This Element provides a comprehensive guide to deep learning in quantitative trading, merging foundational theory with hands-on applications. It is organized into two parts. The first part introduces the fundamentals of financial time-series and supervised learning, exploring various network architectures, from feedforward to state-of-the-art. To ensure robustness and mitigate overfitting on complex real-world data, a complete workflow is presented, from initial data analysis to cross-validation techniques tailored to financial data. Building on this, the second part applies deep learning methods to a range of financial tasks. The authors demonstrate how deep learning models can enhance both time-series and cross-sectional momentum trading strategies, generate predictive signals, and be formulated as an end-to-end framework for portfolio optimization. Applications include a mixture of data from daily data to high-frequency microstructure data for a variety of asset classes. Throughout, they include illustrative code examples and provide a dedicated GitHub repository with detailed implementations.

This Element addresses the viability of categoricity arguments in philosophy by focusing with some care on the specific conclusions that a sampling of prominent figures have attempted to draw – the same theorem might successfully support one such conclusion while failing to support another. It begins with Dedekind, Zermelo, and Kreisel, casting doubt on received readings of the latter two and highlighting the success of all three in achieving what are argued to be their actual goals. These earlier uses of categoricity arguments are then compared and contrasted with more recent work of Parsons and the co-authors Button and Walsh. Highlighting the roles of first- and second-order theorems, of external and internal theorems, the Element concludes that categoricity arguments have been more effective in historical cases that reflect philosophically on internal mathematical matters than in recent questions of pre-theoretic metaphysics.

For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics (1934–1951) grew from his Early (1912–1921) and Middle (1929–33) philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.