2009-2010 Annual Report
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ED16 Abstracts 73
ED16 Abstracts 73 IP1 industrial problems. She will give examples of some indus- Mathematical Modeling with Elementary School- trial research problems that student teams have tackled, Aged Students discuss some of the skills that are needed to be successful working with and in industry, discuss the challenges that Modeling, a cyclic process by which mathematicians de- one may face when working with corporate partners, and velop and use mathematical tools to represent, understand, present a summary of some of the lessons that have been and solve real-world problems, provides important learning learned over the years in these collaborations. opportunities for school students. Modeling opportunities in secondary schools are apparent, but what about in the Suzanne L. Weekes younger grades? Two questions are critical in mathemati- Worcester Polytechnic Institute (WPI) cal modeling in K-5 settings. (1) How should opportunities [email protected] for modeling in K-5 settings be constructed and carried out? (2) What are the tasks of teaching when engaging el- ementary students in mathematical modeling? In this talk IP5 I will present a framework for teaching mathematical mod- Title Not Available at Time of Publication eling in elementary classrooms and provide illustrations of its use by elementary grades teachers. Abstract not available at time of publication. Elizabeth A. Burroughs Philip Uri Treisman Montana State University The University of Texas at Austin [email protected] [email protected] IP2 CP1 Graduate Student Education in Computational Regime Switching Models and the Mental Account- Mathematics and Scientific Computing ing Framework Abstract not available at time of publication. -
2020 Mathsoc Integration Bee Qualifiers Solutions
2020 MathSoc Integration Bee Qualifiers Solutions 1. Standard integral, but the bounds are tricky: Z 507 1 x dx = 5072 − 5032 503 2 1 = (507 + 503) (507 − 503) 2 1 = · 1010 · 4 2 = 2020: 2. Rewrite 3ln x as xln 3 using log laws, so now we have a standard integral: Z Z x1+ln 3 3ln x dx = xln 3 dx = + C: 1 + ln 3 3. This is simply integrating ex=2: Z p Z p ex dx = ex=2 dx = 2 ex + C: p 4. Substitute u = ex − 1: Z p Z u2 Z 1 ex − 1 dx = 2 du = 2 1 − du u2 + 1 1 + u2 = 2 u − tan−1 u + C p p = 2 ex − 1 − tan−1 ex − 1 + C: 5. Substitute x = eu then the integral becomes Z eu cos u du: Apply integration by parts twice: Z Z eu cos u du = eu cos u + eu sin u du Z = eu cos u + eu sin u − eu cos u du: Rearrange to obtain Z 1 eu cos u du = eu (cos u + sin u) ; 2 then Z 1 cos (ln x) dx = x (cos (ln x) + sin (ln x)) + C: 2 6. Substitute u = e2x, then Z e2x 1 Z 1 1 1 p dx = p du = sin−1 u + C = sin−1 e2x + C: 1 − e4x 2 1 − u2 2 2 Z 7π=4 4x cos x 7. This is an odd function from "−a to a" so 2 dx = 0. −7π=4 x − sin jxj + cos jxj c UNSW Mathematics Society 2020 π 8. -
2006 - 2007 Annual Report Department of Mathematics College of Arts & Sciences Drexel University Photo by R
2006 - 2007 Annual Report Department of Mathematics College of Arts & Sciences Drexel University Photo by R. Andrew Hicks Andrew R. by Photo TABLE OF CONTENTS PEOPLE 1 Message From the Department Head 2 Tenure Track Faculty 4 Auxiliary Faculty 5 Visiting Faculty & Fellows 5 Emeritus Faculty 6 Staff 6 Teaching Assistants & Research Assistants 7 New Faculty Profiles AWARDS / HIGHLIGHTS 8 Faculty Awards 9 Faculty Grants 10 Faculty Appointments / Conference Organizations 11 Faculty Publications / Patents 13 Faculty Presentations 17 Faculty New Course Offerings 18 Honors Day Awards 20 Graduate Student Day Awards 21 Albert Herr Teaching Assistant Award 21 Student Presentations 22 Bachelor of Science Degrees Awarded 22 Master of Science Degrees Awarded 22 Doctor of Philosophy Degree Awarded DEPARTMENT 23 Colloquium Photo by R. Andrew Hicks 25 Analysis Seminars 27 Dean’s Seminar 28 Departmental Committees 30 Mathematics Resource Center 31 Departmental Outreach 33 Financial Mathematics Advisory Board EVENTS 35 Student Activities 36 SIAM Chapter / Math Bytes 37 Departmental Social Events GIVING 38 Support the Mathematics Department MESSAGE FROM THE DEPARTMENT HEAD Dear Alumni and Friends, It has been another great year for our department. It is wonderful to have award winning faculty in the department. Dr. Pavel Grinfeld received the College of Arts and Sciences Excellence Award for both his research and teaching accomplishments, and Ms. Marna Mozeff Hartmann received the Barbara G. Hornum Award for Excellence in Teaching for her dedication to teaching and advising our undergraduates. Also several of our students have been recognized. Teaching Assistants Emek Kose and Jason Aran have won two of Drexel’s Teaching Assistant Excellence Awards. -
Philosophical Magazine A
This article was downloaded by:[Massachusetts Institute of Technology] On: 7 January 2008 Access Details: [subscription number 768485848] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Philosophical Magazine A Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713396797 Towards thermodynamics of elastic electric conductors M. Grinfeld a; P. Grinfeld b a The Educational Testing Service, Princeton, New Jersey, USA b Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA Online Publication Date: 01 May 2001 To cite this Article: Grinfeld, M. and Grinfeld, P. (2001) 'Towards thermodynamics of elastic electric conductors', Philosophical Magazine A, 81:5, 1341 - 1354 To link to this article: DOI: 10.1080/01418610108214445 URL: http://dx.doi.org/10.1080/01418610108214445 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. -
Praising the Hard Work of Faculty, Staff, and Students: Excellent Job!
