GATE questions, answered.

An Electrical Engineering Technology degree program prepares students to design, develop and implement electrical devices and systems. These skills can be applied to a number of professions, from the drafters who design electrical equipment to the electricians who install and maintain it. This article will discuss the average pay for some common Electrical Engineering Technology jobs. Salaries of Common Electrical Engineering Technology Professions Graduates with an Electrical Engineering Technology degree can earn high wages in a variety of fields. Here is a list of jobs you could get with an associate's degree in Electrical Engineering Technology, along with each career's average yearly pay. Electrical Engineering Technician Electrical engineering technicians work under the direction of electrical engineers to install, build, repair and calibrate components. They assist the engineers in making decisions by modifying and maintaining electrical parts and systems as needed. They also maintain the testing equipment used to evaluate those parts. According to the Bureau of Labor Statistics (BLS), the average annual salary of electrical engineering technicians nationwide as of May 2008 was $53,990. The highest-paying industry for electrical engineering technicians is the federal government, with an average annual salary of $72,610. Electrician Electricians install the wiring that powers homes, offices, factories and other buildings. Many electricians specialize in either installation during construction or repair of existing systems, but some handle both. The vast majority of electricians work as building equipment contractors, whose average annual salary is $49,460, according to the BLS. Electricians can earn much higher wages working in other industries, such as $82,450 per year with the motion picture industry. But these groups hire very few electricians compared to the field as a whole. Electrical Drafter Electrical drafters create diagrams of electrical systems. They design circuit boards, lay out wiring plans for buildings, and draw schematics for the creation of electrical equipment. Drafters often use computer aided design, or CAD, for this purpose. In the U.S.A., electrical drafters earn average salaries of $53,770 each year, as reported by the BLS. The average is higher for drafters working in high-tech manufacturing industries such as aerospace and communications.

The discipline of Electrical Engineering entails designing, testing and developing electrical equipment. Electrical engineers work with all types of electrical apparatus and systems: from bringing electricity into homes to fabricating supercomputers. Most electrical engineers hold at least a bachelor's degree in Electrical Engineering; those who want to specialize in a particular area of Electrical Engineering typically earn a Master of Science in Electrical Engineering. Electrical Engineering at Work Electrical Engineering powers modern day technology. Whether you are using a calculator, watching digital television, surfing the Web, talking on your wireless phone or listening to your MP3 player, electrical engineers contributed significantly to that technology's development. Electrical engineers facilitate the process by which energy travels from hydroelectric plants, solar panels, fuel cells and turbines to homes, businesses and factories. Electrical Engineering as a Career According to the U.S. Bureau of Labor Statistics, approximately 153,000 electrical engineers practiced in the United States in 2006. This occupation is expected to grow faster than the average for other positions from 2006-2016. Electrical Engineering is a high-paying occupation. Electrical engineers earned an average salary of $85,350 in 2008. Electrical engineers work in a wide variety of industries, including aerospace, electrical power, construction, consumer products and semiconductors. Electrical Engineering Coursework Students who complete the coursework for Electrical Engineering degree programs learn through a combination of classroom theory and lab work. Students are taught how to analyze problems by thinking through issues and applying various concepts to form a range of possible solutions. The typical bachelor's degree curriculum covers these topics: * Classical Physics * Probabilistic Methods for Electrical Engineers * Electromagnetic Fields and Waves * Electric Circuits * Engineering Economic Analysis * Fundamentals of Logic Design Specializations in Electrical Engineering Electrical Engineering is comprised of a variety of sub-disciplines; each area of specialization requires specific training. Students working for a Bachelor of Science degree will get a solid general education in Electrical Engineering. Once they become upperclassmen or graduate students they choose one or two fields for developing their expertise. Here are a few of the choices students can make: * Communication * Computers and Digital Circuit Design * Control Systems * Electronic Circuit Design * RF (Radio Frequency) & Microwaves

The Department offers specialization in: a) ASIC/VLSI Design b) Digital Design c) Digital Signal Processing d) Analog/Digital Communication e) Analog/Mixed Signal IC Design f) Networking g) Control and Power Electronics

Electronics and Communication

It covers a wide range of applications we daily require and which make our lives easier and enjoyable such as Computers, Print Media, Audio and Video Media, Communication sector and memories etc.

