Collection

2002 ASEE North Midwest Section Conference

Authors

Mani Mina

Teaching Technology to Web-affected Computer-game-influenced Students in the Early 21st Century: Hopes and Despairs Mani Mina Department of Electrical and Computer Engineering Iowa State University Ames, Iowa 50011 mmina@iastate.eduThis paper reviews many of the observed characteristics and study habits of first-yearstudents in Iowa State University's electrical engineering program. Based on students'behavior in studying and problem solving, dominate characteristics are identified,strengths and weaknesses are reviewed, and critical symptoms

Collection

2009 Pacific Southwest Section Meeting

Authors

Gordon W. Romney

, deal with the ten domains associatedwith Certified Information Systems Security Professional (CISSP) preparation (Harris, 2008) andare taken just prior to the Senior Capstone sequence. The IT triad of effectively managingPeople, Technology and Processes emphasizes the dynamic nature of the project developmentcycle. The ability to complete a specific assignment where the problem has one solution nolonger is the rule. Clients change their minds on what they want, technology does not alwayswork the way it should and processes are frequently ill-defined. The IT professional must learn Proceedings of the 2009 American Society for Engineering Education Pacific Southwest Regional Conference

Conference Session

LEES 5: Preparing and Practicing Culturally and Ethically Sensitive Engagement

Collection

2022 ASEE Annual Conference & Exposition

Authors

Todd Nicewonger; Stacey Fritz; Lisa McNair, Virginia Polytechnic Institute and State University

thathave historically shaped home building projects in remote Alaska Native communities. However,this paper does not (nor is it meant to) provide a template or recipe for guiding future buildingprojects involving diverse actors. Instead, this paper offers a conceptual framework for inspiringinquiry and discussion among collaborators, especially those from the lower 48 who have neverworked in Alaska before or who have limited on the ground experience with home building inremote Alaska Native communities.That said, it is important to keep in mind that homeowners, engineers, and builders from Alaskado not regularly use terms like modes of complexity nor refer to theories of reductionism versusmultiplicity in their everyday collaborations on building

Conference Session

Community Engagement in Diverse Contexts

Collection

2019 ASEE Annual Conference & Exposition

Authors

Jerrod A. Henderson, University of Houston (CoE & CoT); Virginia Snodgrass Rangel, University of Houston; Rick P. Greer, University of Houston; Mariam Manuel, University of Houston; Sara Jolly Jones, University of Houston; Victoria Doan, University of Houston

Tagged Topics

Diversity

Tagged Divisions

Community Engagement Division

Paper ID #26879STEM Engagement through Mentoring: Motivations of STEM MentorsDr. Jerrod A. Henderson, University of Houston (CoE & CoT) Dr. Jerrod A. Henderson (”Dr. J”) is an Instructional Assistant Professor in the Cullen College of Engi- neering at the University of Houston. He joined the University of Houston after six years as a chemical engineering faculty member at the University of Illinois. He has dedicated his career to increasing the number of students who are in the pipeline to pursue STEM careers. He believes that exposing students to STEM early will have a lasting impact upon their lives and academic

Conference Session

Aerospace Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Hank D Voss, Taylor University; Jeff F Dailey; William A Bauson, Taylor University; Bill Chapman, Taylor University

Tagged Divisions

Aerospace

ability to have students keep in mind possible 5.2 obstacles and errorsTSAT and ELEO Satellite Documentation and ASEE PublicationsAnother assessment marker was the evaluation of all of the documentation (Figure 15) byEngineers at the AF. In addition, the students gave their Critical Design Review (CDR) forTSAT to an engineering review panel at the ITT Aerospace (Exelis) company and werequestioned and approved for their work. For ELEO-Sat the AF flew four engineer reviewers toour university for a 12 hr. student design review. In competition the students were commendedfor their thoughtful work. Figure 15. Documentation.The students also worked in four small groups to write four professional engineering

