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Number Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory.

Machine learning models have become significantly more popular in recent years and are increasingly being used in areas where reliability is crucial. Think, for example, of self-driving cars or analyzing CT scans. To have confidence in a model, it is necessary to quantify its uncertainty. Since machine learning models differ from classical models in crucial ways – they typically have more parameters than data points and are slightly different each time they are created – classical techniques for quantifying uncertainty cannot be directly applied. This work provides new contributions to address this problem.

Mathematics can be formalized to allow a computer to execute proof steps and recognize whether a statement has been proven. Computer systems that automate mathematics are called automated theorem provers (ATP). The system has inference rules, which prescribe how the axioms and conjecture may be handled during a search for a proof. The number of possible choices at each point in the process can become very large. It would be useful to have a system that can predict which choices are better than other ones, so that a proof may be reached earlier.

This dissertation investigates the adversarial robustness of machine learning (ML)-based malware detection systems, focusing on practical limitations. While ML has advanced malware detection, it remains vulnerable to adversarial manipulations that enable malicious software to evade malware classifiers. This work rethinks both attack and defense strategies from a practical perspective, aiming to bridge the gap between theoretical approaches and real-world applicability. On the offensive side, it introduces a black-box evasion attack that generates query-efficient adversarial malware through realistic code injections, preserving malicious functionality while evading detection.