Internship Opportunities (Fall, 2. If so, that information will almost always be included in the details found in the organization’s postings. In this list, 1) click on the organization's name to go to its homepage, and 2) click on “co- op” to go to an organization’s current postings (or to a website from which you can then access the postings). All positions are listed in alphabetical order by their locations. Adirondack Mountain Club, Lake Placid, NY, co- op: scroll down to Seasonal Positions and select Summer Naturalist Intern. Agricultural Research Service (USDA), Washington, DC (and other locations), co- op: numerous ongoing opportunities. Alabama A& M University, Huntsville, AL, co- op: REU- China: Ecological and Environmental Research in an Urbanized Landscape - . Travel, housing, and research related expenses will be covered. The deadline for submitting applications and supporting materials is October 1. American Society of Plant Biologists, Rockville, MD, co- op: applications accepted starting December 1. Archbold Biological Station, Lake Placid, FL, co- op: Research internships in the Avian Ecology Lab - opportunities are 6- 8 months in length. Arizona Game and Fish Department, co- op: Apply at www. Applicable majors would include biochemistry, biotechnology, cell biology, entomology, microbiology, molecular biology, plant pathology or plant physiology and bioinformatics. Engineering Research Center (ERC) for Re- Inventing the Nation’s Urban Water Infrastructure (Re. NUWIt), affiliated with several research investigators in California, Colorado and New Mexico. Information on applying to the 2. REU Program will be available in October. Field Museum of Natural History, Chicago, IL, co- op: annual summer REU opportunities. Pathways to Science Summer Research Opportunities. In our summer program. REU Aquatic Chemical Ecology at Georgia Tech When: 10 weeks Stipend. Summer REU in Aquatic Chemical Ecology at Georgia Tech January 14. Pacific Lutheran University 12180 Park Avenue S. Fossil Rim Wildlife Center, Glen Rose, TX, co- op: ongoing interest in interns to aid in veterinary care of free- range zoo animals. Friday Harbor Laboratory, San Juan Island, WA, co- op: REU: Integrative Biology and Ecology of Marine Organisms. Opens application process in February 2. Great Basin Institute, Reno, NV, co- op: regularly has opening in plant ecology, botany or related fields. Great Lakes Environmental Research Laboratory, Cooperative Institute for Limnology and Ecosystems Research, Ann Arbor & Muskegon, MI, co- op: Great Lakes Summer Student Fellows; applications open January 2. Houston Zoo, Houston, TX, co- op: paid internships in the zoo’s Collegiate Conservation Program. Applications open in December 2. Howard Hughes Research Institute, Janelia Farm Research Campus, Ashburn, VA, co- op: will be accepting applications for its 2. Fall 2. 01. 6; evolutionary biology and computational biology. Hudson River Foundation, New York, NY, co- op(2. Tibor T. Polgar Fellowship Program to pursue research on the Hudson River. Huyck Preserve and Biological Research Station, Rensselaerville NY, co- op: Annually offers Odum Internships in Field Ecology. Unpaid, housing and equipment are provided. Indiana University, Center for the Integrative Study of Animal Behavior, Bloomington, IN, co- op: REU summer program applications close February 1, 2. Primary Institution: Georgia Institute of Technology City: Atlanta State: GA: Job Duration: 10 weeks running from late May to the end of July Class Requirement: Freshman or sophomore or. Aquatic Chemical Ecology NSF-REU at Georgia Tech. As in the first 7 years of our REU program, the research theme of Aquatic Chemical Ecology is broadly interpreted. REU in Aquatic Chemical Ecology at Georgia Tech NSF-Sponsored Research Experience for Undergraduates in Aquatic Chemical Ecology at Georgia Tech. Aquatic Chemical Ecology (ACE) at Georgia Tech is a summer undergraduate. Longwood Gardens, Kennett Square, PA - co- op, application(2. Rotational. Louis Caldor Center Biological Field Station, near Armonk, NY, co- op: REU program will be restarted in 2. Marine Biological Laboratory, Woods Hole, MA, co- op: click on Search MBL jobs; several opportunities will be listed at various locations; check the details for each listing. Monterey Bay Aquarium Research Institute, Moss Landing, CA, co- op: will open up the application process for Summer 2. November 2. 01. 6. Montshire Museum of Science, Norwich, VT, co- op: 1. Mote Marine Laboratory, Sarasota FL, co- op: College Internship Program; REU applications will be posted online in January 2. Mount St. Helens Institute, Amboy, WA, co- op: Education & Interpretation Internships. National Council for Science and the Environment, Washington, DC, co- op: several positions/locations listed with many different organizations. National Ecological Observatory Network, Boulder, CO, co- op: will open applications for Summer 2. Fall 2. 01. 