Conference Session

Redefining Manufacturing Education Practices

Collection

2022 ASEE Annual Conference & Exposition

Authors

Allen White, Rose-Hulman Institute of Technology; Jay McCormack, Rose-Hulman Institute of Technology

toimprove student self-efficacy [3], reduce stereotype threat [3], and even improvecreativity [4]. With these considerations in mind, role-playing simulations wereutilized as part of a four week exercise in a quarter-long design for manufacturingcourse.Feeling immersed in the role they play in a simulation is critical because “Role-playingis immersion to an outside consciousness (‘a character’) and interacting with itssurroundings” [5]. Comfort in operating as an engineer, the students “character,” inthe simulated company environment of the simulation requires some confidence as totheir goals and approach. This is achieved via collaboratively developing designconstraints that represent their character’s, and their group’s, viewpoints within

Conference Session

Construction Session 4: Outside of the Construction Curriculum

Collection

2016 ASEE Annual Conference & Exposition

Authors

David Dylan John, Georgia Southern University; Marcel Maghiar, Georgia Southern University; Clint D. Martin, Georgia Southern University

Tagged Topics

Diversity

Tagged Divisions

Construction

Paper ID #15902A Case for International Study in Construction Education and Industry Prac-ticeMr. David Dylan John, Georgia Southern University A graduating Senior Construction Management Student at Georgia Southern University, Dylan John is an active student leader within multiple student organizations. His research interests include Building Information Modelling (BIM), Sustainable Construction, Productivity and Efficiency in the Construction Industry. He is mentored by Dr.Marcel Maghiar and Dr.Clint Martin of the Department of Civil Engineer- ing and Construction Management at Georgia Southern UniversityDr. Marcel

Conference Session

CPDD Session 2 - Professional Development - Where Are We Going?

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Mitchell L. Springer PMP, SPHR, SHRM-SCP, Purdue Polytechnic Institute; Kathryne Newton, Purdue Polytechnic Institute

Tagged Topics

Diversity

Tagged Divisions

Continuing Professional Development

Paper ID #28313Gen Y (Millennial) and Gen Z Cultural Cohort Demographics: Social,Political and Economic Perspectives and ImplicationsDr. Mitchell L Springer PMP, SPHR, SHRM-SCP, Purdue University-Main Campus, West Lafayette (Collegeof Engineering) Dr. Mitchell L. Springer PMP, SPHR, SHRM-SCP Dr. Springer currently serves as an Executive Director for Purdue University’s Polytechnic Institute lo- cated in West Lafayette, Indiana. He has over thirty-five years of theoretical and defense industry-based practical experience from four disciplines: software engineering, systems engineering, program manage- ment and human

Conference Session

Fostering and Assessing Effective Teaming

Collection

2008 Annual Conference & Exposition

Authors

Diane Zemke, Gonzaga University; Steven Zemke, Gonzaga University

Tagged Divisions

Educational Research and Methods

AC 2008-335: IDENTIFYING ROLES AND BEHAVIORS OF INFORMALLEADERS ON STUDENT DESIGN TEAMSDiane Zemke, Gonzaga University Diane Zemke is a PhD candidate at Gonzaga University in Leadership Studies. Her interests include small group dynamics, reflective practices, learning, and qualitative methods. She has co-authored papers on use of small teams in design engineering.Steven Zemke, Gonzaga University Steven Zemke is an Associate Professor of Mechanical Engineering at Gonzaga University. His primary responsibilities are Design courses and assessment. His research interests include effective learning environments and design teaching and learning. Prior to teaching he was a design engineer and

Conference Session

Best Zone Paper Competition

Collection

2011 ASEE Annual Conference & Exposition

Authors

Rebecca A Bates, Minnesota State University, Mankato; Andrew Petersen, University of Toronto Mississauga

Tagged Topics

Council of Sections

is an example of fast-feedback technology. (Koretsky, M. Web-based Interactive Science and Engineering Learning Tool. https://secure.engr.oregonstate.edu/che/WISE/. )about the teaching of the content, with even more weight because the results have been filteredthrough both individual minds and group consideration. When the teacher discusses the exam,the concepts missed after the group exam can be the focus, thus reducing faculty review time.3.3 BenefitsOne model of active learning separates "doing" from "observing" and differentiates betweendialog "with self" and "with others".8 Group tests contain room for both types of dialog. First, thesolo test forces to the student to hold a dialog with self, with the instructor as audience. Next

