Define key information in fundamental engineering

My specialization is computer science and software engineering, and my knowledge of this part starts from Turning machine, a mathematical model of computation.

From the “computer composition” course, I learned that a Turning machine is a Finite State Machine (FSM) and consists of a number of functions, which is able to change FSM from one state to another based on the input.

A more general concept, Universal Turning Machine (UTM), is a Turning machine that can turn into any Turning machine with the description of the target machine as input. It means we don’t need to build specific machines for specific tasks.

For me, the theory of Turning machine has influence in two areas. One is that it helps to understand the modern computer systems (which I will describe later). The other is “Turning complete”, a way to measure the capability of a computer. There are four elements in “Turning complete”: unlimited storage, ability to do arithmetic, evaluation with condition and the support of repetition of execution. They are mandatory for a model with maximum capability of computation. Once we find them in a model, we can prove it has reached the limit of computation and therefore is “Turning complete”. That is the reason why I spent a large amount of time in my dissertation of a model-based framework (2005) to implement functional programming (or formally Lambda calculus) in an imperative programming language. Recently (2014), I implemented a Domain Specific Language (DSL) for healthcare business and filled a gap using this thesis.

Mathematics, statistics and numerical methods

The course of “Fourier analysis” mainly focuses on the idea of mapping a function in the time domain to the one in the frequency domain.

I did not realize the usefulness in signal processing until I did a research on the compress algorithm of MP3, which is a file format to store sound wave in file system. When computer records a sound, first it receives the sound wave via a microphone. The sound becomes electronic signals and after processed by sound card, it is saved into file system with the original format WAV. Fourier transformation can convert the original signals (in the time domain) into a series of numbers which represent offsets on different frequencies. In this way, MP3 has enormous compression rate compared to the WAV format and therefore nowadays a portable music player is able to keep thousands of songs.

Fundamental quantitative knowledge of physical world

In “physics” course, I learned the following fundamental concepts.

Mass is an important property for a physical body. For example, to build a software model for the movement of a racing car, we need to calculate its mass by

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∫density * d(volume)

In practice, a car consists of many parts and each of them has different densities. So an approximation is:

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∑ density-of-part * volume-of-part = density-of-engine * volume-of-engine 
+ density-of-tyre * volume-of-tyre + density-of-chassis * volume-of-chassis
+ …