How many bugs are in 1,000 lines of code?

• Typical code: 1-10
• Platform code: 0.1-1
• The best—NASA: 0.01-0.1

Never assume your software doesn’t have bugs.

Test-Driven Development

Test before you build!

• Specs are already written
• We know what the expected behavior is
• We can write tests for the expected behavior first
• All tests fail to start
• We know we are done writing code when all tests pass

“NYI” (not-yet implemented)

Take a document \(d\) and assign a fixed set of classes \(\{c_1, c_2, …, c_{j}\}\) to that document. You want to predict \(f(d) = c \in C\).

two main parts:

• tokenization
• lemmatization

The Unreasonable Effectiveness of Mathematics in the Natural Sciences is an article by the famous mathematician Eugene Wigner. (Wigner 1990)

Reflection

What I found most peculiarly interesting is the focus on many mathematical/physics texts on the idea of the “beauty” of the expressions; and, it seems, the clear pleasure that Wigner gets from analyzing the systems with the aforementioned “beauty.”

Setting aside whether or not this beauty is “deserved”/appropriate, I love that my attraction to physics is somewhat similar to what Wigner describes. Under the appropriate conditions, with constraints, it is possible to build a solution to physics problems simply through the evolution of mathematics.

Theory of Computing is a science which attempts to identify “what the most efficient way to solve a given computational task?”

“efficient”

…with respect to what resources?

• time
• space/memory
• randomness
• communication / interaction
• quantum-ness (https://theory.stanford.edu/~abouland/)

“most”

study of impossibilities: lower bounds

For instance, we want a result like “SAT cannot be solved in Polynomial Time” (then in which case P != NP)

history of the theory of computing

computability theory

computability theorists consider themselves to deal with the problem of: “what computational tasks can be solved at all?” We know that because of the halting problem, not everything is solvable. (Turing 1936)