Conference Session

Faculty Development Lightning Talk Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Kenya Z. Mejia, University of Washington; Jennifer A. Turns, University of Washington; Yuliana Flores; Hadas Ritz, Cornell University; Jiehong Liao, Florida Gulf Coast University; John Chen, California Polytechnic State University, San Luis Obispo ; Boni Frances Yraguen, Georgia Institute of Technology

Tagged Divisions

Faculty Development Division

reflection?,”“how are reflections shared with students and feedback given?” These questions alone offered avariety of lenses through which to view an exam wrapper assignment.The impact of the guided exercises on exam wrapper development was compounded by theperspectives and discussions between the instructors who participated in the co-design study. Ofthe six participants, there was a significant range of experience with exam wrappers. Some werecompletely new to the concept and some had already been using them in their individual courses.A broad range of class topics, styles, and sizes within engineering curricula was also representedin the group. While each instructor came to the study with an exam wrapper in mind targeted atachieving a certain

Conference Session

Innovative Teaching Techniques in Mechanics

Collection

2007 Annual Conference & Exposition

Authors

Christopher Papadopoulos; Josh Bostwick, Cornell University; Andrew Dressel, University of Wisconsin-Milwaukee

Tagged Divisions

Mechanics

local student performance data that, while as yet inconclusive, suggests apossible method for assessment of the strategies’ efficacy.IntroductionMechanics provides the scientific foundation for nearly all branches of engineering andconstitutes an essential component of the education of nearly all engineering students.Through mechanics, students learn not only fundamental principles that govern thebehavior of structures and machines, but they also develop the rigorous habits of mind ofestablishing and critiquing assumptions, translating physical problems into well-posedmathematical equations, and assessing the meaning and validity of their solutions(possibly leading to reformulation and new solutions). It is this broader understanding

Conference Session

Special Session Celebrating the 10th Anniversary of the MATE International ROV Competition

Collection

2011 ASEE Annual Conference & Exposition

Authors

Douglas E. Oppliger, Michigan Technological University; Valorie Troesch, Michigan Technological University; Jean Kampe, Michigan Technological University

Tagged Divisions

Ocean and Marine

mind, let’s turn to some of the current projects of the TCROVteam.The HSE program requires that each team submit a set of goals at the start of the year. It isexpected that these will be modified as the year progresses, and this is almost always the case.Here are the goals submitted by the team in NOV 2010: TCROV – 2010-11 Goals9 The following is a brief synopsis and summary of potential goals for the HSE underwater ROV engineering project, Traverse City Central Senior High, Traverse City Michigan The emphasis for 2010-2011 will involve three high school teams concentrating on five primary areas: 1) Increase the use of technology into the ROV system and building process. Possible

Collection

2000 Annual Conference

Authors

Joseph Rencis, University of Arkansas

AC 2000-246: The Formula SAE Racecar Project at WPIJoseph Rencis, University of Arkansas Page 5.622.1© American Society for Engineering Education, 2000 Session 3268 The Formula SAE® Racecar Project at WPI Joseph J. Rencis1 Worcester Polytechnic InstituteAbstractThe Formula SAE (Society of Automotive Engineers) is a design-based competition that isattended by universities throughout the world. The competition is for engineering students toconceive, design, fabricate, construct, test, and market

Collection

1998 Annual Conference

Authors

Lia F. Arthur; Irem Y. Tumer

educationcomponent to change even in traditionally research-oriented universities. Hence, as doctoralcandidates preparing for academic careers, we must be prepared for the challenges of teachingeven more than before. Yet, while we learn many important aspects of conducting competitiveresearch as graduate research assistants, preparing doctoral students to become educators is stillnot a regular component of our doctoral studies. Even if some graduate students get teachingexperience as Teaching Assistants, this does not provide a full picture of the teaching aspects ofacademia.In this paper, we present a promising approach to preparing future engineering faculty for thedifficult task of teaching while conducting research. Specifically, we propose that

Conference Session

NSF Grantees Poster Session

Collection

2011 ASEE Annual Conference & Exposition

Authors

Steve Warren, Kansas State University; Xiongjie Dong, Kansas State University; Tim J. Sobering, Kansas State University; Jason Yao, East Carolina University

