori Singularities of the systems of two differential equations 9 Abdul Rashid 1969 Dr. A.H. Baloch Convegence Theory in Statistics M. Phil. Produced (1967 to 2018) Department of Mathematics 1 of 91 Year of Name of Supervisor S# Name of Student Award of Dissertation Title/Approved on Approved on Degree 10 A.B. Masudul Alam Ch. 1969 Dr. A.H. Baloch Multicillinearity problems in linear models 11 Miss Razia Begum 1969 Dr. Q.K. Ghori Singular points and limit cycles 12 Miss Khudaja Begum 1969 Dr. Q.K. Ghori On conditions for existence of stable & unstable centres. 13 Shaukat Hussain 1969 Dr. C.M. Hussain Three Dimensional rotation Group 14 Hafiz Ali Muhammad 1970 Dr.
    [Show full text]
  • For Website UNCLAIMED DIVIDEND and SHARES 1964-2016 INTERIM
    MURREE BREWEREY CO. LTD. 3-National Park Road, Rawalpindi Unclaimed Dividend and Shares from 1964 to 2016 as on 30-06-2019 Sr Name of Shareholder/ Certificate holder Nationality CNIC/ Incorporation Old Folio / CD New Folio No. of Unclaimed Amount of No./ Registration Acct No. No. Shares Unclaimed No. Dividend 1 MR AHMED ABDUL REHMAN NOOR AHMED INDIA NA A004 10004 6,881 673,098 2 MRS ALMANI D DUBASH INDIA NA A006 10006 - 6,478 3 MR AMAR NATH RAWALPINDI NA A008 10008 7,055 330,961 4 MR ABDUL RAHIM DADI KARACHI NA A018 10018 - 6,611 5 MR AKHTAR ALI BHIMJI KARACHI NA A023 10023 352 19,138 6 MRS A C KEADY UK NA A024 10024 - 81 7 MR A S TURNER ESQR UK NA A034 10034 - 912 8 MR ANWAR AHMED WARRIACH LAHORE NA A040 10040 536 39,103 9 M/S ADAMJEE SONS LTD KARACHI NA A044 10044 - 295 10 MR ABA UMAR NOOR MOHAMMAD CHITTAGONG NA A049 10049 - 170 11 MR AMANULLAH SHEIKHZADA KARACHI NA A050 10050 - 771 12 MR ABDUL MANAN MOZANDAR KARACHI NA A059 10059 - 319 13 MR AMIN ISSA TAI KARACHI NA A060 10060 - 1 14 MR A QUDDUS KARACHI NA A065 10065 - 14 15 MR A R KHAN KARACHI NA A066 10066 92 7,565 16 MR AFTAB ALI GAZDAR KARACHI NA A070 10070 271 26,734 17 MRS ASMA AFZAL KARACHI NA A071 10071 - 111 18 LT COL AIJAZ AHMAD KHAN KHOSKI, BADIN NA A073 10073 2,810 203,145 19 MRS AKHTAR BANOO LAHORE NA A078 10078 134 7,945 20 MR ABDUL RAUF GILL LAHORE NA A082 10082 71 6,443 21 MR ABDULLA HAJI KARACHI NA A083 10083 84 5,774 22 MR ABOOBAKAR SULEMAN KARACHI NA A087 10087 - 2,412 23 MR AZAR AWAN KARACHI NA A088 10088 186 15,883 24 MR AHMED DADA KARACHI NA A095 10095 - 8,727 25 MR ABDULLAH GULAB SHAIKH KARACHI NA A098 10098 235 16,514 26 MR ANJUM M SALEEM FAISALABAD.