RooMath News Department of Mathematics & Statistics Newsletter http://cas.umkc.edu/Mathematics Volume 10, Issue 1 Praising the Hard Work of Faculty, Fall 2017 Staff, and Students: Excellent Job! Inside this issue: Alumni, students, friends old and students on numerous administrative new, welcome! tasks. Greetings from the De- 1 partment Since the last issue of RooMath News Our graduate and undergradu- The Importance of Sum- 2 there have been several activities fos- ate students have been actively partic- mer Internships tered by faculty, staff and students of ipating and presenting their research Interview: Mary Ellen 2 the UMKC math and stat department. at different conferences such as the Cox -Summer Internship In this short note, we highlight a few Undergraduate Symposium of Re- Industrial Math 4 of them. search & Scholarly Creativity, the Recent Graduates, 6 Math and Stat Research Day, the An- Student News During the 2016-2017 school nual Meeting of SIAM Central States, UMKC Alumna—Love of 15 year, math and stat faculty members Math published more than 24 research arti- and the Joint Mathematics Meetings. UMKC’s Math Competition team par- Post-Quantum Cryptog- 16 cles in well-regarded journals, orga- raphy ticipated in the Missouri Collegiate nized several conferences, seminars, Faculty News Mathematics Competition. 17 and symposia, presented research at Golden Ratio 1-6-18 22 Some students obtained sum- various national and international Math Club, MSGSO mer internships, joined different Re- 23 conferences, trained several graduate Department Contacts search Experience for Undergraduates 24 students and taught more than 60 math and stat courses at both the Summer Programs, published their graduate and undergraduate levels. -
Applications of Symbolic Computation to the Calculus of Moving Surfaces a Thesis Submitted to the Faculty of Drexel University B
Applications of Symbolic Computation to the Calculus of Moving Surfaces A Thesis Submitted to the Faculty of Drexel University by Mark W. Boady in partial fulfillment of the requirements for the degree of Doctor of Philosophy June 2016 c Copyright 2016 Mark W. Boady. All Rights Reserved. i Dedications To my lovely wife, Petrina. Without your endless kindness, love, and patience, this thesis never would have been completed. To my parents, Bill and Charlene, you have loved and supported me in every endeavor. I am eternally grateful to be your son. To my in-laws, Jerry and Annelie, your endless optimism and assistance helped keep me motivated throughout this project. ii Acknowledgments I would like to express my sincere gratitude to my supervisors Dr. Jeremy Johnson and Dr. Pavel Grinfeld. Dr. Johnson's patience and insight provided a safe harbor during the seemingly endless days of debugging and testing code. I cannot thank him enough for improvements in my writing, coding, and presenting skills. This thesis could not have existed without Dr. Grinfeld's pioneering research. His vast knowledge and endless enthusiasm propelled us forward at every roadblock. A special thanks also goes out to the members of my thesis committee: Dr. Bruce Char, Dr. Dario Salvucci, and Dr. Hoon Hong. Without their valuable input, this work would not have been fully realized. They consistently helped to keep this project focused while I was buried in the details of development. All the members of the Drexel Computer Science Department have provided endless help in my development as a teacher and researcher. -
Lecture Notes: Mathematical Methods
LECTURE NOTES IMPERIAL COLLEGE LONDON DEPARTMENT OF COMPUTING Mathematical Methods Instructors: Marc Deisenroth, Mahdi Cheraghchi Version: November 30, 2016 Contents 1 Course Overview3 2 Sequences6 2.1 The Convergence Definition.......................6 2.2 Illustration of Convergence.......................7 2.3 Common Converging Sequences.....................8 2.4 Combinations of Sequences.......................9 2.5 Sandwich Theorem............................9 2.6 Ratio Tests for Sequences........................ 11 2.7 Proof of Ratio Tests............................ 12 2.8 Useful Techniques for Manipulating Absolute Values......... 13 2.9 Properties of Real Numbers....................... 14 3 Series 15 3.1 Geometric Series............................. 16 3.2 Harmonic Series............................. 16 3.3 Series of Inverse Squares......................... 17 3.4 Common Series and Convergence.................... 