6. National Oceanographic and Atmospheric Administration (NOAA), Washington, D. C. Hollings Undergraduate Scholarship Program includes summer internship at NOAA’s facilities. National Park Service, many locations, co- op: many internships open on a regular basis. National Renewable Energy Laboratory, Golden, CO, co- op: applications will open for the 2. Summer Term in October 2. Science Undergraduate Laboratory Internships (SULI) Program. Oak Ridge National Laboratory, Oak Ridge, TN, co- opapplication: Higher education research experiences in Environmental and Marine Sciences. Perry Institute for Marine Science, Jupiter, FL and Lee Stocking Island, Bahamas; co- op: internships are unpaid, however, interns receive a fully or partially subsidized room (shared accommodation) and board. Transportation to Exuma International Airport (Georgetown, Bahamas) will be the responsibility of the chosen interns. Point Blue Conservation Science, several locations in California, co- op: internships in numerous scientific specialties. Rocky Mountain Biological Laboratory, Crested Butte, CO, co- op: routine offerings in Summer; check back in November 2. Experience. The Arboretum at Flagstaff, Flagstaff, AZ, co- op: Several positions for interns in arid mountain botany. The Conservancy of Southwest Florida, Naples, FL, co- op: some positions are for six months, others for three months; some require a bachelor's degree; all others require applicant to be a senior undergraduate. University Corporation for Atmospheric Research, Boulder, CO, co- op: Applications for SOARS will open in November 2. University of Colorado, Department of Ecology and Evolutionary Biology, Boulder, CO, co- op: “check back in Fall 2. Summer 2. 01. 7 program.”US Fish & Wildlife Service, Washington, DC, co- op: several positions listed in many different locations; most are at National Wildlife Refuges. Virginia Institute of Marine Science, Gloucester Point, VA, co- op: REU for Summer 2. November 2. 01. 6. Whitney Laboratory for Marine Bioscience, St. Augustine, FL, co- op: REU; online applications for Summer will open in February 2. Wide range of projects in many different areas of the life sciences. Zoological Society of Milwaukee, Milwaukee, WI, co- op: applications for Summer 2. November 2. 01. 6.
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Human Resources; Information Systems. In the finance and accounting development program. Office of Innovation & Improvement. Home » What We Do » Teacher Quality » School Leadership Program » Awards. Physician Quality Program Manager at Baylor Scott. Humboldt State University: Summary. Reach the right Quality Improvement Program Manager candidates with. Home » What We Do » Teacher Quality » School Leadership Program » Awards. California State University. Georgia Leadership Institute for School. STRATEGIC PLANNING & QUALITY IMPROVEMENT. California State University. Included below is information regarding the new awards made in each fiscal year since FY 2. Fiscal Year (FY)Number of new awards. FY 2. 01. 40. FY 2. FY 2. 01. 20. FY 2. FY 2. 01. 01. 4FY 2. Complete list of School Leadership Program Grants MS Excel (3. MB). Year awarded. The 2006 California State University Quality Improvement. Quality Improvement Program have. New York State Coverdell Stroke Quality Improvement Program Enlists. York State Coverdell Stoke Quality Improvement and Registry. Quality Initiatives & Training. Quality improvement is the concept of promoting continuous quality and productivity improvement in the California. Grantee. Project Title. Duration (Years)Year 1. Total Expected Funding. City. State. Score. Abstract. Application. Reviewer's comments. California State University, Dominguez Hills. Innovative School Leadership Innitiative. Carson. CA1. 00. 0. PDF(2. 3 KB)PDF(4. KB)PDF(1. 55 KB)2. Center for Collaborative Education. Building a High Quality Leadership Pipeline for LAUSD’s Autonomous Schools. Boston. MA9. 8. 3. Quality Improvement Specialist at. University of California, San Francisco, Humboldt State University. Reach the right Quality Improvement/program Manager. 2006 California State Information Technology Annual Report: The Information Technology Workforce Improvement Program. State University for the. PDF(9. 0 KB)PDF(1,2. KB)PDF(1. 51 KB)2. Delta State University. Delta School Leadership Pipeline (DSLP) Project. Bachelor of Science Quality Assurance. California State University Dominguez Hills provides the following information for its online and. Academic Quality Improvement Plan. Program Academic Quality Improvement. Cleveland. MS9. 8. PDF(1. 31 KB)PDF(8. KB)PDF(1. 56 KB)2. Foundation for Educational Administration. Rs for School Leadership: Recruit, Retain, Renew. Monroe Township. NJ9. PDF(1. 2 KB)PDF(2. KB)PDF(1. 53 KB)2. Georgia Leadership Institute for School Improvement, Inc. High Calling: Coaching and Learning for Leaders. Lawrenceville. GA9. PDF(8 KB)PDF(3. 33 KB)PDF(1. KB)2. 01. 3Granite School District Granite's Objective for Accomplished Leadership 2. Salt Lake City. UT9. PDF(1. 2 KB)PDF(5. KB)PDF(1. 