    [Show full text]
  • Letters to the Editor
    Letters to the Editor Mathematics in Pakistan ones on account of its more rigorous We found the article “The Abdus requirements for its postgraduate Salam School of Mathematical Sci- programs and the broad base pro- ences in Pakistan” by Loring W. Tu vided. It has already started pro- (Notices, August 2011) very interest- ducing extremely good Ph.D.’s and ing. It is highly commendable that M.Phils. in mathematics and physics, the efforts made in Pakistan to im- many of whom have already received prove the state of education in gen- international recognition. eral and mathematics, in particular, The COMSATS Institute of Infor- are acknowledged and appreciated mation Technology is producing the internationally. It is also desirable largest quantum of mathematical re- that these actions get support from search in the country and a very large mathematicians across the globe as number of research graduates. As at well as phase. A picture using this mathematics is essentially an interna- the SMS and QAU, the graduates are scheme appeared in the Mathematical tional activity. These include specific more limited in their backgrounds. Art Exhibit at the Joint Mathematics forms of support mentioned in this The Lahore University of Manage- Meetings in San Antonio in January article for SMS as well. ment Sciences started a graduate 2006 [see accompanying graphic]. As efforts towards improving the program in mathematics a long time Visual Basic code for this color map- state of education and research in ago. However, it did not become a ping can be found at http://w. Pakistan do not get much interna- major producer of graduates or re- american.edu/cas/mathstat/ tional attention, we have an appre- search at the time.
    [Show full text]
  • QUAID-I-AZAM UNIVERSITY DEPARTMENT of MATHEMATICS Ph.D
    QUAID-I-AZAM UNIVERSITY DEPARTMENT OF MATHEMATICS Ph.D. Produced (1971 to 2018) Year of Award S# Name of Student Name of Supervisor Approved on Dissertation Title/Approved on of Degree 1 Muhammad Saddiq Ansari 1971 Dr. A.H. Baloch Mixture of Normal Distributions On the Equations of Motion of a Nonholonomic Dynamical 2 Ch. Munawar Hussain 1971 Dr. Q.K. Ghori System in Poincare-Cetaev Variables 3 Saleem Asghar 1976 Dr. M. A. Rashid Some Diffraction Problems using the Wiener-Hopt Technique 4 Jawaid Quamar 1984 Dr. Asghar Qadir Relativistic Gravito-Dynamics and Forces 5 Muhammad Rafique 1985 Dr. Asghar Qadir Some Implictions of the ΨN-Formalism Syed Ashfaque Hussain 6 1987 Dr. Asghar Qadir Conformal Extension of ΨN-Formalism Bokhari 7 Naseer Ahmed 1987 Dr. Q.K. Ghori Some Problems in the Dynamics of Nonholonomic Systems 8 Mohammad Sharif 15-10-1991 Dr. Asghar Qadir19-09-1988 Forces in Non-Static Spacetimes29-05-1990 9 Akbar Azam 01-04-1992 Dr. Ismat Beg19-09-1988 Fixed Points of Multivalued Maps29-05-1990 10 Muhammad Ziad 29-01-1992 Dr. Asghar Qadir19-09-1988 Spherically Symmetric Spacetimes29-05-1990 Ph.D. Produced (1971 to 2018) Department of Mathematics 1 of 15 Year of Award S# Name of Student Name of Supervisor Approved on Dissertation Title/Approved on of Degree 11 Muhammad Ayub 06-10-1992 Dr. Saleem Asghar19-09-1988 Diffraction of Acoustic Waves by half Planes 29-05-1990 12 Qamar Iqbal 15-10-1992 Dr. Qaiser Mushtaq10-02-1988 Some Studies in Left Almost Semigroups10-02-1988 13 Farhana Shaheen 22-10-1992 Dr.
    [Show full text]
  • Revized Voter's List for PPS Election 2014 Membership Title Name of Member Position Postal Address No
    Revized Voter's List for PPS Election 2014 Membership Title Name of Member Position Postal Address No 1 Dr G Murtaza Professor Salam Chair in PhysicsG. C. University, Lahore 2 Dr Asghari Maqsood Professor NUST, Rawalpindi Associate Department of Physics,Quaid-i-Azam University, 3 Dr Imrana Ashraf Professor Islamabad 4 Mr Farid A. Khawaja Professor Islamabad 5 Dr A. H. Nayyar Professor Sustainable Development Institute of Pakistan Department of Physics, Quaid-i-Azam University, 6 Dr M Zakaullah Professor Islamabad. 7 Dr M. Aslam Baig Professor Quaid-i-Azam University, Islamabad 8 Dr Sajjad Mamood Professor USA 9 Dr Kamaluddin Ahmed Professor House 178, Street 18, F-10/2, Islamabad Associate 10 Dr Muhammad Iqbal University of Engineering and Technology, Lahore Professor Associate 11 Dr Khalid Khan Quaid-i-Azam University, Islamabad Professor 12 Dr Samina S. Masood USA C/o National Centre of Physics at Quaid-i-Azam 13 Dr Fayyazuddin Professor University, Islamabad 14 Dr Riazuddin Professor Deceased Department of Physics, Quaid-i-Azam University, 15 Dr Arshad M. Mirza Professor Islamabad Department of Physics, Quaid-i-Azam University, 16 Dr S. K. Hasanain Professor Islamabad Centre for Advanced Mathematics & Physics, 17 Dr Asghar Qadir Professor National University of Sciences & Technology 18 Dr A. J. Hamdani Professor H. No. 522, St. 46, G-10/4, Islamabad Air University, PAF Complex Sector E-9, 19 Dr Abdullah Sadiq Professor Islamabad 20 Dr M. Anwar Professor Ex. C.S.O. PAEC H# 51, St #62, F- 10/3 Islamabad 21 Dr Khalid Rashid Scientist 473-B, St. 10, F-10/2, Islamabad.