Tagged Topics

NSF Grantees

AC 2011-1927: A RAPID ANALYSIS AND SIGNAL CONDITIONING LAB-ORATORY (RASCL) DESIGN COMPATIBLE WITH THE NATIONAL IN-STRUMENTS MYDAQ PLATFORMSteve Warren, Kansas State University Steve Warren received a B.S. and M.S. in Electrical Engineering from Kansas State University in 1989 and 1991, respectively, followed by a Ph.D. in Electrical Engineering from The University of Texas at Austin in 1994. Dr. Warren is an Associate Professor in the Department of Electrical & Computer Engineering at Kansas State University. Prior to joining KSU in August 1999, Dr. Warren was a Principal Member of the Technical Staff at Sandia National Laboratories in Albuquerque, NM. He directs the KSU Medical Component Design Laboratory, a

Collection

ASEE Mid-Atlantic Section Spring Conference

Authors

Rowena Kay Mascarenhas, TiE Boston; Adam B. Carter, TiE Boston

, CEESA Conference, NESA Conference. He was also Keynote Speaker at Bill Clinton’s School of Public Service, Valparaiso University and the Phi Beta Kappa Con- vention. ©American Society for Engineering Education, 2024 From STEM to Startup: Empowering High School Youth with Entrepreneurial Skills through the TYE programAbstractSTEM fields rely heavily on innovation to solve complex problems and create newtechnologies. Entrepreneurship education nurtures students' ability to think creatively,identify opportunities, and develop innovative solutions, making them better equipped totackle the challenges they will encounter in their engineering and STEM careers. It preparesthem for future success

Conference Session

NSF Grantees' Poster Session

Collection

2013 ASEE Annual Conference & Exposition

Authors

Kathleen L Kitto, Western Washington University; Debra S. Jusak, Western Washington University

Tagged Topics

NSF Grantees Poster Session

”, Definitions, Comparisons, and Research Bases”, Journal of Engineering Education, April, 2006, pp. 1-16. 6. National Research Council Commission on Behavioral and Social Sciences and Education, How People Learn: Brain, Mind, Experience and School, Commission of Behavioral and Social Sciences and Education, Washington, DC, National Academy Press, 2000 (on-line free access, http://books.nap.edu/books/0309070368/html/). 7. Svinicki, M., “Synthesis of the Research on Teaching and Learning in Engineering Since the Implementation of ABET Engineering Criteria 2000”, National Academies, https://www7.nationalacademies.org/bose/1DBER_Svinicki_October_Paper.pdf . 8. Felder, R., “Learning and Teaching

Collection

2017 ASEE Midwest Section Conference

Authors

Poster Abstract 2017 ASEE Midwest Section Conference Oklahoma State UniversityProgram Chair- Kevin DreesTechnical Program Committee Chair- Gouranga Banik, Ph.D., P.E., F. ASCE1. Virtual Reality Classroom Experiences to Help Engineering Students Understand Moments of Inertia and Aircraft DesignDominic Halsmer, Richard Ernst, John Voth (Oral Roberts University,USA)The undergraduate engineering curriculum is extremely challenging, largely due to the complexity of the processes and concepts it introduces. One good way to handle this complexity andassist

Conference Session

Continuing Professional Development Division Technical Session 1

Collection

2015 ASEE Annual Conference & Exposition

Authors

Michael Richey, The Boeing Company; Timothy Kieran O'Mahony, University of Washington; Michael J. Prince, Bucknell University; Fabian Zender, The Boeing Company; Barry McPherson, Boeing

Tagged Divisions

Continuing Professional Development

Paper ID #11291Revert to Default: Insights on Transfer of Expertise in a Complex Competi-tive WorkplaceDr. Michael Richey, The Boeing Company Michael Richey is an Associate Technical Fellow currently assigned to support workforce development and engineering education research. Michael is responsible for leading learning science research, which focuses on learning ecologies, complex adaptive social systems and learning curves. Michael pursues this research agenda with the goal of understanding the interplay between innovation, knowledge trans- fer and economies of scale as they are manifested in questions of growth

Conference Session

Computers in Education Division Technical Session 5: Online Teaching and Learning

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Alisa Gilmore P.E., University of Nebraska, Lincoln; Tareq Daher, University of Nebraska, Lincoln; Markeya S. Peteranetz, University of Nebraska, Lincoln