50 KB)2. Green River Regional Educational Cooperative. Learning 2 Lead. 5$1,0. Bowling Green. KY1. PDF(6. 6 KB)PDF(5. KB)PDF(1. 61 KB)2. Illinois State University. The Illinois Partnership Advance Rigorous Training Project. Normal. IL9. 6. 3. PDF(4. 2 KB)PDF(6. KB)PDF(1. 51 KB)2. New Leaders, Inc. The Leadership Development Program. New York. NY9. 9. PDF(5. 7 KB)PDF(9. KB)PDF(1. 57 KB)2. North Carolina State University The Northeast Leadership Academy 2. Raleigh. NC9. 8. 0. PDF(7. 6 KB)PDF(7. KB)PDF(1. 59 KB)2. Region 5 Education Service Center. Principal Leadership Certification and Mentoring Program. Beaumont. TX9. 8. PDF(7. 7 KB)PDF(5. KB)PDF(1. 57 KB)2. Relay Graduate School of Education. Relay GSE National Principals Academy. New York. NY9. 7. PDF(1. 91 KB)PDF(8. KB)PDF(1. 60 KB)2. The Board of Education of the County of Mc. Dowell. Rural West Virginia Principal Development Program Demonstration Project. Welch. WV1. 00. 0. PDF(1. 17. KB)PDF(4. KB)PDF(1. 54 KB)2. The Board of Trustees of the University of Illinois. Cycles of Innovation and Continuous Improvement. Chicago. IL9. 9. 0. PDF(2. 82 KB)PDF(3. KB)PDF(1. 51 KB)2. The New Teacher Project, Inc. Camden. PLUS+: Developing Great Leaders for Camden City Public Schools. Brooklyn. NY9. 9. PDF(8. 4 KB)PDF(6. KB)PDF(1. 58 KB)2. Tulsa Independent District No. Tulsa Public Schools. Student Leadership Project. Tulsa. OK9. 6. 6. PDF(1. 2 KB)PDF(1. KB)PDF(1. 51 KB)2. Universidad del Este. Leadership in Educational Administration. Carolina. N/A9. 6. PDF(2. 7 KB)PDF(5. KB)PDF(1. 60 KB)2. Wheaton R3 School District. Leadership Initiative Networking Change. Kalamazoo. MI9. 7. PDF(1. 54 KB)PDF(7. KB)PDF(1. 50 KB)2. William Paterson University. Leaders as Learners. Wheaton. MO9. 8. 6. PDF(1. 25 KB)PDF(4. KB)PDF(1. 52 KB). Albuquerque Public School District. Alliance for Leading and Learning 5$6. Albuquerque. NM9. MS Word(3. 3 KB)- PDF(1. KB)2. 01. 0California League of Middle Schools. Schools to Watch Leadership Academy at Compton United School District. Long Beach. CA1. 05. MS Word (3. 2 KB)- PDF(1. KB)2. 01. 0California State University, Dominguez Hills. Charter and Autonomous School Leadership Academy. Carson. CA9. 3. 6. MS Word (3. 2 KB)- PDF(1. KB)2. 01. 0East St. Louis School District 1. Leadership Innovation for Today. East St. Louis. IL9. MS Word (3. 3 KB)- PDF(1. KB)2. 01. 0Hampton University. Hampton University Leadership Academy. Hampton. VA9. 1. 6. MS Word (3. 3 KB)- PDF(1. KB)2. 01. 0Lehigh University. Allentown Principal Leadership Initiative. Bethlehem. PA9. 3. MS Word (3. 2 KB)- PDF(1. KB)2. 01. 0Long Beach Unified School District. Principals' Professional Learning Community. New York. NY9. 6. MS Word (3. 3 KB)- PDF(1. KB)2. 01. 0Memphis City Schools (Shelby County)School Leadership Initiative. Memphis. TN9. 5. 3. MS Word (3. 3 KB)- PDF(1. KB)2. 01. 0New Leaders, Inc. The New Leaders New York City Principal Support Program. New York. NY9. 6. MS Word (3. 3 KB)- PDF(1. KB)2. 01. 0North Mississippi Education Consortium. Mississippi Leadership Excellence for Acceleration in Developing Schools. University. MS9. 4. MS Word (3. 3 KB)- PDF(1. KB)2. 01. 0Saint Paul Public Schools - Independent School Dist # 6. Camden. PLUS+: Turnaround St. Paul. 5$6. 38,3. 05$3,0. Saint Paul. MN1. 00. MS Word (3. 4 KB)- PDF(1. KB)2. 01. 0School Board of Miami- Dade County. Building Capacity through Residency. Miami. FL9. 2. 0. MS Word (3. 2 KB)- PDF(1. KB)2. 01. 0Western Michigan University. Learning- Centered Leadership Development Program. Kalamazoo. MI9. 7. MS Word (3. 5 KB)- PDF(1. KB)2. 01. 0Winthrop University. Network of Leaders for Equity, Achievement, and Development. Rock Hill. SC9. 1. MS Word(3. 3 KB)- PDF(1. KB). 2. 00. 92. 00. Elizabeth City State University. Northeastern North Carolina School Leadership Program. Elizabeth City. NC1. MS Word(3. 2 KB)- PDF(3. KB)2. 00. 9Houston Independent School District. Alternative Certification Program Principal Academy for Collaborative Engagement. Houston. TX1. 06. MS Word(3. 2 KB)- PDF(9. KB)2. 00. 9New Leaders, Inc. New Orleans Public Schools New Leaders Program. New Oreleans. LA1. MS Word(3. 2 KB)- PDF(4. KB)2. 00. 9School Board of Orange County. Building Rigor into Developing Great Educational Leadership. New Orleans. 10. 4. MS Word(3. 2 KB)- PDF(4. KB)2. 00. 9Southeast Kansas Education Service Center. Kan. Lead Kansas. Girard. KS1. 05. 0. MS Word(3. 2 KB)- PDF(7. KB)2. 00. 9Terrebonne Parish School District. TPSD School Leadership. Houma. LA1. 06. 6. MS Word(3. 2 KB)- PDF(1. KB)2. 00. 9Texas A& M University System. Leadership: Education and Development. College Station. TX1. MS Word(3. 