The project

A gallery of some mathematica projects The mathematica lab is on (.nb file) had to be submitted until Saturday August 3, 2024. We will look at a gallery. As mentioned:

• The questions are at the end of that notebook.
• There is a creative part, where we want you to combine some 3D objects. If possible, make it "printable" in the sense that surfaces are thickened and curves are given by tubes. A good strategy is to start drawing and putting together objects until you get to something which you want to refine.
• Try to be creative.

Mathematica Installation

Note that there is a site licence available also for Summer school students. You need a Harvard Student email. If you have trouble with that, HUIT in the science center can help you. Here is a website about IT and Email services.
• You can get Mathematica from here. There are instructions there to download and install Mathematica. Use the latest Mathematica version 14.0.
• Go here to make an account (use your Harvard summer school email address). Once you start Mathematica the first time, you need to log in to the portal. The activation should then go automatic.
• Please network around if you have trouble. Time before class, during the break or after class are good opportunities to help each other.

Mathematica

• The mathematica notebook written during the July 2 lecture. At the end is the proof that curvature is |r'(t) x r''(t)|/|r'(t)|^3.
• Here is one possibility to check that a function satisfies a differential equation. In this case we check that a Gaussian with variance t satisfies the heat equation.

  f[t_,x_]:=(1/Sqrt[t])*Exp[-x^2/(4t)]; FullSimplify[D[f[t,x],t] == D[f[t,x],{x,2}]]

  
  
  One can do the same computation but give the function f as an expression and not a rule. We add Clear[f] before so that the previous definition does not interfere.

  Clear[f]; f=(1/Sqrt[t])*Exp[-x^2/(4t)]; FullSimplify[D[f,t] == D[f,{x,2}]]

  
  
  

AI

While AI has become a valuable tool, you can not use it to solve your homework problems nor do your final project. We were more lenient in the last two years when the machines were still stupid. These times are gone. The reason is common sense: You simply do not learn to think and how to solve problems by just having somebody else (AI is just an other person) solve the problems for you. And also, we do not want to grade machine generated output. We all know what AI can do by now. The world has hyperventilated about it during almost 2 years now. Almost the entire population of the planet has used it. There had been enough preaching what the tools can do. Now, having enough experience in education, we know that it can makes us dependent. Like drugs, it temporarily has made us feel high and powerful. Once the "high" is over, it makes us depressed and weak and powerless. The tools have started to enslave us. Writing a paper or a homework with AI is like doing a mountain climb with the helicopter or running a marathon with the car. It is not an achievement. In this course we have in class proctored assessments without any tools. It will be important to keep human intelligence alive: once the drug dealers giving the stuff out for free will start charging more heavily for ``stronger stuff" and ``stretch the material" with advertisement, propaganda and spin to whoever party pays for it. Learn to think for yourself. You will need it for the future! Computers have helped us more and more in the last decades. It started to explode in the 1940ies when the first mechanical, electric and then electronic computers became available. Computer algebra systems developed in the 1960ies have grown more and more sophisticated. AI developments started during that time too. After a shorter AI winter, it reemerged at the beginning of the 21st century. More than 20 years ago, we played with bots interacting with computer algebra systems including mathematica see this page. The last few years, large language models or diffusion production tools have multiplied their abilities. We have now learned enough during the last 2 years that we need to ask you not to use it for homework or projects. We simply do not want to grade or admire papers or work done by a machine. It is a waste of your time and a waste of our time.