Conference Session

Mathematics Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Guo Zheng Yew, Texas Tech University; Aimee Cloutier, Texas Tech University; Stephen Michael Morse, Michigan Technological University; Audra N. Morse, Texas Tech University

Tagged Divisions

Mathematics

6.5correct answer. The other 39 students selected the incorrect answer of . 5 Given the triangle in the diagram, compute the value of tan(𝛼). 5 5 A. B. 6.5 7.5 6.5 D. Cannot calculate tan(𝛼

Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

”, Page 25.489.10 J. Physiol. 197, (1968), 551-566. 6. Demirkaya, O., Asyali, M., H., Sahoo, P.K., Image Processing with MATLAB-Applications in Medicine and Biology, CRC Press, Florida, (2009). 7. Gonzalez, R.C., &Wintz, P., Digital Image Processing, Addison-Wesley Publ. Co., MA. (1987). 8. Jain, A., K., Fundamentals of Digital Image Processing, Prentice Hall, NJ, (1989) 9. Kalanad, A. and Rao, B., N., Detection of Crack location and size in structures using improved damaged finite elements, IOP Conf. Series: Materials Science and Engineering, IOP Publishing, 10, (2010), 1-10. 10. Lim, J., S., Two-Dimensional Signal and Image Processing, Prentice Hall, NJ, (1990). 11. Mannan, M.,A

Conference Session

Mathematics Division Technical Session 2

Collection

2019 ASEE Annual Conference & Exposition

Authors

Rajendran Swamidurai, Alabama State University; Cadavious M. Jones, Alabama State University ; Carl Pettis, Alabama State University ; Uma Kannan, Alabama State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

the take-home project. Students were provided with somesimulation examples relevant to the real world. Topics for recommendation included (a)gambling games; (b) biological evolution; (c) finance; (d) social network; (e) forensic science;etc. Depending on the students programming background, some template codes that wereamenable to plug-and-play experimentation were provided to facilitate the activity and reducethe effort of writing a program. Those who wished to write their own programs were stronglyencouraged to do so. In both cases, students were asked to examine and manipulate the pythoncode provided.During the discussion and review session, students would compare their results and discussopen-ended questions that related to the project

Conference Session

Mathematics Division Technical Session 4: Assessing Success in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Rebecca Ann George, University of Houston; Weihua Fan, University of Houston; Daijiazi Tang, University of Houston

Tagged Topics

Diversity

Tagged Divisions

Mathematics

during which the surveys were administered.MeasuresThe survey consists of (a) section of demographic information and (b) section of questions onself-beliefs in success (academic self-efficacy and subjective values), academic engagement(efforts and persistence), learning climate, and achievement emotions (enjoyment, anxiety,hopeless, shame, and anger before, during, and after class). In (a) section, the demographicitems measure students’ gender (male= 0, female =1), age, race, major, academic year, andself-reported GPA. The (b) section includes 98 Likert-scaled items from 1 (strongly disagree)to 5 (strongly agree) and from 1 (not at all true of me) to 7 (very true of me). All Likert-scaled items were adapted from existing research [9]. Some

Conference Session

Engineering and Mathematics Potpourri

Collection

2009 Annual Conference & Exposition

Authors

Murray Teitell, DeVry University, Long Beach

Tagged Divisions

Mathematics

. (2007). An Investigation of the Mutation Operator using Different Representations in Grammatical Evolution. Proc. Int. Multiconf. Comp. Sci. and Infor. Page 14.1133.11 Tech., 1, 409-419. 13. Checkland, P. (1999). Systems Thinking. In Currie, W. L. & Galliers, B. (eds), Rethinking Management Infor. Sys .(45-57) Oxford: Oxford University Press.14. Josephy, A., Gordon, A, & McFarland, M. W. (1962). The american heritage history of flight. New York: Simon and Schuster. Page 14.1133.12Page