2 KB)- PDF(1. KB)Note: Documents coming soon are marked with a dash. Programs & Courses Apply & Enrol. Police & Investigations - Police Studies. Police & Investigations - Police Studies. Policing in the 21st Century. Building a new public safety model in Ontario AMO’s Policing Modernization Report. Programs, Courses and Workshops. Date modified: 2016-06-17. Explosives Training Unit. Advanced Render Safe Procedures (ARSP). Professional Development Centre for Aboriginal Policing. Aboriginal Gang Reduction Strategies (AGRS). Community policing; Programs. Family Programs; Women's Programs; Youth Programs; Sisters Speak. One of the central roles of VACPC is to create a safe space where Aboriginal community members can feel comfortable reporting. Police Foundations College Program, Ontario??? Police Programs, Courses and Degrees in Ontario Police Foundations - Algonquin College of Applied Arts and Technology Algonquin College's 2- year Police Foundations diploma prepares students 'to become police constables,' particularly in Ontario. Students will be provided with 'a broad education in human relations skills and the interpretations of social interaction' and equipped with a thorough knowledge and understanding of 'police powers and procedures, community policing, investigation processes, race relations, professional ethics and communication.' Police Foundations - Intensive - Algonquin College of Applied Arts and Technology Algonquin College's 3- term Police Foundations - Intensive diploma is designed 'for University graduates and graduates of two- year or three- year College programs' aspiring to achieve a career in police services, or related areas like private security. Students will be equipped with the academic, practical, and physical abilities to challenge the various entrance assessments, examinations, and/or programs that police departments may require as part of their hiring process. Police Foundations - Cambrian College of Applied Arts and Technology Cambrian College's 2- year Police Foundations diploma provides students `with a combination of academic and generic skills training as preparation for potential employment with a police service in Ontario.' The Program provides participants with an in- depth knowledge and understanding of the police profession and relevant issues and will 'compliment subject matter covered by the Ontario Police College.' Police Foundations - Canadore College Canadore College's 2- year Police Foundations diploma trains students in the academic, practical, and physical abilities to challenge the various entrance assessments, examinations, and/or programs that police departments may require as part of their hiring process. A unique learning opportunity presented by the Program is the Summer Ambassador Program, 'a paid placement program where students have the chance to work alongside North Bay Police Officers.' Police Foundations - Centennial College of Applied Arts and Technology Centennial College's 2- year Police Foundations program prepares students for careers in policing and related areas. The Program will be 'very intense,' with training being 'equivalent to that of a paramilitary environment.' Course work in the Program will be 'based on real life experiences and case studies through which students can assimilate a fundamental perspective on life.' Police Foundations - Confederation College Confederation College's 2- year Law and Security Administration program readies students for careers in various areas of criminal justice system administration, particularly Correctional Services, Customs and Immigration, and Law Enforcement. An Ontario policing regulation specifies that policing services must have. The Office of the Auditor General’s responsibility was to conduct an independent. Community Policing Unit. If you have any inquiries regarding our Community Policing Programs, please contact the Community Policing Unit, Office of Operations, at 213-486-6960 or e-mail us at ComPolicing@lapd. Toronto Police Service Youth in Policing Initiative. The initiative is a part of the “Summer Jobs for Youth” program created by Ontario’s Ministry of. Adopt a Child; Back to School Safety. Volunteer applications are available at the Belleville Community Policing Office or the Belleville Police. Belleville, Ontario K8N 1C2 Emergency Once a cadet successfully completes their prescribed training at both colleges. The fees for the Ontario Police College Recruit Training are $11,065. The Program's 'course matter is given in a practicum setting.' Law Enforcement (Advanced Law Enforcement and Investigations) - Durham College Durham College's 2- year Diploma in Law and Security Administration equips learners with the a broad range of knowledge and skills required to work in a 'diverse range of career options' in criminal justice system administration. The College believes that students' interests are best served by graduating with a general rather than specialized knowledge of criminal justice administration. Police Foundations - Durham College Durham College's 1- year Penology and Youth Certificate prepares students for a diverse range of careers in corrections and related areas of the criminal justice system, particularly those concerned with young offenders. The Program has been designed through consultations between the College and its 'community agency partners' thus ensuring that what students learn and the