They design, fabricate, produce, test and supervise the manufacture of complex products and systems i.e., electronic equipments and components for a number of industries including hospitals, computer industry, electronic data processing systems for communication and in defense etc. à They supervise production and manufacturing processes and oversee installation and maintenance of computers, peripherals and components.

Increased production and demand by government, Public sector and businesses for communication equipment, computers and military electronics along with consumer demand and increased research and development on robots and other types of automation contributes to the growth of employment opportunities in the field.

Candidates having a creative and inventive mind and also good at physics and mathematics will probably find electronics engineering both a challenging and lucrative career.

Telecom, hardware and Networking, applications of all kinds, embedded system allied areas such as VLSI Design and fabrication and Mobile computing and software development etc with some added specialization.

Yes. The list is endless. An electronics & communication engineer can get a job in Central Government, State Governments and their sponsored corporations in public sector and in all wings of the Armed Forces and also the private organizations.

As an Electronic Engineer, entry for junior posts Astt. Engineer in the Government departments is by direct recruitment through advertisements in newspapers. Selection to Gazetted posts is through the competitive examinations conducted by Union and State Public Service Commission. UPSC conducts an Engineering Service Examination (Telecommunication and Electronics Engineering group) annually for vacancies in Central Engineering Services and various State Public Service commissions conduct their own competitive Exams for vacancies in State engineering services.

The biggest employment opportunities for EC Engineer are in the computer related fields to related hardware & components and Networking and in the Telecom Sector. So you can apply for them.

Electronic Engineers can start their own small businesses by manufacturing electronic parts and goods. They can also set up repair or assembly shop for television receivers, amplifiers, recording equipment, etc. & outsourced activities from bigger organizations

* All Software Companies * TCS * Infosys * L & T Infotech * HCL * I-Gate * NIIT Technologies * Torry Harris * Wipro Infotech * EDS * Webcom * R Systems * Global Logic * Netchasers * Sapient * Sapient Informatics * FreeScale (Motorola) * LG * STM * Cadence * Agilent * NI * GE Electrical etc.

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There is not now and has never been a state-suggested pacing guide for mathematics. Collaborative creation of such a guide by experienced teachers is an excellent staff development activity that not only draws upon the expertise of teachers but also serves as an affirmation of their experience. This office has shared sample pacing guides with teachers to illustrate the various forms these guides can take. At the end of the Week-by-Week Essentials you will find the guide we used to organize these materials. This should not be considered a suggested pacing guide for schools but does help teachers locate the order in which the Week-by-Week Essentials are arranged.

The State Board of Education requires that schools and school districts implement assessments at grades K, 1, and 2 that include documented, on-going, individualized assessments throughout the year and a summative evaluation at the end of the year. These assessments monitor achievement of benchmarks in the North Carolina Standard Course of Study. They may take the form of the state-developed materials, adaptations of them, or unique assessments adopted by the school board. Grades K, 1, and 2 assessments were first implemented during the 2000-2001 school year.

The intended purpose of these assessments is fourfold: (1) to provide information about the progress of each student for instructional adaptations and early interventions, (2) to provide next-year's teachers with information about the status of each of their incoming students, (3) to inform parents about the status of their children relative to grade-level standards at the end of the year, and (4) to provide the school and school district information about the achievement status and progress of groups of students (e.g., by school and grade level) in grades K, 1, and 2.

They can't and shouldn't try if they want to remain sane. What they need to do is produce a pacing guide to map out which objectives will be taught when, and when assessment of those objectives is appropriate. Then they can consult the wealth of materials presented for assessment and choose those parts that meet their needs. This on-going assessment needs to be documented and at the conclusion of the academic year a summative assessment needs to be administered and shared with each student's next-year's teacher.

It is definitely important for all students to acquire the fundamental ideas of mathematics early in school, including operational facility with numbers (basic facts), and then build on those ideas to learn more advanced content. In the past, much of mathematics was learned through rote memorization; however, we now know that memorization is not an effective means of learning for understanding. Educational research indicates that the most permanent learning occurs when students learn concepts through applied problems prior to or concurrent with emphasis on skills. Approaching these applied problems with calculators enables students to concentrate on the problem rather than the computation, which will often be messy as are many real problems. Sound instructional practice recommends that students should have access to calculators for both instruction and testing, and they should be instructed in thoughtful and appropriate use of this powerful mathematical tool.