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

approaching from or number of computationsyou can count here? …in terms of location, what is the difference?RP 15: This is around zero (pointing the Maclaurin series), this (pointing the series centered at x=2) is 2.Interviewer: ….is there a difference between them in terms of function?RP 15: This is (pointing the series centered at x=2) bigger than this one (pointing the Maclaurin)Overall only 16 out of 17 participants responded to question (c). Only 37.5 % of the participants had the correctresponse to question (b). Majority of the participants corrected or responded right to the question during theinterviews. One of the participants preferred to not answer the question.Finite & Infinite Maclaurin Series DifferenceIn this section participating

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Carl Pettis, Alabama State University; Rajendran Swamidurai, Alabama State University; Ash Abebe, Auburn University; David Shannon, Auburn University

Tagged Divisions

Mathematics

solutions obtained using hand calculation.Lab-2: In this lab, the main contents include graphical visualization for some real data. Manydatasets are publically available from sites such as kaggle.com and data.gov. Graphicalvisualization ranges from simple graphics such as histogram, boxplot, and scatterplot toadvanced graphics such as PCA projection plots, trellis plots, maps, etc. Students need to exploresome real data using graphics to explore and discover information from the real data.Take-home project: Students were used some simulation examples relevant to the real world.Topics for recommendation include (a) gambling games; (b) biological evolution; (c) finance; (d)social network; (e) forensic science; etc. Depending on the students

Conference Session

Innovative Instruction Strategies

Collection

2006 Annual Conference & Exposition

Authors

Jonathan Lambright, Savannah State University

Tagged Divisions

Mathematics

equations.Students must be taught the fundamentals of developing and solving these numericalapproximations by hand. However, theory must be combined with technology and hands onpractice to emphasize the need for tools such as Matlab and Excel in solving engineeringproblems through numerical approximations. By implementing such tools in the classroom,students sharpen their programming and analytical thinking skills. In addition, students canexperience the need for and the power of these tools in solving real world problems and use theexperience to creatively think of newer ways to solve engineering problems.References[1] Hanselman, D., and Littlefield, B., “Mastering MATLAB 7: A Comprehensive Tutorial andReference”, Prentice Hall Publishers.[2] Chapra, S.C

Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

Bipin K. Pai, Purdue University, Calumet

Tagged Divisions

Mathematics

Page 25.1435.52 Least Squares Fitting 2. If we know that the function is a power function y = a*x^b, then Student Response Value Correct Answer Feedback 1. it is better to use the exponential data as it exists and do a linear least squares fit. 2. it is better to linearize the data by taking natural logarithms of both the independent and dependent variables and do a linear least squares fit. 3. it is better to take the natural log of just the independent variable and do a linear least squares fit. 4. it is better to take the natural log of just 0% the dependent variable and do a least squares fit. 5. it is better to

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Doug Bullock, Boise State University; Kathrine E. Johnson; Janet Callahan, Boise State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

+/-grades, so the conversion is A+ = 4.0, A = 4.0, A- = 3.7, B+ = 3.3, etc. We count W’s and CW’sas 0.0, along with F’s. This is consistent with DWF used more generally as a student successmetric, in that it considers an F and a W to be equally unsuccessful.Calc II Grade = (Total grade points) / (Cohort size – Audits – Incompletes)It is possible that there one cohortcould be better prepared for college level work than anothercohort. So we tracked four control variables for each cohort: GenACT: About 70% of our students have either an ACT or an SAT Math score. SAT Math scores are converted to ACT using published concordances.7 If this results in two scores (some students have both ACT and SAT) we take the higher. This is averaged