skills they are acquire are current and relevant to the needs of employers in the field. Ontario College Certificate in 9. Emergency Response - Durham College Durham College's 2- year Legal Office Administration diploma prepares students for careers in legal office administration. Students will be equipped with 'a basic understanding of law, with emphasis on the rules of procedure' as well as with the attitudes, work habits, and skills required to effectively perform the duties required of those employed in a legal administration environment. Police Foundations - Fanshawe College of Applied Arts and Technology Fanshawe College's 2- year Law Clerk diploma program provides 'students with the solid grounding in business law' as well as 'the practical law clerk/paralegal training' enabling them 'to enter the diverse, fast- paced, ever- changing field of law.' Students will be exposed to a broad array of 'areas of Canadian law' as well as to 'a variety of cutting- edge legal software applications and online commercial legal databases and services.' Police Foundations - Georgian College of Applied Arts and Technology Georgian College's 2- year Legal Office Administration diploma prepares students for careers in legal office administration and related areas. The Program's main goal is to equip students with the attitudes, work habits, and skills required to effectively perform the duties required of those employed in legal administration, such as 'in legal and paralegal organizations.' Through training that extends beyond the diploma, particularly via experience, graduates may specialize 'in conveyancing, litigation, family, estate and corporate practice, with a law firm, or' assume 'administration duties in a paralegal or business setting.' Police Foundations - Humber College Institute of Technology and Advanced Learning Humber College's 2- year Police Foundations diploma equips students with the theoretical and practical knowledge and skills required for effective police work, including the ability to address, effectively, the myriad of problems faced by the communities in which they will work. Students will have the opportunity to apply what they learn in the classroom to real- world situations via unpaid community service work experience placements of varying length. Police Foundations - Lambton College of Applied Arts and Technology Lambton College's 2- year Police Foundations diploma equips candidates with the knowledge and skills required for effective police work. Candidates will also be provided with 'a broad education in human relations skills and the interpretations of social interaction' as well as with 'an understanding of how to conduct a job search' Police Foundations - Loyalist College of Applied Arts and Technology Loyalist College's 2- year Police Foundations diploma prepares students for a career in policing or related areas, like security. The Program will train candidates in 'the most rigorous physical fitness standard used in any' police recruitment 'process, preparing Loyalist graduates to place among the top tier of applicants in this competitive field.' Police Foundations - Mohawk College of Applied Arts and Technology Mohawk College 2- year Police Foundations diploma prepares students for a career in policing or related areas. Candidates will be trained in the academic, practical, and physical abilities to be able to challenge the various entrance assessments, examinations, and/or programs that police departments may require as part of their hiring process. Police Foundations - Niagara College Niagara College's 2- year Police Foundations diploma prepares students for careers in policing or related areas, like private investigation or private security, and meets the mandated requirements for police work as established by the Government of Ontario. Students may opt for the Collaborative Study in Policing and Criminal Justice Program (CSPCJ) allowing them to earn both the Diploma from the College and a Bachelor's (Honours) degree from Brock University. Police Foundations (Accelerated) - Niagara College Niagara College's 1- year Accelerated Police Foundations diploma prepares students for careers in policing or related areas, like private investigation or private security, and meets the mandated requirements for police work as established by the Government of Ontario. Students may opt for the Collaborative Study in Policing and Criminal Justice Program (CSPCJ) allowing them to earn both the Diploma from the College and a Bachelor's (Honours) degree from Brock University. Police Foundations - Northern College of Applied Arts and Technology Northern College of Applied Arts and Technology's 2- year Police Foundations diploma prepares students for a career in policing or related areas. Candidates will also be trained in the academic, practical, and physical abilities to pass the various entrance assessments, examinations, and/or programs that police departments may require as part of their hiring process. First Nations Constable - Northern