Many folks are definitely evaluating the practice of offering Algebra 1 in the Middle School in light of the mathematics content that is now included in the grades 6-8 North Carolina Standard Course of Study (NCSCS). As you look at the middle grades curriculum, you will note a rich curriculum that includes a significant amount of algebra and geometry in addition to the material from the Number & Operation, Measurement, and Data Analysis & Probability strands. Much of what had been in the former Algebra 1 curriculum is now moved to the middle school. There are middle school students who are definitely talented in mathematics and probably could master the 6-8 curricula along with an Algebra 1 course; however, you need to be careful about screening and placing students in this situation. It is mandatory that students master all the material outlined in the 6-8 NCSCS prior to taking an Algebra 1 course. An excellent resource that addresses this topic is the SREB (Southern Region Education Board) publication, Getting Students Ready for Algebra 1: What Middle Grades Students Need to Know and Be Able to Do.

The DPI Accountability section has a wealth of information available on EOG and EOC tests including test specifications, sample test items, and calculator requirements. You can access this information at the following web sites: www.ncpublicschools.org/accountability/testing/eog www.ncpublicschools.org/accountability/testing/eoc

The courses are to be offered and coded as shown. Except for Pre-Calculus, AP Calculus and AP Statistics, the Standard Course of Study defines the STANDARD version of each course. Introductory Mathematics (2020): standard only Algebra 1 (2023): standard only Geometry (2030): standard and honors Algebra 2 (2024): standard and honors Technical Mathematics 1 (2015): standard only Technical Mathematics 2 (2017): standard only Advanced Functions and Modeling (2025): standard and honors Discrete Mathematics (2050): standard and honors Pre-Calculus (2070): honors only Integrated Mathematics 1 (2051): standard only Integrated Mathematics 2 (2052): standard and honors Integrated Mathematics 3 (2053): standard and honors Integrated Mathematics 4 (2054): standard and honors AP Statistics (2065): AP only AP Calculus (2076): AP only

Introductory Mathematics (2020) is NOT an accelerated course for middle school students. It is a revisit of middle school mathematics for high school students who are not ready for Algebra 1.

The standard-only designation for Algebra 1 and honors-only designation for Pre-Calculus were established by State Board policy in 1995. The standard-only designation for Integrated Mathematics 1 was established by State Board policy in 2004.

High school students are required to successfully complete at least three courses for Career Prep and College Tech Prep Courses of Study and at least four courses for the College/University Prep Course of Study.

Beginning in the 2007-2008 school year, students who pass mathematics or foreign language courses taken during grades 6-8 that are described in the North Carolina Standard Course of Study for Grades 9-12 must achieve a Level III or IV on the end-of-course assessment, if available, to meet the high school graduation requirement.

A general answer to this question is that constructive mathematics is mathematics which, at least in principle, can be implemented on a computer. There are at least two ways of developing mathematics constructively. In the first way one uses classical (that is, traditional) logic. Unfortunately, that logic allows us to prove theorems that no computer can implement, so in order to do things constructively, we have to work within a strict algorithmic framework such as recursive function theory [22] or Weihrauch’s Type Two Effectivity theory [35]. This can make the resulting mathematics appear rather hard to read and certainly different from normal analysis, algebra, or the like. The second way of approaching constructivity is to replace classical logic by intuitionistic logic, which neatly captures the proof processes used when you work in a rigorously computational manner. This way has the advantage that, once you get used to a logic which does not allow, for example, the application of the law of excluded middle (LEM) P∨¬P, you find yourself working in the style of a traditional algebraist, analyst, and so on, without referring continually to a special algorithmic language and symbolism. In these comments I will use constructive mathematics (CM for short) to mean mathematics with intuitionistic logic. (Actually, we need a bit more than just a change of logic: namely, some kind of number–theoretic or set–theoretic foundation that does not conflict with that logic. One such foundation is constructive Zermelo–Fraenkel set theory [3].)

