Questions that deal with research, strategies, math and theories

[WilliamJ]

I read that theories are a framework of explanations of experimental data and that they predict experimental results. I have also read that sometimes data comes before there is a theoretical explanation and vice versa; theoretical explanations predict data that has not been yet proven by experiment. Also, if experimental data proves a theory wrong, the theory has to be reworked.
I am also confused by the fact that Galileo proved Aristotle and his school of philosophy wrong (about how the Earth is not the center of the universe and how larger masses were thought to fall at faster accelerations than smaller masses) by developing a systematic method of observation, experimentation, and analysis. The Greeks in the philosophical school of Aristotle simply tried to explain observed things by solely logical arguments. Galileo started his method to disprove Aristotle.
I read “There is no single ‘scientific method.’ All scientists combine systematic experimentation with careful measurements and analysis of results. From these analyses, conclusions are drawn. These conclusions are then subjected to additional tests to find out if they are valid.” I see a jump from observation as the first step for both Aristotle and Galileo to experimentation by modern researchers. Also, from the beginning of these questions I wrote about what they said in this book about how theories are frameworks of explanations of experimental results and that predict new experimental data. I see that with Galileo there is also experimentation before analysis. This leads to conclusions that are then tested to see if those conclusions are valid. Are these conclusions forerunners of explanations that when put together in a framework are a theory? Are these conclusions the explanations that make a framework called a theory (and what is meant by a framework?), or are these conclusions the actual theories (these conclusions explain the analysis of data and can be tested to see if these conclusions are valid or not)?
Also, professors, “Much of their work consists of doing research—that is, exploring ideas, creating hypotheses, performing experiments and publishing findings.” In what way do they do research differently than the rest of the researchers? It sounds different that the other research I’ve read.
I’m reading about research and also about strategies I’m not sure if this is strategy solely employed in physics, but I feel it may be used in all kinds of ways, but for such an abstract study as mathematics and physics, I feel it work especially well.
I need examples or at least a clue to the following quote from the book.
“A strategy is an organized approach to a problem that breaks down the task of obtaining and organizing information into stages. Strategies can be the ‘bridge’ in solving problems. Several strategies are in the following list:
Strategies:
List all possible solutions
Look for a pattern
Construct a table, graph, or figure
Make a model
Guess and check
Work backwards
Make a drawing
Solve a simpler or similar related problem.”
I know that mathematics is the language of physics, but I don’t have a clue how all of the parts (and what are all of the parts? Corollaries, postulates, theorems, if-then statements, premises, independent and dependent variable from experiments that make equations that can be graphed, etc.) work together to be used for the advancements in physics and its applied math as well as pure mathematics? Whoever replies, keep it simple, I’m only a little ways into Calculus and my understanding of Algebra is far from complete. I need to know what each part is and how they work together and what each part does from a bird’s eye view.

 

[Valerie Park]

The strategies listed above are tools for problem solving. They can be used to break down a complex problem into smaller, more manageable parts. For example, the strategy of "list all possible solutions" can be used to identify all of the potential solutions to a given problem. The strategy of "look for a pattern" can be used to identify patterns or trends in data or in a system of equations that can then be used to generate hypotheses or predictions. The strategy of "make a model" can be used to create a visual representation of a system or process that can be used to test and analyze various scenarios. The strategy of "guess and check" can be used to systematically try out different solutions to a problem in order to identify the one that works. The strategy of "work backwards" can be used to start with the end goal and work back to the beginning in order to identify the steps necessary to achieve that goal. The strategy of "make a drawing" can be used to create diagrams or illustrations of a system or process that can help to better understand it. Finally, the strategy of "solve a simpler or similar related problem" can be used to tackle a complex problem by first solving a simpler version of the same problem or a related problem. In physics, theories are frameworks that explain and predict experimental data. They are constructed from observations, experiments, and mathematical analysis. Theories can also be used to make predictions about the behavior of a system or process, which can then be tested by performing experiments. If the experiments prove the theory wrong, the theory must be modified or discarded. Galileo's work disproving Aristotle was an example of this. He used systematic observation, experimentation, and analysis to demonstrate the validity of his theories and disprove those of Aristotle.