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dr. heap

Discover the foundations of computer science.
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On Invariance and Inconsistency Download the PDF version of this article. invariance-inconsistency.pdf 301 KB How can you explain important concepts from program correctness in a simple and intuitive manner? In this blog post, we shall have a look at some puzzles and analyze them from the perspective of program correctness.

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Can the Collatz conjecture be proven, or not? Download the PDF version of this article. collatz.pdf 236 KB In 1937, shortly after the mathematician Lothar Collatz obtained his doctorate, he wrote down a problem in his notebook that later became known as Collatz’ problem or the \(3x+1)\-problem . The problem is remarkable since it is easy to state, but for more than eighty years no solution had been found.

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In university, one sees students attending lectures and labs, working together on assignments, and doing exams. But—standing still for a moment—what is the purpose of all this business? The answer involves education, in the sense that students are being educated. But what is an education, precisely? In this blog post, I will summarize my views on the matter. Some say that an education is more than professional training.

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Correctness of Two Sorting Algorithms Download the PDF version of this article. two-sorting-algorithms.pdf 200 KB On Wednesday, 8th of March, 2023, I gave a lecture about two sorting algorithms for the course Program Correctness (see also the lecture series on YouTube, available only in Dutch). Then, due to limited time, I only discussed a sketch of the correctness proof.