degree

a position on a scale of intensity or amount or quality

"a moderate grade of intelligence"

"a high level of care is required"

"it is all a matter of degree" a specific identifiable position in a continuum or series or especially in a process

"a remarkable degree of frankness"

"at what stage are the social sciences?" an award conferred by a college or university signifying that the recipient has satisfactorily completed a course of study

"he earned his degree at Princeton summa cum laude" a measure for arcs and angles

"there are 360 degrees in a circle" the highest power of a term or variable a unit of temperature on a specified scale

"the game was played in spite of the 40-degree temperature" the seriousness of something (e.g., a burn or crime)

"murder in the second degree"

"a second degree burn"

This article is about the term "degree" as used in mathematics. For alternate meanings, see degree (disambiguation).''In mathematics, there are several meanings of degree depending on the subject.

Degree of a polynomial - See main article Degree of a polynomial''The ''degree of a term of a polynomial'' in one variable is the exponent on the variable in that term; the ''degree of a polynomial'' is the ''highest'' such degree. For example, in 2''x''³ + 4''x''² + ''x'' + 7, the term of highest degree is !2''x''³ ;? this term, and therefore the entire polynomial, are said to have ''degree 3''.For polynomials in two or more variables, the degree of a term is the ''sum'' of the exponents of the variables in the term; the degree of the polynomial is again the highest such degree. For example, the polynomial !''x''²' 'y''²? + 3''x''³ + 4''y'' has degree 4, the same degree as the term !''x''²' 'y''².< br>
Degree of a vertex in a graph - See main article degree (graph theory)''In graph theory, the degree of a vertex in a graph is the number of edges incident to that vertex — in other words, the number of lines coming out of the point.

Degree of a continuous map - See main article degree (continuous map)''In topology, the term degree is applied to continuous function (topology)continuous maps between manifolds of the same dimension.

From a circle to itself - The simplest and most important case is the degree of a continuous map :$f\backslash colon\; S^1\backslash to\; S^1\; \backslash ,$.There is a projection :$\backslash mathbb\; R\; \backslash to\; S^1=\; \backslash mathbb\; R/\; \backslash mathbb\; Z\; \backslash ,$, $x\backslash mapstox$, where $x$ is the equivalence class of $x$ modulo 1 (i.e. $x\backslash sim\; y$ iff $x-y$ is an integer). If $f\; :\; S^1\; \backslash to\; S^1\; \backslash ,$ is continuous then there exists a continuous $F\; :\; \backslash mathbb\; R\; \backslash to\; \backslash mathbb\; R$, called a ''lift'' of $f$ to $\backslash mathbb\; R$, such that $f(z)\; =F(z)\backslash ,$. Such a lift is unique up to an additive integer constant and $deg(f)=\; F(x\; +\; 1)-F(x)\; \backslash ,$. Note that $F(x\; +\; 1)-F(x)$ is an integer and it is also continuous with respect to $x$; therefore the definition does not depend on choice of !$x$.

Between manifolds - Let $f:X\backslash to\; Y\; \backslash ,$ be a continuous map, $X$ and $Y$ closed oriented !$m$-dim ensional? manifolds.Then the degree of $f$ is an integer such that :$f\_m(X)=\backslash deg(f)Y.\; \backslash ,$ Here $f\_m$ is the map induced on the $m$ dimensional homology group, $X$ and $Y$ denote the fundamental classes of $X$ and !$Y$.Her e? is the easiest way to calculate the degree: If $f$ is smooth and $p$ is a regular value of $f$ then $f^\; (p)=\backslash \; \backslash ,$ is a finite number of points. In a neighborhood of each the map $f$ is a homeomorphism to its image, so it might be orientation preserving or orientation reversing. If $m$ is the number of orientation preserving and $k$ is the number of orientation reversing locations, then $deg(f)=m-k\; \backslash ,$.The same definition works for compact manifolds with boundary but then $f$ should send the boundary of $X$ to the boundary of $Y$.One can also define degree modulo 2 !(deg₂(' 'f''))? the same way as before but taking the ''fundamental class'' in Z₂ homology. In this case !deg₂('' f'')? is element of Z₂, the manifolds need not be orientable and if $f^\; (p)=\backslash \; \backslash ,$ as before then !deg₂('' f'')? is ''n'' modulo 2.

Properties - The degree of map is a homotopy invariant; moreover for continuous maps from the sphere to itself it is a ''complete'' homotopy invariant, i.e. two maps $f,g:S^n\backslash to\; S^n\; \backslash ,$ are homotopic if and only if deg(''f'') = deg(''g'').