Tagged Divisions

Computers in Education

Paper ID #28847A Multi-Year Case Study in Blended Design: Student Experiences in aBlended, Synchronous, Distance Controls CourseProf. Alisa Gilmore P.E., University of Nebraska, Lincoln Alisa N. Gilmore is an Associate Professor of Practice in the department of Electrical and Computer En- gineering at the University of Nebraska – Lincoln. Her expertise is in teaching and developing courses in robotics, telecommunications, circuits and control systems. She serves as the chair of the Continuous Improvement of Teaching and Learning committee in the College of Engineering, and assessment coor- dinator for the ECE department

Conference Session

Community Engagement Division Technical Session 5

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Glen Hordemann, Texas A&M University; Malini Natarajarathinam, Texas A&M University; Sharon Lynn Chu, University of Florida; Mathew Kuttolamadom, Texas A&M University; Francis Quek, Virginia Polytechnic Institute and State University; Osazuwa John Okundaye Jr, Texas A&M University

Tagged Topics

Diversity

Tagged Divisions

Community Engagement Division

management projects. She works extensively with food banks and food pantries on supply chain management and logistics focused initiatives. Her graduate and undergraduate students are integral part of her service-learning based logistics classes. She teaches courses in strategic relationships among industrial distributors and distribution logistics. Her recent research focuses on engineering education and learning sciences with a focus on how to engage students better to prepare their minds for the future. Her other research interests include empirical studies to assess impact of good supply chain practices such as coordinated decision making in stochastic supply chains, handling supply chains during times of crisis and

Conference Session

Course Transformation in ECE

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Rabih Younes, Duke University; Cecilé Sadler, Duke University

Tagged Topics

Diversity

Tagged Divisions

Electrical and Computer

Paper ID #31303Simple Steps to Lower Student Stress in a Digital Systems Course WhileMaintaining High Standards and ExpectationsDr. Rabih Younes, Duke University Rabih Younes is an Assistant Professor of the Practice in the Department of Electrical and Computer Engineering at Duke University. He received his PhD in Computer Engineering from Virginia Tech, Blacksburg, VA after having received his BE and MSE in Computer Engineering from the Lebanese American University, Byblos, Lebanon. Rabih speaks nine languages (fluent in three) and holds a number of certificates in education, networking, IT, and skydiving. He is a member

Conference Session

Tricks of the Trade

Collection

2013 ASEE Annual Conference & Exposition

Authors

Joi-lynn Mondisa, Purdue University, West Lafayette; Junaid A. Siddiqui, Purdue University, West Lafayette; Mel Chua, Purdue University; Linda Vanasupa, California Polytechnic State University; Roberta J Herter, California Polytechnic State University; Robin Adams, Purdue University, West Lafayette

Tagged Divisions

Student

Paper ID #7044Lessons Learned from Others’ Stories: How Changemakers’ Stories ChangedUsMs. Joi-Lynn Mondisa, Purdue University, West Lafayette Joi-Lynn Mondisa is a doctoral student in the School of Engineering Education at Purdue University, West Lafayette. Her research interests focus on examining how mentoring intervention programs promote the success of undergraduates in STEM majors and how mentoring can increase the retention rates of underrepresented populations in STEM programs.Mr. Junaid A. Siddiqui, Purdue University, West Lafayette Junaid A. Siddiqui is a doctoral candidate at the School of Engineering

Conference Session

Equity, Culture & Social Justice in Education Division (EQUITY) Technical Session 9

Collection

2023 ASEE Annual Conference & Exposition

Authors

Jennifer Ackerman, Texas A&M University; América Soto-Arzat, Texas A&M University; Christine A Stanley, Texas A&M University; Reuben A Buford May, University of Illinois at Urbana - Champaign

Tagged Topics

Diversity

Tagged Divisions

Culture & Social Justice in Education Division (EQUITY), Equity

Paper ID #37423Intersectionality Between Race and Gender in LSAMP-NSF STEM ProgramMentorshipMs. Jennifer Ackerman, Texas A&M University I am a third year PhD student at Texas A&M University in College Station, and am a first-generation, queer, female student from New York. I am in the higher education administration program and my research interests include engineering education for underrepresented students, especially women in the field. I am interested in how their mental health is affected by being an outsider in and out of the classroom.Am´ rica Soto-Arzat, Texas A&M University e The second author is

