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EECS 70 Discrete Mathematics and Probability Theory Spring 2021 and Note 12 Self-Reference and Computability In this lecture we will explore the deep connection between proofs and computation. At the heart of this connection is the notion of self-reference, and it has far-reaching consequences for the limits of computation (the Halting Problem) and the foundations

EECS 70 Discrete Mathematics and Probability Theory Fall 2021 1 Graph Theory: An Introduction One of the fundamental ideas in computer science is the notion of abstraction: capturing the essence or the core of some complex situation by a simple model. Some of the largest and most complex entities we might deal with include the

CS 70 Discrete Mathematics and Probability Theory Fall 2021 1 Extended Euclid In this problem we will consider the extended Euclid’s algorithm. The bolded numbers below keep track of which numbers appeared as inputs to the gcd call. Remember that we are interested in writing the GCD as a linear combination of the original inputs,

EECS 70 Discrete Mathematics and Probability Theory Fall 2021 1 The Stable Matching Problem In the previous two notes, we discussed several proof techniques. In this note, we apply some of these techniques to analyze the solution to an important problem known as the Stable Matching Problem, which we now introduce. The Stable Matching Problem

CS 70 Discrete Mathematics and Probability Theory Fall 2021 Due: Friday 9/10, 10:00 PM Grace period until Friday 9/10, 11:59 PM Before you start writing your final homework submission, state briefly how you worked on it. Who else did you work with? List names and email addresses. (In case of homework party, you can just

CS 70 Discrete Mathematics and Probability Theory Fall 2021 Due: Friday 9/24, 10:00 PM Grace period until Friday 9/24 11:59 PM Before you start writing your final homework submission, state briefly how you worked on it. Who else did you work with? List names and email addresses. (In case of homework party, you can just