Conference Session

Mathematics Division Technical Session 3

Collection

2019 ASEE Annual Conference & Exposition

Authors

Stacie Pisano, University of Virginia; Bernard Fulgham, University of Virginia

Tagged Divisions

Mathematics

? Yes Yes No AP score of 5 Yes Pass Calculus II on BC test? Section? Yes No Have No Calculus II Take Calculus II. credit? Yes Take Multivariable Calculus or beyond based on Multivariable credit.Appendix 2 – Grade Point Average Assignment Letter Grade GPA A+ 4.3 A 4.0 A- 3.7 B+ 3.3 B 3.0 B- 2.7 C+ 2.3 C

Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Cynthia Young, University of Central Florida; Michael Georgiopoulos, University of Central Florida; Tace Crouse, University of Central Florida; Alvaro Islas, University of Central Florida; Scott Hagen, University of Central Florida; Cherie Geiger, University of Central Florida; Melissa Dagley-Falls, University of Central Florida; Patricia Ramsey, University of Central Florida; Patrice Lancey, University of Central Florida

Tagged Divisions

Mathematics

: C1= Tw-Tcanswer in class. An A) – 23.8 [W]example of a clicker Coo ling airquestion (and the correct B) +23.8 [W] H ot w all at T c Copper cooling fin aanswer) is provided to the at tem perature Tw

Conference Session

Innovative Instruction Strategies in Calculus

Collection

2007 Annual Conference & Exposition

Authors

Jenna Carpenter, Louisiana Tech University; Ruth Ellen Hanna, Louisiana Tech University

Tagged Divisions

Mathematics

” is defined as “making an “A”, “B” or “C” in the course” (since all engineering andscience majors are required to earn a grade of “C” or higher in all math courses which areprerequisites for other courses).ALEKS is a web-based system (versus software-based) that can be accessed from any computerwith web access and a java-enabled web browser. The ALEKS syllabus for each course isaligned with the actual content of the syllabus for the corresponding course at our university. Page 12.1170.2Students who purchase an ALEKS access code and are provided a course code by the instructorof their mathematics class can then access the ALEKS program for

Conference Session

Engineering and Math Potpouri

Collection

2008 Annual Conference & Exposition

Authors

Bertram Pariser, Technical Career Institute, Inc.; Cyrus Meherji, Technical Career Institute, Inc.

Tagged Divisions

Mathematics

AC 2008-1657: VIDEO LECTURE ON THE PYTHAGOREAN THEORYBertram Pariser, Technical Career Institute, Inc.Cyrus Meherji, Technical Career Institute, Inc. Page 13.1383.1© American Society for Engineering Education, 2008 Video Lecture on PYTHAGOREAN THEORYAbstractPythagoras derived the famous equation a2 +b2 =c2. This discovery enabled the Greeks tobuild the Acropolis and the Parthenon. This equation is probably the most famous equation inmathematics. There are hundreds of proofs to the Pythagorean Theorem in mathematical literature.My derivation of "A GEOMETRICAL PROOF OF PYTHAGORAS’ THEOREM" 1 is difficult for ourstudents to understand. Students, who use the video

Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Guenter Bischof, Joanneum University of Applied Sciences; Thomas Singraber B.Sc., Joanneum University of Applied Sciences; Christian J. Steinmann, HM&S IT-Consulting; Marton Szabo-Kass B.Sc., Joanneum University of Applied Sciences; Stefan Woerndl B.Sc., Joanneum University of Applied Sciences

Tagged Divisions

Mathematics

University of Applied Sciences Thomas Singraber obtained his B.Sc. in Automotive Engineering at the FH Joanneum, University of Applied Sciences Graz, Austria. Currently he is working on finalizing his Master’s Thesis at the same faculty with a company partner supplying components to top motorsport teams all over the world. During his time at the Formula Student team he focused his work on aerodynamics and chassis developement and achieved therefore practical knowledge on a wide spectrum of racing topics. On completion of his studies, he intends to pursue an interdisciplinary career in the automotive sector with a strong motorsport affiliation.Mr. Christian J. Steinmann, HM&S IT-Consulting Christian Steinmann has