Why did I choose to do CM? Because I found it interesting, and because the idea of actually finding objects, instead of merely showing that they could not possibly fail to exist, was one that appealed to me. When I first came across Errett Bishop’s book, in 1968, I had been working on von Neumann algebra theory as a graduate student, and had been vaguely—and certainly inarticulately—dissatisfied with the prevailing style of existence proofs in my reading in that subject. Such proofs typically either proceeded by assuming the non–existence of the desired object and deducing a contradiction, or else applying Zorn’s lemma to ‘construct’ a maximal family of projections with some property or other. Somehow, beautiful though those proofs were, they left me with a feeling that I had been cheated. What did those objects whose existence was proved really look like? How could they be described explicitly? It was only on reading Errett’s book that I understood what was bothering me and that it was possible to give satisfactory answers to those questions. Now, don't get me wrong. Just because I find CM particularly appealing it is not the case that I dislike classical (that is, traditional) mathematics, let alone that I am advocating that classical mathematics is somehow not a proper activity for mathematicians to be engaged in. I find most classical mathematics (at least, what I can understand of it) very interesting and a worthy scientific/cultural pursuit. However, if, as I am, you are interested in computability/constructivity within pure mathematics (as distinct from, say, numerical analysis), then you should seriously investigate constructive mathematics. By working constructively—that is, with intuitionistic logic—you will learn to appreciate the distinction between idealistic existence (the impossibility of non–existence) and constructive existence. This distinction is one that, in my view, should be heeded and appreciated far more than it is. As Bishop wrote, "Meaningful distinctions deserve to be maintained" [6] If, however, you are not interested in questions of computability, then you should stick to classical logic. There are even areas of mathematics where the content is so highly nonconstructive that it would make little sense to give up classical logic; the higher reaches of modern set theory would seem to be just such an area. To summarise: CM should interest people who would like to understand better the distinction between classical and constructive existence, and who are interested in pushing beyond the former to a real construction of the object whose existence is asserted.

Generally, constructive proofs are quite complicated. This is hardly surprising, since they produce more (computational) information than their classical counterparts (if the latter have any). Consider, for example, the constructive proofs of Picard’s theorem in the following two classically equivalent forms. PTp Let ƒ be a holomorphic function on the punctured disc D (0,1) := {z ∈ C : 0 < |z| < 1} that omits two complex values from its range. Then ƒ has a pole of determinate order at 0. PTs Let ƒ be a holomorphic function on D(0,1) that has an essential singularity at 0, and let ζ, ζ′ be two distinct complex numbers. Then either there exists z ∈ D(0,1) with ƒ (z) = ζ or else there exists z ∈ D(0,1) with ƒ (z) = ζ′ These two theorems, although classically equivalent, are totally different from a constructive point of view. In PTp we use the data comprising the function ƒ and the two complex values omitted from its range, to construct an integer ν, show that the νth Laurent coefficient of ƒ is 0, and to show that all Laurent coefficients with index less than ν are zero. In PTs our data consist of the holomorphic function ƒ and the two distinct complex numbers ζ, ζ′, and the constructive proof embodies an algorithm converting those data to solution z of one of the equations ƒ (z) = ζ, ƒ (z) = ζ′; moreover, the proof shows which equation is actually solved. Now, it is hardly surprising that the constructive proofs of both PTp and PTs are rather complicated. For one thing, they rely on delicate estimates involving winding numbers and requiring a number of preliminaries that the classical proof of Picard’s theorem does not require. In addition, those algorithms could actually be extracted from the proofs and implemented on a computer. So we pay more in terms of effort and complexity of proof, but we get more for our money as well. The complexity of constructive proofs, other than those that use the Church–Markov–Turing thesis as an additional hypothesis (see [21]) is still largely untouched terrain. However, anecdotal evidence from Bas Spitters suggests that, perhaps contrary to one’s initial expectations, many of the proofs in Bishop’s book are remarkably efficient when implemented on a computer.