College of Applied Arts and Technology Northern College of Applied Arts and Technology's 2- semester First Nations Constable program prepares students 'for a career in reserve and off- reserve policing and policing services.' The Program is not, however, a replacement for formal police training as provided 'by the Ontario Provincial Police, the Ontario Police College and employers of prospective reserve first nations constables.' Police Foundations - Sault College Sault College's 2- year Police Foundations diploma equips students with the knowledge and skills 'for an entry- level position in policing,' and will deal primarily 'with the development, purpose, and operation of the legal system, law enforc. In this article we'll look at the best Windows 7 email. New users of Windows 7 have to look for a Windows 7 Mail program because Microsoft. Users of Outlook Express in XP or Windows Mail in Vista have to. Pegasus Mail for Windows. 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Program Schedule Program Information Donate One-Time Cash Donation Donation With Thank-You Gift. Copyright 2012-2016 WBAI Pacifica Radio in New York City. Beyond the Pale (radio program) Beyond the Pale is a weekly radio program broadcast on WBAI New York which 'explores cutting edge Jewish culture and offers local. Beyond the Pale is a weekly radio program broadcast on WBAI New York which 'explores cutting edge Jewish culture. Beyond the Pale is a weekly radio program broadcast on WBAI New York which 'explores cutting edge Jewish culture and offers.
Criminal brings a thoughtful approach to stories beyond the pale of typical radio listening. Roman Mars calls it 'truer crime.' Get to know Criminal. A Visual, Intuitive Guide to Imaginary Numbers – Better. Explained. Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories: It’s a mathematical abstraction, and the equations work out. Deal with it. It’s used in advanced physics, trust us. Just wait until college. Gee, what a great way to encourage math in kids! Basics of Complex Numbers Name Complex Numbers: Basics W. Complex Conjugate Fig. 7: Complex conjugate of a complex number z* = x – i y is the complex conjugate of z = x. Complex Numbers Basics I am assuming some familiarity with complex numbers. If you feel a bit queasy about them, you may want to read, for example, Sections 1 and 2. Today we’ll assault this topic with our favorite tools: And our secret weapon: learning by analogy. We’ll approach imaginary numbers by observing its ancestor, the negatives. Here’s your guidebook: It doesn’t make sense yet, but hang in there. By the end we’ll hunt down i and put it in a headlock, instead of the reverse. Video Walkthrough: Really Understanding Negative Numbers. Negative numbers aren’t easy. Imagine you’re a European mathematician in the 1. You have 3 and 4, and know you can write 4 – 3 = 1. Simple. But what about 3- 4? What, exactly, does that mean? How can you take 4 cows from 3? How could you have less than nothing? Negatives were considered absurd, something that “darkened the very whole doctrines of the equations” (Francis Maseres, 1. Yet today, it’d be absurd to think negatives aren’t logical or useful. Try asking your teacher whether negatives corrupt the very foundations of math. What happened? We invented a theoretical number that had useful properties. Negatives aren’t something we can touch or hold, but they describe certain relationships well (like debt). It was a useful fiction. Rather than saying “I owe you 3. I’m up or down, I can write “- 3. I’m in the hole. If I earn money and pay my debts (- 3. I can record the transaction easily. I have +7. 0 afterwards, which means I’m in the clear. The positive and negative signs automatically keep track of the direction — you don’t need a sentence to describe the impact of each transaction. Math became easier, more elegant. It didn’t matter if negatives were “tangible” — they had useful properties, and we used them until they became everyday items. Today you’d call someone obscene names if they didn’t “get” negatives. But let’s not be smug about the struggle: negative numbers were a huge mental shift. Even Euler, the genius who discovered e and much more, didn’t understand negatives as we do today. They were considered “meaningless” results (he later made up for this in style). Basics of complex numbers Robin Chapman 13 January 2012 This is a summary of the basic facts about complex numbers. I shall assume that everyone coming to this course. It’s a testament to our mental potential that today’s children are expected to understand ideas that once confounded ancient mathematicians. Enter Imaginary Numbers. Imaginary numbers have a similar story. We can solve equations like this all day long: The answers are 3 and - 3. But suppose some wiseguy puts in a teensy, tiny minus sign: Uh oh. This question makes most people cringe the first time they see it. You want the square root of a number less than zero? There’s no “real” meaning to this question, right? Wrong. So- called “imaginary numbers” are as normal as every other number (or just as fake): they’re a tool to describe the world. In the same spirit of assuming - 1, . That is, you multiply i by itself to get - 1. What happens now? Well, first we get a headache. But playing the “Let’s pretend i exists” game actually makes math easier and more elegant. New relationships emerge that we can describe with ease.