Conference Session

Computers and Software in Teaching Mathemathetics

Collection

2009 Annual Conference & Exposition

Authors

Raymond Jacquot, University of Wyoming; Jeffrey Anderson, University of Wyoming; David Walrath, University of Wyoming

Tagged Divisions

Mathematics

AC 2009-214: SCRIPTS IN MATLAB FOR ANIMATION OF THE SOLUTIONS TOPARTIAL DIFFERENTIAL EQUATIONSRaymond Jacquot, University of Wyoming Ray Jacquot, Ph.D., P.E., received his BSME and MSME degrees at the University of Wyoming in 1960 and 1962 respectively. He was an NSF Science Faculty Fellow at Purdue University where he received the Ph.D. in 1969. He joined the Electrical Engineering faculty of the University of Wyoming in 1969. He is a member of ASEE, IEEE and ASME and has been active in ASEE for over three decades serving as Rocky Mountain Section Chair and PIC IV Chair. His professional interests are in modeling, control, simulation and animation of dynamic systems. He is currently Professor

Conference Session

Innovative Instruction Strategies in Calculus

Collection

2007 Annual Conference & Exposition

Authors

Elton Graves, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

AC 2007-1169: STUDENTS WITH CALCULUS CREDIT: WHAT CAN WE DO?Elton Graves, Rose-Hulman Institute of Technology Elton Graves is a member of the Mathematics Department at Rose-Hulman Institute of Technology, where he has taught since 1981. He received his doctorate in mathematics from Idaho State University in 1981. He co-authored the first $100,000 ILI Grant to incorporate the use of CAS into the teaching of calculus, and differential equations. He is currently the director of the Fast Track Calculus Program. Page 12.1324.1© American Society for Engineering Education, 2007

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Rebecca Bourn, Tribeca Flashpoint Media Arts Academy; Sarah C. Baxter, University of South Carolina

Tagged Divisions

Mathematics

Engineering and Applied Science. Page 23.405.1 c American Society for Engineering Education, 2013 Developing Mathematical Intuition by Building Estimation SkillsAbstractOpen-ended problems are challenging for many students because they often have little sense ofwhat a “correct” answer would be and struggle with evaluating the quality of an answer derivedfrom a calculator or computer model. It is difficult for them to see patterns or associate one typeof problem with another and they have few intuitive skills to use to judge the completeness oftheir answers. These can be significant obstacles for

Conference Session

Innovative Instruction Strategies in Calculus

Collection

2007 Annual Conference & Exposition

Authors

Martha Allen, Georgia College & State University; Amy Kelley, Georgia College & State University

Tagged Divisions

Mathematics

AC 2007-1216: EMPHASIZING TEAMWORK AND COMMUNICATION SKILLSIN INTRODUCTORY CALCULUS COURSESMartha Allen, Georgia College & State University Dr. Martha Allen is an Associate Professor in the Department of Mathematics at Georgia College & State University in Milledgeville, Georgia. She received her Ph.D. in mathematics from the University of South Carolina in 2001. She was selected as a 2001-2002 Project NExT National Fellow. Project NExT (New Experiences in Teaching) is a Mathematical Association of America program for new or recent Ph.D.s in mathematics. Dr. Allen is currently serving as co-director of the MAA's Southeastern Section NExT program. In 2005, Dr. Allen was the recipient of the

Conference Session

Mathematics Division Technical Session 2: Poster Presentations

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Yosi Shibberu, Rose-Hulman Institute of Technology

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Paper ID #29911Mathematics Content of an Undergraduate Course on Deep LearningProf. Yosi Shibberu, Rose-Hulman Institute of Technology Dr. Yosi Shibberu is professor of mathematics at Rose-Hulman Institute of Technology. He has taught undergraduate courses on data mining, machine learning, bioinformatics and computational biology. Dr. Shibberu spent a year at Jimma University, Ethiopia, as a Fulbright Scholar and formerly held the en- dowed chair for innovation in science, engineering and mathematics education at Rose-Hulman Institute of Technology. c American Society for Engineering Education, 2020