Conference Session

New Teaching Methods in Mechanics

Collection

2014 ASEE Annual Conference & Exposition

Authors

Daniel Takashi Kawano, Rose-Hulman Institute of Technology; Benson H. Tongue, University of California, Berkeley

Tagged Divisions

Mechanics

Paper ID #8402Video-based Online Learning: The Other Side of the Looking GlassDr. Daniel Takashi Kawano, Rose-Hulman Institute of Technology Daniel Kawano is an Assistant Professor of Mechanical Engineering at Rose-Hulman Institute of Technol- ogy. He received his B.S. degree in Mechanical Engineering from California Polytechnic State University, San Luis Obispo. He obtained his M.S. and Ph.D. degrees in Mechanical Engineering, with a focus in dynamical systems, from the University of California, Berkeley.Dr. Benson H. Tongue, University of California, Berkeley GA Tech 1983-1988, UC Berkeley 1988-present. Author of

Conference Session

COED: Online and Remote Learning

Collection

2023 ASEE Annual Conference & Exposition

Authors

James Edward Toney, The Ohio State University

Tagged Topics

Diversity

Tagged Divisions

Computers in Education Division (COED)

Paper ID #36975Application of Mastery Learning in an Online MATLAB Programming CourseDr. James Edward Toney, The Ohio State University James Toney earned the Ph.D. in applied physics from Carnegie Mellon University in 1998 and the B.S. in electrical engineering from Rensselaer Polytechnic Institute in 1984. He is a Senior Lecturer in the Department of Engineering Education at Ohio State, where his focus is on curriculum development for teaching computer programming, primarily in MATLAB. He has previously held R&D positions at Bat- telle, Penn State Electro-Optics Center, and SRICO, Inc., where he worked on modeling

Conference Session

Electrical and Computer Division Technical Session 1

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Amy Fritz, Stanford University; Mark Horowitz, Stanford University; Atindra Jha, Stanford University

Tagged Divisions

Electrical and Computer

Paper ID #33334Online, Interactive Tool for Studying How Students Troubleshoot CircuitsAmy Fritz, Stanford University Amy Fritz is an electrical engineering PhD student at Stanford University who works with Professor Mark Horowitz in the department of electrical engineering on education research.Prof. Mark Horowitz, Stanford University Mark Horowitz is the Yahoo! Founders Professor at Stanford University and was chair of the Electrical Engineering Department from 2008 to 2012. He co-founded Rambus, Inc. in 1990 and is a fellow of the IEEE and the ACM and a member of the National Academy of Engineering and the American

Collection

2018 ASEE Mid-Atlantic Section Spring Conference

Authors

Jeffrey L. Schwartz P.E., Queensborough Community College

Tagged Topics

Diversity

ancient method of Egyptian fractionscan be used for this purpose when teaching parallel resistors, whether a professor has a totalresistance or a particular resistor in mind, or whether they want to use standard manufacturers’values.KeywordsAlgebra, Electrical Engineering Education, IEC Standards, Mathematical Analysis, ResistorsIntroductionWhen teaching introductory electronics courses, I try to use examples with integer solutions inorder to give students a better sense of the quantities involved in the circuits. This is similar to“when a teacher is first introducing students to the Pythagorean Theorem, she usually likes to giveexamples that have easy numbers, ones that don’t get too ‘messy’ in their calculations.”1 Whenteaching the Pythagorean

Collection

2021 Fall ASEE Middle Atlantic Section Meeting

Authors

Andrew Grossfield Ph. D, Vaughn College of Aeronautics and Technology

the common singularities and computational problems of the common functionsand curves of calculus. Discontinuities like those possessed by the Dirichlet function, were notincluded but should be delayed, if needed, for future study.By the end of the 18th century mathematicians, led by Leonhard Euler and Daniel Bernoulli, hadcrystallized the calculus currently taught to engineers and physicists. The engineers andphysicists of the 18th century would not have been perturbed by the previous examples. At thebeginning of the 19th century, starting with Fourier, cracks were discovered in themathematicians’ logical system. The finest 19th century mathematical minds explored all thecontradictions and combinations in the real number system culminating