You may not believe in i, just like those fuddy old mathematicians didn’t believe in - 1. New, brain- twisting concepts are hard and they don’t make sense immediately, even for Euler. But as the negatives showed us, strange concepts can still be useful. I dislike the term “imaginary number” — it was considered an insult, a slur, designed to hurt i. The number i is just as normal as other numbers, but the name “imaginary” stuck so we’ll use it. Visual Understanding of Negative and Complex Numbers. As we saw last time, the equation x^2 = 9 really means: or. What transformation x, when applied twice, turns 1 to 9? The two answers are “x = 3” and “x = - 3”: That is, you can “scale by” 3 or “scale by 3 and flip” (flipping or taking the opposite is one interpretation of multiplying by a negative). Now let’s think about x^2 = - 1, which is really. What transformation x, when applied twice, turns 1 into - 1? Hrm. We can’t multiply by a positive twice, because the result stays positive. We can’t multiply by a negative twice, because the result will flip back to positive on the second multiplication. But what about! It sounds crazy, but if we imagine x being a “rotation of 9. Yowza! And if we think about it more, we could rotate twice in the other direction (clockwise) to turn 1 into - 1. This is “negative” rotation or a multiplication by - i: If we multiply by - i twice, the first multiplication would turn 1 into - i, and the second turns - i into - 1. So there’s really two square roots of - 1: i and - i. This is pretty cool. We have some sort of answer, but what does it mean? Multiplying i is a rotation by 9. Multiplying by - i is a rotation of 9. Two rotations in either direction is - 1: it brings us back into the “regular” dimensions of positive and negative numbers. Numbers are 2- dimensional. Yes, it’s mind bending, just like decimals or long division would be mind- bending to an ancient Roman. It’s a strange, new way to think about math. We asked “How do we turn 1 into - 1 in two steps?” and found an answer: rotate it 9. It’s a strange, new way to think about math. When multiplying negative numbers (like - 1), you get a pattern: 1, - 1, 1, - 1, 1, - 1, 1, - 1. Since - 1 doesn’t change the size of a number, just the sign, you flip back and forth. For some number “x”, you’d get: This idea is useful. The number “x” can represent a good or bad hair week. Suppose weeks alternate between good and bad; this is a good week; what will it be like in 4. So - x means a bad hair week. Notice how negative numbers “keep track of the sign” — we can throw (- 1)^4. Week 1 is good, week 2 is bad. Things that flip back and forth can be modeled well with negative numbers. Ok. Now what happens if we keep multiplying by i? Very funny. Let’s reduce this a bit: Represented visually: We cycle every 4th rotation. This makes sense, right? Any kid can tell you that 4 left turns is the same as no turns at all. Now rather than focusing on imaginary numbers (i, i^2), look at the general pattern: X, Y, - X, - Y, X, Y, - X, - Y. Or anything with a cyclic, circular relationship — have anything in mind? There’ll de Moivre be more in future articles. Who says we have to rotate the entire 9. If we keep 1 foot in the “real” dimension and another in the imaginary one, it looks like this: We’re at a 4. It’s like a hotdog with both mustard and ketchup — who says you need to choose? In fact, we can pick any combination of real and imaginary numbers and make a triangle. The angle becomes the “angle of rotation”. A complex number is the fancy name for numbers with both real and imaginary parts. They’re written a + bi, wherea is the real partb is the imaginary part. Not too bad. But there’s one last question: how “big” is a complex number? We can’t measure the real part or imaginary parts in isolation, because that would miss the big picture. Let’s step back. The size of a negative number is not whether you can count it — it’s the distance from zero. In the case of negatives this is: Which is another way to find the absolute value. But for complex numbers, how do we measure two components at 9. It’s a bird. Yes, we are making a triangle of sorts, and the hypotenuse is the distance from zero: Neat. While measuring the size isn’t as easy as “dropping the negative sign”, complex numbers do have their uses. Let’s take a look. A Real Example: Rotations. We’re not going to wait until college physics to use imaginary numbers. Let’s try them out today. There’s much more to say about complex multiplication, but keep this in mind: Let’s take a look. Suppose I’m on a boat, with a heading of 3 units East for every 4 units North. I want to change my heading 4. What’s the new heading? Some hotshot will say “That’s simple! Just take the sine, cosine, gobbledegook by the tangent. Sorry, did I break your calculator? Care to answer that question again? Let’s try a simpler approach: we’re on a heading of 3 + 4i (whatever that angle is; we don’t really care), and want to rotate by 4. Well, 4. 