It all depends on what you mean by “brand new result”. If you take the classical viewpoint that every statement is either true or false and hence that once proved, a result is no longer new, then much of what we are doing will look like rewriting classical results. However, if you interpret a constructive theorem and its proof properly, then it is quite clear that, even if the statement of the theorem looks like something that is well known classically, both the properly–interpreted theorem and its proof are brand new. Consider yet again the Picard theorems discussed above. The full constructive interpretation of PTp is this: There is an algorithm which, applied to a holomorphic function ƒ on D(0,1) and to two complex values omitted from the domain of ƒ, computes the order ν of the pole that ƒ has at 0. I know of no proof of this statement other than the constructive one in [12] the theorem, as presented in my statement, is brand new. Moreover, that proof, while drawing on a classical proof of the classical Picard theorem for inspiration, is also new. Similarly, we have the constructive interpretation of PTs: There is an algorithm which, applied to a holomorphic function ƒ on D(0,1) , the data showing that ƒ has an essential singularity at 0 (that is, the sequence of Laurent coefficients of ƒ which contains infinitely many negatively indexed terms), and two distinct complex numbers ζ and ζ′, computes a complex number z and shows that either ƒ (z) = ζ or ƒ (z) = ζ′. Once again, this is a brand new theorem, nowhere found (to my knowledge) in the classical literature; and once again, its proof is also new. There are aspects of constructive mathematics that are clearly new, in that the classical mathematician would see nothing to prove where the constructive mathematicians does. For example, many theorems of constructive analysis require a certain subset S of a metric space X to be located, in the sense that the distance ρ(x,S) := inf { ρ(x,s) : ∈ S } exists (is computable). Proving that S is located may be a nontrivial matter. This is related to the failure of the classical least–upper–bound principle. For the constructive existence of the least upper bound of a nonempty subset S of R that is bounded above we need the additional condition (it is both necessary and sufficient) that S be order located: that is, for all real α, β with α < β, either β is an upper bound of S or else there exists s ∈ S with s > α. (Note that the “or” here is decidable: in constructive mathematics, to prove the disjunction p ∨ q, we must either produce a proof of p or else produce a proof of q.)

Yuk! I hate those management jargon words like “final products”. However, since people use them in questioning what we do, we’d better deal with them, like it or not. What is the final product of any branch of pure mathematics? Do, for example, set theorists like Hugh Woodin, working with extremely high–level abstractions, have a final product? If the questioner means “something that has applications in the real world”, then it seems totally unreasonable to expect constructive analysis to justify itself by the production of such a final product when that justification is not required of classical pure mathematics. If pushed, however, I would say that the final product of all pure mathematics, constructive and nonconstructive, is a body of results, proofs and techniques that contribute to the higher levels of human culture and that may, (as history shows) frequently will, have significant applications in the future.

Yes, it is. Research groups in Japan, the States, the United Kingdom, Sweden and Germany have been active in this area for many years [14, 18, 23, 30] A constructive proof of (let's use this one again) Picard‘s Theorem PTs really does contain an extractable algorithm for computing the point z with the properties stated in the conclusion of that theorem. Moreover, the proof is itself a proof that the program is correct—that is, meets its specifications. So the constructive result gives us two things for the price of one: an algorithm and a proof of its correctness. That's a real bargain!

On one level, this one is relatively easy to answer: the full Axiom of Choice (AC), (1) ∀x∈X ∃y∈Y P(x,y) ⇒ ∃ƒ ∈Y X ∀x∈X P(x,ƒ (x)), implies the Law of Excluded Middle (LEM), as was shown by Diaconescu [15] and later by Goodman–Myhill [17]. Contrary to a popular misconception that a dislike of, or disbelief in, AC is the reason why people do constructive mathematics, it is not AC, but LEM, that is the primary object of suspicion; However the fact that AC implies LEM confirms one’s instinct that AC is nonconstructive. In view of the Diaconescu–Goodman–Myhill theorem, what did Bishop mean when he said that under the hypotheses of (1), "A choice function exists … because a choice is implied by the very meaning of existence"? I believe that he meant that the constructive interpretation of the hypothesis in (1) is that there is an algorithm which leads us from elements x of X to elements y of Y such that P(x,y) holds. However, to compute the y from a given x, the algorithm will use not just the data describing x itself, but also the data proving that x satisfies the conditions for membership of the set A. Thus the algorithm will not be a function of x but a function of both x and its certificate of membership of A. The value at x of a genuine function from X to Y would depend only on x and not on its membership certificate. At a deeper level, the question is tricker to answer, at least if recast in the form, “What, if any, choice axioms are permissible in constructive mathematics?”. Some constructive mathematicians, notably Fred Richman, doubt the constructive validity of even countable choice (and hence of dependent choice). The argument in favour of countable choice is that one has to do no work to show that a natural number x belongs to the set N of natural numbers: each natural number is, as it were, its own certificate of membership of N. Thus in the case X = N, the choice algorithm implied “by the very meaning of existence” in (1) is, in fact, a genuine function on N. Needless to say, those who distrust even countable choice as a constructive principle do not buy into this argument.

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