Conference Session

Mathematics Division Technical Session 2

Collection

2019 ASEE Annual Conference & Exposition

Authors

Cathy Poliak, University of Houston

Tagged Topics

Diversity

Tagged Divisions

Mathematics

one semester Calculus-Based undergraduate Statistics course for the engineering student is aservice course for most Mathematics departments. The typical student uses this course to gainunderstanding of how data is analyzed and interpreted. Technology allows a better way to givethe tools an engineer needs to understand the concepts and ideas in statistics. This paper willshow what has been implemented so that a student is successful in this course and beyond theclassroom.The technology that we use is through many different avenues in a course. One way thattechnology has helped us teach this course is through the delivery of the lectures. We havedesigned an online course that is as successful and no different as if the student is sitting in

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Samantha Nacole Andrews, Georgia Institute of Technology; Greg Mayer, Georgia Tech; Rui Hu, CEISMC, Georgia Institute of Technology; Connelly Hunter Connelly, Google, Inc.; Nathaniel William Tindall III; Neva Rose, Georgia Institute of Tecnology - CEISMC

Tagged Divisions

Mathematics

Paper ID #7361Development of an Online High School Multivariable Calculus-themed Intro-duction to Engineering CourseDr. Samantha Nacole Andrews, Georgia Institute of Technology Samantha Andrews obtained her PhD in Biomedical Engineering from the Georgia Institute of Technol- ogy and Emory University in 2010. Currently she is a Postdoctoral Fellow at the Georgia Institute of Technology where she focuses on science education and outreach. Her work includes conducting teacher professional development workshops and developing online science courses for students and teachers for the Race to the Top grant.Dr. Greg Mayer, Georgia

Conference Session

Bridging the Gap and Freshman Programs

Collection

2009 Annual Conference & Exposition

Authors

James Sullivan, Dallas Independent School District

Tagged Divisions

Mathematics

AC 2009-2352: THE “BOX METHOD” FOR TEACHING RATIO/PROPORTIONPROBLEMSJames Sullivan, Dallas Independent School District Page 14.1266.1© American Society for Engineering Education, 2009 The “Box Method” for Teaching Ratio/Proportion ProblemsAbstractThis paper details a systematic method for teaching high school students how to set up and solveratio and/or proportion problems. Such problems frequently occur in a wide variety ofengineering applications. The author, while teaching high school algebra courses, noticed aremarkable fact: Students were able to solve such problems correctly once the problems hadbeen set up properly. In other words, their major difficulty was not

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Seunghyun Chun, California Baptist University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

ApplicationsAbstract In this paper an example of a method to present a basic numerical analysis method’s such as the Secant Method, Bisection method and the Regula Falsi Method is described in the way it is used in sustainable energy application. A solar panel is examined and students are provided with its P-V characteristic curve. The arbitrary function f(x), that was the target of finding the root for in a numerical analysis textbook, is no longer a function without any significance (Fig. 3). It becomes a derivative of the P-V characteristic curve which has a root that corresponds to the maximum power point for efficient power extraction of the solar panel. This can be applied to wind energy, fuel cells and so on.Introduction The need for

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Paul Wlodkowski, Maine Maritime Academy

Tagged Divisions

Mathematics

-disciplinary interaction among engineering, physics, and mathematics. In addition, he holds an appointment with the Academy’s Loeb-Sullivan School, a graduate program in International Business and Logistics. He has sixteen years of industrial, manufacturing and academic experience that encompasses the fields of materials engineering, applied physics, reliability engineering, acoustics, applied statistics, shock and vibration, sensor design, radiation effects, and technical marketing. As the Principal Staff Engineer and Program Manager at Wilcoxon Research, Inc., he led several of the Company's high technology programs in the research, development, and commercialization of directional, acoustic