    [Show full text]
  • Nustnews Volume-Ii / Issue-Iv October-December 2011
    QUARTERLY NEWSLETTER NUSTNEWS VOLUME-II / ISSUE-IV OCTOBER-DECEMBER 2011 Int’l training workshop on Flood Warning & Management 10 IEEE Student Congress in New Zealand 08 Meet the Scientist: Dr. Ishfaq Ahmad 12 Paragliding Training Course 30 INSIDE HIGHLIGHTS PAGE 03 01 CO-CURICULARS CORNER PAGE 27 04 VISITS PAGE 14 02 SPORTS NEWS PAGE 31 05 UPDATES FROM SCHOOLS PAGE 17 03 ACHIEVEMENTS PAGE 33 06 The last quarter of 2011 has been rewarding for the entire NUST community: students continued bringing laurels to the University; graduates passed out in graceful convocation ceremonies; international conferences on emerging issues held; and linkages with the world’s top-notch universities progressively flourished, needless to mention the unstinting support of NUST management and hard work of both faculty and students. Though each and every endeavour at NUST reflects rational exuberance for making a difference, the successful culmination of first ever Prime Minister’s Entrepreneurial Challenge in October was a great achievement. The event, to be held annually under the direct support of the government stakeholders including MoST and HEC, kindles hope for economic resurrection of the country through the promotion of entrepreneurial culture. At a time of sheer financial meltdown, NUST has been a vibrant force in pursuing HEC’s vision of attaining prosperity through building knowledge-based economy; the initiative EDITORIAL of business plan competition being a glaring example. In keeping with the tradition of bringing you latest university news, this edition of NUSTNEWS covers a wide range of NUST activities undertaken by faculty, students and staff. I deem it appropriate to acknowledge here the efforts of our editorial staff, which leaves no stone unturned in preparing a comprehensive newsletter for all of our dear readers.
    [Show full text]
  • Some Exact Solutions of the Einstein–Maxwell Field Equations in Spherical Geometry
    Some Exact Solutions of the Einstein–Maxwell Field Equations in Spherical Geometry by Ayesha Mahmood Regn. No. NUST201390124TPSNS7113S A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics Supervised by Prof. Azad Akhter Siddiqui Department of Mathematics School of Natural Sciences National University of Sciences and Technology Islamabad, Pakistan August, 2019 Dedicated to my sweet little daughter Hareem Fatima and my husband Muhammad Younis. Abstract In this thesis, the aim is to present some new classes of non–static and static, spherically symmetric solutions of the Einstein–Maxwell field equations representing compact objects with negative pressure. Throughout this thesis the space–time geometry is spherical, the radial pressure is negative, and the matter density equals the negative value of the radial pressure (either it is considered or it comes out as a con- sequence of the calculations). Several non–static solutions are found by taking an ansatz for the components of the metric tensor and on the square of electric field intensity. The solutions are shown to satisfy physical boundary conditions associated with the exact solutions of the Einstein–Maxwell field equations. Due to negative pressure, these solutions can model physical systems such as expanding compact ob- jects containing negative pressure. Petrov and Segre´ classifications that these obtained solutions admit are also discussed in detail. Two static solutions of the field equations are also obtained with the ansatz similar to that for the non–static cases in order to have a look how the solutions behave for these kind of ansatz in static geometry.
