What is Theoretical Computer Science?

Here we make an important video intended for a general audience about theoretical computer science, namely about what it even is, and giving several reasons for why it is important. We first give an introduction about the subject, by giving some definitions of "theory" and "computer science". Then I highlight the need for why precise writing and formalism are necessary. I then discuss the Collatz conjecture and give an example program to find counterexamples, highlighting that if we had a magical program to solve whether an arbitrary program halts, then we could in principle solve the conjecture.

Then I discuss the halting problem, and show that it is unsolvable by any computer by means of a proof by contradiction. Additionally, I give a brief sketch on why there are more real numbers than natural numbers, which implies that there are more problems to solve (corresponding to real numbers) than there are programs to solve them (corresponding to natural numbers). And finally I give four possible ways of "dealing" with unsolvable problems.

All music was created by and attributed to bensound: https://www.bensound.com/

Chapters: 0:00 - Chapter 1: Intro 2:19 - Chapter 2: What is Theory of Computer Science? 8:02 - Chapter 3: The Need for Formalism 10:20 - Chapter 4: Computer Program Setup 11:31 - Chapter 5: An Example Program 17:05 - Chapter 6: The Halting Problem 24:45 - Chapter 7: Natural and Real Numbers 27:43 - Chapter 8: How to Deal with Unsolvable Problems 30:53 - Chapter 9: Conclusion

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▶ABOUT ME◀ I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes. ... https://www.youtube.com/watch?v=7GWP0oP4_Vc