Conference Session

Engineering Mathematical Potpourri

Collection

2011 ASEE Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

AC 2011-279: EDGE DETECTORS IN IMAGE PROCESSINGJohn Schmeelk, Virginia Commonwealth University/Qatar Dr. John Schmeelk is a Professor of mathematics at Virginia Commonwealth University teaching mathe- matics at VCU/Qatar campus in Doha, Qatar. He received his PhD from George Washington University in Washington, D.C. He has been an invited speaker to conferences in Australia, Brazil, Bulgaria, Canada, China, Hungary, India, United Arab emmirate, Qatar and many other lands. Page 22.518.1 c American Society for Engineering Education, 2011 Edge Detectors in Image

Conference Session

Mathematics Division Technical Session 3

Collection

2017 ASEE Annual Conference & Exposition

Authors

Bailey Braaten, The Ohio State University; Arnulfo Perez, The Ohio State University

Tagged Divisions

Mathematics

Paper ID #19533Integrating STEM and Computer Science in Algebra: Teachers’ Computa-tional Thinking DispostionsMrs. Bailey Braaten, The Ohio State University Bailey Braaten is currently a doctoral student at the Ohio State University, where she is in her second year of the STEM education PhD program. She is a graduate research assistant on the STEM+C NSF funded project, looking at integrating computer science and engineering concepts into algebra classrooms. Bailey received her BS in mechanical engineering from Ohio Northern University and her M.Ed. in curriculum and instruction from University of Cincinnati. Her

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Dianne Raubenheimer, North Carolina State University; Hatice Ozturk, North Carolina State University; Alina Duca, NCSU

Tagged Divisions

Mathematics

AC 2010-214: BRIDGING MATHEMATICS CONCEPTS TO ENGINEERINGCONTEXTS: JUST-IN-TIME REVIEW MODULESDianne Raubenheimer, North Carolina State University Dr. C. Dianne Raubenheimer received her PhD from the University of Louisville and is Director of Assessment in the College or Engineering and Adjunct Assistant Professor in the Department of Adult and Higher Education at NC State University. Within the College of Engineering she serves as the coordinator of ABET and other accreditation processes, acts as a resource/consultant to faculty in the different programs, develops and implements assessment plans, and serves as the primary educational assessment/data analyst adviser on the Dean’s staff. A

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Bruno Osorno, California State University-Northridge

Tagged Divisions

Mathematics

2006-783: STUDENT ENGAGEMENT THROUGH MATHEMATICALAPPLICATIONS IN ELECTRICAL POWER SYSTEMSBruno Osorno, California State University-Northridge Bruno Osorno has been teaching for over 20 years. He has written over 20 technical papers all related to electrical engineering. His interests are reasearch in engineering education, application of new technologies into the curriculum and computer applications in electric power systems. He received an MSEE from the University of Colorado, Boulder and continued studies towards a PHD degree resulting in ABD. He has a great deal of industrial and consulting experience, more recently he was involved in consulting for NASA-JPL in the analysis of an electrical

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jamiiru Luttamaguzi, Elizabeth City State University; Ka'Ren Ladoris Byrd; Akbar M. Eslami, Elizabeth City State University; Ehsan O Sheybani, Virginia State University; Giti Javidi, Virginia State University

Tagged Divisions

Mathematics

Paper ID #6229Case Study: Numerical Convergence Study on Simulated Spaceborne Mi-crowave Radiometer Measurements of EarthDr. Jamiiru Luttamaguzi, Elizabeth City State University Dr. Jamiiru Luttamaguzi is an Assistant Professor in Elizabeth City State University. His main research interest is in Optimal Control Theory. Most of his professional career has been spent teaching graduate and undergraduate math courses. He has supervised students in the McNair Internship program and the ECSU- NAM Summer Research Computational Science-Scientific Visualization programs. He graduated with a PhD is MAthematics and MS in