18 3.5 Convergence Tests............................ 19 3.6 Absolute Convergence.......................... 22 3.7 Power Series and the Radius of Convergence.............. 23 3.8 Proofs of Ratio Tests........................... 24 4 Power Series 27 4.1 Basics of Power Series.......................... 27 4.2 Maclaurin Series............................. 27 4.3 Taylor Series............................... 31 4.4 Taylor Series Error Term......................... 33 4.5 Deriving the Cauchy Error Term..................... 34 4.6 Power Series Solution of ODEs..................... 34 5 Linear Algebra 36 5.1 Linear Equation Systems........................ -
From Boxes to Bees: Active Learning in Freshmen Calculus Flora S
From Boxes to Bees: Active Learning in Freshmen Calculus Flora S. Tsai, Karthik Natarajan, Selin Damla Ahipas¸aoglu,˘ Chau Yuen, Hyowon Lee, Ngai-Man Cheung, Justin Ruths, Shisheng Huang, and Thomas L. Magnanti [email protected], natarajan karthik | ahipasaoglu | yuenchau | hlee | ngaiman cheung | justinruths | shisheng huang | [email protected] Abstract—The vehicles of education have seen significant III describes a typical active learning approach used in the broadening with the proliferation of new technologies such as cohort classroom. Sections IV and V provides details on social media, microblogs, online references, multimedia, and the types of activities that were implemented. Section VI interactive teaching tools. This paper summarizes research on the effect of using active learning methods to facilitate presents the results before concluding in Section VII. student learning and describes our experiences implementing group activities for a calculus course for first year university II. BACKGROUND students at Singapore University of Technology and Design, a new design-centric university established in collaboration with As SUTD is a unique design-centric university, the current Massachusetts Institute of Technology (MIT). We describe the best practices in educational theory and design are being educational impact of different pedagogical techniques, such used in conjunction with interactive tools and hands-on ac- as real-time response tools, hands on activities, mathematical tivities. Design as a discipline cuts across the curriculum and modeling, visualization activities and motivational competitions on students with differing learning preferences in a unique provides a framework for the research and educational pro- cohort classroom setting. Based on faculty reflection and survey grams. -
2011- 2012 | Department of Mathematics | Drexel University
2011- 2012 | Department of Mathematics | Drexel University 2011- 2012 | Department of Mathematics | Drexel University Message From the Department Head 3 Tenured/Tenure-Track Faculty 4 Tenured/Tenure-Track Faculty and Teaching Faculty 6 Teaching Faculty, Visiting Faculty/Post Doctoral Associates 8 Adjunct Faculty, Emeritus Faculty, and Professional Staff 9 Teaching Assistants and Research Assistants 10 New Visiting Faculty Profiles 11 New Teaching Faculty Profiles and New Staff Profile 12 Department of Mathematics Photo and Employee Service Award Recipients 13 Faculty Awards 14 Faculty Grants 16 Faculty Appointments / Conference Organizations 17 Faculty Publications 19 Faculty Presentations 21 Faculty Presentations, US Patent Issued, Editorial Positions and Special Topics Courses 24 Honors Day Awards 25 Undergraduate Awards 27 Degrees Awarded 28 Distinguished Visitor Lecture 29 Colloquium 30 Analysis Seminar 32 Combinatorics and Algebraic Geometry Seminar 35 PDE / Applied Mathematics Seminar 36 SIAM Seminar 38 Departmental Committees 39 Mathematics Resource Center 40 Graduate Presentations 42 Graduate Presentations, Graduate Publications and Undergraduate Research Co-op 43 Student Activities 44 Graduate Student Awards and Nominations 47 Annual End of Year Reception 49 Social Events and Donations 50 Video 51 2 2011- 2012 | Department of Mathematics | Drexel University Message From the Department Head Dear Alumni and Friends, It is my pleasure to present our department's annual report which highlights and documents the many activities and accomplish- ments of our faculty and students. Again our department has enjoyed recognition by numerous awards to our faculty and students. Assistant Professor Simon Fou- cart won the Antelo Devereux Award for Young Faculty in support of his research in Compressive Sensing, and Teaching Assis- tant Professor Daryl Falco won the Barbara G. -