    [Show full text]
  • Metric in Cartesian Co-Ordinates, G
    ic/aa/77 With the advent of supergrsvity theories ~ the Vierbein fonttalisE INTERNAL REPORT (Limited distribution) has come into extensive use. Basically a Vierbein, .converts a flat metric in Cartesian co-ordinates, g. into a general metric, International Atomic Energy Agency according to the equation (1) ted Kations Educational. Scientific and Cultural Organization ItJTERHATICKAL CENTRE FOR THEORETICAL PHYSICS In some sense, then, the Vierbein may be regarded as a "four-dimensional square root" of the general metric tensor. In fact this applies in more or less the same sense that the Dirac spinor is regarded as "the square root of the Minkowski It-vector". The curved space-time generalization of the flat apace- time Dirac matrices, Y- > given by the commutation relations, A PRESCRIPTION! FOH n-DIMEHSIONAL VIERBEINS * [ (2) V eab transform according to the rule Ashf&que H. Bokhari (3) Mathematics Department, Quaid-i-Azam University, Islamabad, Pakistan, These generalized Y-matrices are frequency used when dealing with spinor and fields in general relativity . It would be useful to be able to write Asghar Qadir ** dovm Vierbeins in an arbitrary space-time. Further, higher dimensional International Centre for Theoretical Physics, Trieste, Italy. Vierbeins would be useful when dealing, for example, with the eleven- dimensional supergravity which reduces to SU(8) supergravity , or in tiieher dimensional theories of the Kaluza-Klein variety such as those of Chodos and ABSTRACT Detweiler or Halpern . In this paiser we provide a prescription to be able to write down a Vierbein given a metric in any number of dimensions. Recent developments in supergravity have brought the n-dimensional Before swing on we need to introduce certain notation.
    [Show full text]
  • December 2006
    IMU BULLETIN of the INTERNATIONAL MATHEMATICAL UNION No. 54 December 2006 Secretariat: Institute for Advanced Study Einstein Drive Princeton, New Jersey 08540, USA as of January 1, 2007 c/o Konrad-Zuse-Zentrum Takustr. 7 D-14195 Berlin, Germany http://www.mathunion.org List of Abbreviations CDE Commission on Development and Exchange CEIC Committee on Electronic Information and Communication ICHM International Commission on the History of Mathematics ICMI International Commission on Mathematical Instruction ICSU International Council for Science IUHPS International Union of the History and Philosophy of Science 2 Dear Members of the International Mathematical Union, The present bulletin is the 54th in the series of bulletins edited by the International Mathematical Union so far. It has been a many years’ tradition to publish one bulletin per year or even two or three bulletins in the year of an International Congress of Mathematicians. Bulletin No. 54 covers the year 2006 and is referring especially to the 15th General Assembly in Santiago de Compostela, Spain, August 19-20, 2006 and the International Congress of Mathematicians 2006 in Madrid, Spain, August 22-30, 2006. The Report of the General Assembly gives a statement on IMU’s life during the term 2003- 2006, reports on the outcome of the elections of the Executive Committee and the other committees and commissions for the term 2007-2010, accounts on IMU’s finance and gives an overview of the decisions, recommendations, resolutions, etc. adopted by the General Assembly some of which are of importance in the short term and some need implementation in the longer term.
    [Show full text]
  • NONLINEAR ANALYSIS and VARIATIONAL PROBLEMS Springer Optimization and Its Applications
    NONLINEAR ANALYSIS AND VARIATIONAL PROBLEMS Springer Optimization and Its Applications VOLUME 35 Managing Editor Panos M. Pardalos (University of Florida) Editor–Combinatorial Optimization Ding-Zhu Du (University of Texas at Dallas) Advisory Board J. Birge (University of Chicago) C.A. Floudas (Princeton University) F. Giannessi (University of Pisa) H.D. Sherali (Virginia Polytechnic and State University) T. Terlaky (McMaster University) Y. Ye (Stanford University) Aims and Scope Optimization has been expanding in all directions at an astonishing rate dur- ing the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences. The series Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multiobjec- tive programming, description of software packages, approximation tech- niques and heuristic approaches. NONLINEAR ANALYSIS AND VARIATIONAL PROBLEMS In Honor of George Isac Edited By PANOS M. PARDALOS Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida THEMISTOCLES M. RASSIAS Department of Mathematics, National Technical University of Athens, Athens, Greece AKHTAR A.
    [Show full text]