5 degrees is 1 + i (perfect diagonal), so we can multiply by that amount! Here’s the idea: Original heading: 3 units East, 4 units North = 3 + 4i. Rotate counter- clockwise by 4. If we multiply them together we get: So our new orientation is 1 unit West (- 1 East), and 7 units North, which you could draw out and follow. But yowza! We found that out in 1. There were no vectors, matrices, or keeping track what quadrant we are in. It was just arithmetic with a touch of algebra to cross- multiply. Imaginary numbers have the rotation rules baked in: it just works. Even better, the result is useful. We have a heading (- 1, 7) instead of an angle (atan(7/- 1) = 9. How, exactly, were you planning on drawing and following that angle? With the protractor you keep around? No, you’d convert it into cosine and sine (- . Complex numbers beat you to it, instantly, accurately, and without a calculator. If you’re like me, you’ll find this use mind- blowing. And if you don’t, well, I’m afraid math doesn’t toot your horn. Sorry. Trigonometry is great, but complex numbers can make ugly calculations simple (like calculating cosine(a+b) ). This is just a preview; later articles will give you the full meal. Aside: Some people think “Hey, it’s not useful to have North/East headings instead of a degree angle to follow!”Really? Ok, look at your right hand. What’s the angle from the bottom of your pinky to the top of your index finger? Good luck figuring that out on your own. With a heading, you can at least say “Oh, it’s X inches across and Y inches up” and have some chance of working with that bearing. Complex Numbers Aren’t. That was a whirlwind tour of my basic insights. Take a look at the first chart — it should make sense now. There’s so much more to these beautiful, zany numbers, but my brain is tired. Portland State Maseeh College of Engineering & Computer Science: Engineering & Technology Management. This program significantly enhances the capabilities of engineers and managers who are involved in researching, defining, designing or developing new products, processes, hardware, software or services. Students tend to hold technical or managerial positions in product marketing engineering, technology marketing engineering, advanced R& D management, engineering management, software engineering, design engineering or project management. Sixteen credit hours are needed for the Graduate Certificate in New Product Development Management. Learning Outcomes: This program significantly enhances the capabilities of engineers and managers who are involved in researching, defining, desinging or developing new products, processes, hardware, software or services. It this class students will learn how to reduce risks inherent to all new product related decisions, justify an investment in new products, select the right ideas for development, create new product concepts, assemble and. Product Development Leadership Program. Product Development Graduate. Post Graduate Diploma Programs. Post Graduate Diploma in Quality Management; Post Graduate Diploma in Operation Management; Problem Solving. New Product Development. Human Error Prevention. New Product Development jobs. The Product Development Lead is responsible. Graduate Certificate in New Product Development (NPD). Sixteen credit hours are needed for the Graduate Certificate in New Product Development Management.Degree Programs; Development Engineering. New Product Development: Design Theory and Methods: 3. Home » Programs » Graduate. Those professionals who have a passion for product design and development will learn the necessary skills to ensure. Orange Mushroom's Blog ! This one contains the second area of Arcane River, Chew Chew Island, as well as the V Core Maker system and a few other changes. The next patch will be on August 1. MapleStory’s next mobile app. The next patch will be on August 18. Follow Orange Mushroom's Blog on WordPress.com. MapleStory Season 2 update available in. The patch will be released in six separate. Watch this video to learn what will be coming to the world of MapleStory in the Unleashed update coming next week. MapleStory RED update announced. New patch for Korean MMO to feature large scale boss. City of Dreams Lacheln, and a new boss, commander Lucid. 3DS DS iOS PC PS3 PS4 PSP Vita Wii U Xbox 360 Xbox One More Systems. Android; Ouya; Arcade; PlayStation; Dreamcast; PlayStation 2; Game Boy Advance. When does the next patch come out? Search Forums; Recent Posts; Members. MapleStory Private Server. Forums Support Question & Answer Resolved. Discussion in 'Resolved' started by. 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