Engineering mathematics - Wikipedia
Math is designed, just like software programs are designed, and using a linear relationship is represented as a linear operator — a matrix. connections between math, music, engineering, and science. relationships among frequency, wavelength, and speed of waves traveling in various media. 5. Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and .
What Kind of Math Is Expected of a Civil Engineering Student? | Education - Seattle PI
Mathematics is the language of physical science and engineering. Mathematics is more than tool for solving problems; mathematics courses can develop intellectual maturity. Computers do not make traditional mathematical analysis obsolete! First, computer programs contain mathematical relations; understanding these relations is still necessary. Second, debugging computer programs is a difficult art. One of the best ways to validate a program is to compare the computer simulation to the analytical solution for the same situation.
Knowledge of traditional mathematical analysis is essential for this method of validating computer programs. Third, it is relatively easy to write brute-force computer code that requires a long runtime and produces significant error, owing to accumulation of errors from the limited resolution of machine numbers. Great increases in both speed and accuracy can be obtained by using analytical solutions for parts of the problem, or by careful development of appropriate algorithms.
About 37 percent of engineering jobs are found in manufacturing industries and another 28 percent in professional, scientific, and technical services, primarily in architectural, engineering, and related services. Many engineers also work in the construction, telecommunications, and wholesale trade industries.
Some engineers also work for Federal, State, and local governments in highway and public works departments.
The algebraic operations of multiplication and addition translate to rotation and scaling of vectors in vector space. This allows us to analyze the geometric effects of a linear operator using algebra, breaking down the matrix into its constituent parts: The construction of linear algebra serves as an example of a pattern that is common throughout mathematics: Courtesy of Alice Zheng The design of mathematics encompasses a number of other principles that are also present in software engineering.
Take abstract algebra, for instance. Abstract algebra is essentially an exercise in object hierarchy design, where the goal is to use as few ingredients as possible, adding one more ingredient at a time, to see what kinds of interesting and useful constructs we can get.
A ring is a special type of group endowed with two operations that can be considered as generalizations of addition and multiplication. A field is a specialized ring with four operations generalizations of addition, subtraction, multiplication, and division. This should immediately start to sound familiar to a software engineer: This is another example of hierarchical object design, but with some interesting twists in the details.
We start with the natural numbers, which is a natural extension of our fingers. Next, we add their mirror image across the zero-divide — the negative numbers. This gives us the integers, which, when combined with the operations of addition and multiplication, form a ring as defined above.
Striking parallels between mathematics and software engineering
Throw in the operations of multiplication and division, and we get the rational numbers, which is now a field. Both the rationals and irrationals are useful numbers, and it would be nice to have a representation that can handle both.
But they are such different beasts, all due to a pesky notion called infinity: The rationals are orderly and countable, whereas there are uncountably as many irrationals.The Math Needed for Computer Science
It took us a few thousand years to figure out a solution. Right now, our best proposal is to represent everything as a limit: This structure is hierarchical, and most of the elements are in fact non-computable by a finite Turing machine. These are but a few examples of mathematical design at work. But from an alternative perspective, mathematics contains striking parallels with software engineering.
Both disciplines are heavy on jargon and notation. But once we parse through the jargon, we can begin to see the flesh and bones of mathematics. Understanding the design principles within mathematics provides us with an inlet into this strange land of hierarchical objects and changing representations.
Relationship between mathematics and physics - Wikipedia
By becoming more familiar with the landscape of mathematics, we can help with the cross pollination of ideas between mathematics and software engineering.
Maybe we can even begin to make modifications and come up with new designs of mathematics. Hey, that real number system is getting pretty old and cumbersome. Ready for something new? Her experience spans algorithm and platform development and applications. She received a Ph.