Degree of freedom - A degree of freedom is a concept in mathematics, statistics, physics and engineering. See degrees of freedom. Category:AlgebraCategory:Graph theoryCategory:Algebraic topology

Degree Programs - Education Portal & Guide
Portal site that lists degree and online degree programs and offers school and college information, training, articles, school reviews and an extensive education guide.
http://www.findadegreenow.com/

Nursing Jobs
Flexble work schedule. Great pay. Assignments in: Nursing Homes, Hospitals, Residental Treatment Ctrs, Substance Abuse Ctrs, and Home Health.
http://www.allheartstaffing.com/

Homeland Security University project
The Homeland Security University project is a division of the Homeland Security Defense Coalition.
http://www.homeland-security-college.org/

Grand Pacific Education Network
A premier Education Consulants assiting you in the process of study abroad. No matter you are looking for a language program, program in High school, University or post-graduate courses; or it is in Canada, U.S. Switzerland or Europe. We are the expert you could rely on.
http://www.grandpac.com/

Jeevan :: Master of Computer Applications
Includes jeevan's personal & family details, photogallery, greeting cards, wallpapers, college campus stories, school life, babies world, quotes, filmstars, web directory
http://www.jeevan4u.com/

Thermal Degree
We offer a range of IT services for home and business users including web hosting and full website design from small sites to large bespoke projects.
http://www.thermaldegree.com/

Riversystems
Training, development, design, coaching and facilitation of employee and management development processes
http://www.riversystems.com/

Virtual Tours for Real Estate in Hudson, Columbia County, Upstate New York
Virtual Tours for Real Estate in Hudson, Columbia County, Upstate New York
http://www.hudsonhometours.com/

Gantlet: A Love Story
A five star (reader reviews) novel based on a true story of a 10-year custody battle, infanticide, a psychotic grandmother, a three million dollar federal lawsuit to rescue a child held hostage, and an unbelievable ending.
http://www.gantlet.info/

DEFENSEWORKS
Violence prevention and realistic self-defense training for corporations, non-profits, associations, hospitatlity pesonnel, hospitals, schools, military, security personnel, police, groups and individuals. Learn defenses against, strikes, kicks,gang attacks, ground attacks, knives, guns and car jacking while reducing stress, improving relaxation, learning violence prevention and intuition development.
http://www.defenseworks.us/

www.thebridge-ttc.org
The Bridge Theatre Training Company. Affordable, High Quality Actor Training. Based in London.
http://www.thebridge-ttc.org/

Homeland Security Defense Coalition
The Homeland Security Defense Coalition and Homeland Security University project was formed to provide one source for counter-terrorism training and education. The Homeland Security Defense Coalition and Homeland Security University project has recruited national and international counterterrorism experts to design and develop proactive courses to prevent the next terror attack, not just respond to it after it happens. Although several so called homeland security programs have cropped up post 9/11, they are the same only criminal justice and military science programs with a mild change in courses. Our programs are designed and taught by counter-terrorism and topic specific experts. Our programs range from two-day seminars in homeland security to a certificate or diploma in homeland security. Once we meet state educational regulatory compliance and begin the accreditation process, we will be offer undergraduate through graduate degree programs in public administration with a concentration in homeland security. The Homeland Security Defense Coalition and Homeland Security University project has been four years in the planning post 9/11. Our plans include opening 60 campuses across the USA and abroad. Our first campus is scheduled to open in 2006.
http://www.homeland-security-college.us/

eLearn-University.org
Online training courses and resources covering a wide range of subjects from a plethora of online providers.
http://www.elearn-university.org/

R. K. College of Systems & Management
Creating a niche in IT education in New Delhi since 1997
http://www.rkcsm.com/

360 Photos - 360° x 360° virtual tour photography, ipix virtual tours
360 degree photography enables you to offer an online virtual tour to anybody anywhere - 24 hours a day - 365 days a year!. Allowing potential clients to clearly see why they should visit or buy from you.
http://www.360-photos.com/

Instant Degree from only $110
Online Instant College Degrees and Diplomas - your distance learning degree program. Get your online College Degree or Diploma today! Choose from a Bachelor's, Master's or Doctorate College Degree and receive it fast in JUST DAYS.
http://www.fast-degrees-online.com/

John Bear's Degree Network
Learn how to earn Bachelors, Masters, or Doctorate degrees entirely by distance learning or by credit from prior learning, using mail, phone or the Internet. Bear's Guide is a classic in distance learning, and in evaluating the quality of programs.
http://www.degree.net

The Degree Confluence Project
The Degree Confluence Project contains photographs of the intersections of integer latitude and longitude degree lines.
http://www.confluence.org/

Degree.com
Offers online college courses for distant learning leading to a degree.
http://www.degree.com

Degree Controls Inc.
Manufacturer of custom thermal solutions for the communications market. Products include fan tray assemblies, thermal controllers, thermal analysis, system testing and evaluation and custom heat sinks. Online specifications and PDF discussion papers.
http://www.degreec.com/