Electrical engineering deals with the manipulation of electrons and photons to produce products that benefit humanity. The design of these products is based on scientific principles and theories that are best described mathematically. Mathematics is thus the universal language of electrical engineering science. Undergraduate electrical engineering education must provide students with the conceptual skills to formulate, develop, solve, evaluate and validate physical systems. Our students must understand various problem-solving techniques and know the appropriate techniques to apply to a wide assortment of problems. We believe that the mathematics required to enable students to achieve these skills should emphasize concepts and problem-solving skills more than emphasizing repetitive mechanics of solving routine problems.Students must learn the basic mechanics of mathematics, but care must be taken that these mechanics do not become the primary focus of any mathematics course. More generally, it is vitally important that electrical engineering students recognize the importance and beauty of mathematics in their chosen profession. We feel strongly that students will appreciate the power of mathematics if each mathematics course clearly states its objectives at the outset. Students should be told what they are going to study, why they are going to study it, and how it fits into the engineering profession.This motivation will need to be repeated throughout each course. Many undergraduate mathematics curricula currently supporting electrical engineering programs could be modified to better meet the needs of these programs. What follows are common weaknesses (from the viewpoint of electrical engineering) seen in many mathematics curricula.
1. Too much time and emphasis are placed on topics that are not widely used while topics that have widespread use often receive cursory treatment. One example is the excessive time and attention spent on various solution techniques for ordinary differential equations. Although understanding the structure of solutions for first- and second-order, constant coefficient differential equations is important for electrical engineering problems, more useful and widely used are Laplace transforms and related techniques.Yet these latter topics are often given cursory treatment in favor of more general structure theory.
2. There is often a disconnect between the knowledge that students gain in mathematics courses and their ability to apply such knowledge in engineering situations. Perhaps, the use of more engineering or real life examples will reduce this disconnect. Based on current learning theory, efforts to focus on underlying principles (not necessarily abstract statements of mathematical concepts) that are applicable in many different contexts are effective in helping students to transfer knowledge.
3. Current mathematics curricula for engineering are front-end loaded. Consequently, as a matter of timing, many topics are presented too early and cannot be reinforced soon enough through engineering applications before students forget the topics.
4. Too often, mathematics is taught as a list of procedures or as theorem-proof exercises without grounding the mathematics in reality. While we do not expect mathematics instructors to be well versed in all engineering applications, we would like examples of mathematical techniques explained in terms of the reality they represent. We strongly urge that team taught mathematics courses be considered. Teams would consist of mathematics and electrical engineering professors. We feel that team-teaching could better motivate and enthuse our students.
5. Failure to utilize appropriate technological tools while continuing to focus on mastery of symbolic manipulation often encourages memorization and rote algorithm practice at the expense of conceptual and graphical comprehension. Introducing symbolic manipulation programs, e.g., MathCAD, Mathematica, Maple, would be valuable to subsequent electrical engineering courses whose instructors choose to allow/encourage students to perform routine symbolic and numerical manipulations using such programs.
6. The first two years of mathematics that support instruction in electrical engineering should present students with conceptual understanding of mathematical disciplines other than just single variable calculus, multivariable calculus and ordinary differential equations. Other mathematical subjects that are important for electrical engineering students include linear algebra, probability and stochastic processes, statistics, and discrete mathematics.
Electrical engineering is an exciting and creative profession. Those engineers possessing an understanding and facility of mathematics have an opportunity to be among the most creative of designers. Students need to know and to feel how important, how useful, and how meaningful mathematics is. Many courses stress the drudgery, not the beauty. This needs to be changed.
1. Too much time and emphasis are placed on topics that are not widely used while topics that have widespread use often receive cursory treatment. One example is the excessive time and attention spent on various solution techniques for ordinary differential equations. Although understanding the structure of solutions for first- and second-order, constant coefficient differential equations is important for electrical engineering problems, more useful and widely used are Laplace transforms and related techniques.Yet these latter topics are often given cursory treatment in favor of more general structure theory.
2. There is often a disconnect between the knowledge that students gain in mathematics courses and their ability to apply such knowledge in engineering situations. Perhaps, the use of more engineering or real life examples will reduce this disconnect. Based on current learning theory, efforts to focus on underlying principles (not necessarily abstract statements of mathematical concepts) that are applicable in many different contexts are effective in helping students to transfer knowledge.
3. Current mathematics curricula for engineering are front-end loaded. Consequently, as a matter of timing, many topics are presented too early and cannot be reinforced soon enough through engineering applications before students forget the topics.
4. Too often, mathematics is taught as a list of procedures or as theorem-proof exercises without grounding the mathematics in reality. While we do not expect mathematics instructors to be well versed in all engineering applications, we would like examples of mathematical techniques explained in terms of the reality they represent. We strongly urge that team taught mathematics courses be considered. Teams would consist of mathematics and electrical engineering professors. We feel that team-teaching could better motivate and enthuse our students.
5. Failure to utilize appropriate technological tools while continuing to focus on mastery of symbolic manipulation often encourages memorization and rote algorithm practice at the expense of conceptual and graphical comprehension. Introducing symbolic manipulation programs, e.g., MathCAD, Mathematica, Maple, would be valuable to subsequent electrical engineering courses whose instructors choose to allow/encourage students to perform routine symbolic and numerical manipulations using such programs.
6. The first two years of mathematics that support instruction in electrical engineering should present students with conceptual understanding of mathematical disciplines other than just single variable calculus, multivariable calculus and ordinary differential equations. Other mathematical subjects that are important for electrical engineering students include linear algebra, probability and stochastic processes, statistics, and discrete mathematics.
Electrical engineering is an exciting and creative profession. Those engineers possessing an understanding and facility of mathematics have an opportunity to be among the most creative of designers. Students need to know and to feel how important, how useful, and how meaningful mathematics is. Many courses stress the drudgery, not the beauty. This needs to be changed.
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