Handbook of Integration
Handbook of Integration Daniel Zwillinger Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy, New York Jones and Bartlett Publishers Boston London Table of Contents Preface ix Introduction xi How to Use This Book xiii I Applications of Integration 1 Differential Equations: Integral Representations 1 2 Differential Equations: Integral Transforms 6 3 Extremal Problems 14 4 Function Representation 20 5 Geometrie Applications 24 6 MIT Integration Bee 28 7 Probability . 30 8 Summations: Combinatorial 31 9 Summations: Other 34 10 Zeros of Functions 40 11 Miscellaneous Applications 45 II Concepts and Dennitions 12 Dennitions 47 13 Integral Dennitions 51 14 Caveats 58 15 Changing Order of Integration 61 16 Convergence of Integrals 64 17 Exterior Calculus 67 18 Feynman Diagrams 70 19 Finite Part of Integrals 73 20 Fractional Integration 75 21 Liouville Theory 79 22 Mean Value Theorems 83 23 Path Integrals 86 24 Principal Value Integrals 92 25 Transforms: To a Finite Interval 95 26 Transforms: Multidimensional Integrals 97 27 Transforms: Miscellaneous 103 v * VI III Exact Analytical Methods 28 Change of Variable 109 29 Computer Aided Solution 117 30 Contour Integration 129 31 Convolution Techniques 140 32 Differentiation and Integration 142 33 Dilogarithms 145 34 Elliptic Integrals 148 35 Frullanian Integrals 157 36 Functional Equations 160 37 Integration by Parts 162 38 Line and Surface Integrals 164 39 Look Up Technique 170 40 Special Integration Techniques 181 41 Stochastic Integration 186 42 Tables of Integrals 190 IV -
GILBERT STRANG Education Positions Held Awards and Duties
CURRICULUM VITAE : GILBERT STRANG Work: Department of Mathematics, M.I.T. Cambridge MA 02139 Phone: 617{253{4383 Fax: 617{253{4358 e-mail: [email protected] URL: http://math.mit.edu/ gs Home: 7 Southgate Road Wellesley MA 02482 Phone: 781{235{9537 Education 1. 1952{1955 William Barton Rogers Scholar, M.I.T. (S.B. 1955) 2. 1955{1957 Rhodes Scholar, Oxford University (B.A., M.A. 1957) 3. 1957{1959 NSF Fellow, UCLA (Ph.D. 1959) Positions Held 1. 1959{1961 C.L.E. Moore Instructor, M.I.T. 2. 1961{1962 NATO Postdoctoral Fellow, Oxford University 3. 1962{1964 Assistant Professor of Mathematics, M.I.T. 4. 1964{1970 Associate Professor of Mathematics, M.I.T. 5. 1970{ Professor of Mathematics, M.I.T. Awards and Duties 1. Alfred P. Sloan Fellow (1966{1967) 2. Chairman, M.I.T. Committee on Pure Mathematics (1975{1979) 3. Chauvenet Prize, Mathematical Association of America (1976) 4. Council, Society for Industrial and Applied Mathematics (1977{1982) 5. NSF Advisory Panel on Mathematics (1977{1980) (Chairman 1979{1980) 6. CUPM Subcommittee on Calculus (1979{1981) 7. Fairchild Scholar, California Institute of Technology (1980{1981) 8. Honorary Professor, Xian Jiaotong University, China (1980) 9. American Academy of Arts and Sciences (1985) 10. Taft Lecturer, University of Cincinnati (1977) 11. Gergen Lecturer, Duke University (1983) 12. Lonseth Lecturer, Oregon State University (1987) 13. Magnus Lecturer, Colorado State University (2000) 14. Blumberg Lecturer, University of Texas (2001) 15. AMS-SIAM Committee on Applied Mathematics (1990{1992) 16. Vice President for Education, SIAM (1991{1996) 17. -
Electroconducting Sphere Inside Unbounded Isotropic Matrix for ALEGRA Verification by Michael Grinfeld, Pavel Grinfeld, John Niederhaus, and Angel Rodriguez
ARL-TR-8994 ● JULY 2020 Electroconducting Sphere inside Unbounded Isotropic Matrix for ALEGRA Verification by Michael Grinfeld, Pavel Grinfeld, John Niederhaus, and Angel Rodriguez Approved for public release; distribution is unlimited. NOTICES Disclaimers The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. Citation of manufacturer’s or trade names does not constitute an official endorsement or approval of the use thereof. Destroy this report when it is no longer needed. Do not return it to the originator. ARL-TR-8994 ● JULY 2020 Electroconducting Sphere inside Unbounded Isotropic Matrix for ALEGRA Verification Michael Grinfeld Weapons and Materials Research Directorate, CCDC Army Research Laboratory Pavel Grinfeld Drexel University John Niederhaus and Angel Rodriguez Sandia National Laboratories Approved for public release; distribution is unlimited. Form Approved REPORT DOCUMENTATION PAGE OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.