Cover of the book Proofs That Really Count: The Art of Combinatorial Proof by Arthur T. Benjamin and Jennifer I. Quinn

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   John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Friday, 18-Apr-2025 09:04:24 JST John Carlos Baez

   Someone wrote:

   "Please give a step by step plan for someone wishing to pursue a career in applied category theory."

   Someone replied:

   "Okay, here is a step-by-step plan for someone wishing to pursue a career in Applied Category Theory (ACT). This field is relatively niche and often interdisciplinary, so the path requires both strong theoretical foundations and a focus on practical application domains.

   Phase 1: Foundational Knowledge (Undergraduate Level & Early Grad School/Self-Study)

   Step 1: Master Core Mathematics:

   Calculus & Linear Algebra: Essential building blocks for almost all quantitative fields. Ensure a deep, conceptual understanding.

   Discrete Mathematics: Crucial for logic, proofs, graph theory, combinatorics – many areas where ACT finds application.

   Abstract Algebra: Groups, rings, fields, modules. Understanding algebraic structures is fundamental before generalizing with categories. Homomorphisms are precursors to functors.

   Set Theory & Mathematical Logic: Understand the foundations upon which mathematics, including category theory, is built. Formal proofs are essential.

   (Optional but Recommended) Point-Set Topology: Introduces concepts like continuity and open sets in an abstract way, which have categorical analogues (e.g., limits, colimits).

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