Hacker News·2yYou Are NOT Dumb, You Just Lack the Prerequisites
Struggling to learn complex subjects like math often stems from missing prerequisite knowledge, not a lack of capability. Revisiting and mastering foundational concepts can help build the necessary groundwork for understanding more advanced material. It's important to take a step back and re-learn the basics using effective methods and consistent practice.
Community Picks·2yWhy Democracy Is Mathematically Impossible
Democracy may be mathematically impossible due to fundamental flaws in the voting methods we use, a fact established mathematically and leading to a Nobel Prize. The first-past-the-post system, though widely used, often results in unrepresentative outcomes and strategic voting. Alternative methods like ranked-choice voting and instant runoff voting aim to address some issues but still have their own pitfalls. Arrow's impossibility theorem further complicates the matter, proving no ranked-choice method can satisfy all rational criteria simultaneously. However, rated voting systems like approval voting offer a potential solution, increasing voter turnout and reducing negative campaigning while preventing the spoiler effect.
Hacker News·2yDiscrete Mathematics
The 4th edition of 'Discrete Mathematics: an Open Introduction' is now available and features significant improvements, including a new content organization starting with logic and proofs, followed by graph theory, counting, and sequences. The edition emphasizes discrete structures, making it more useful for computer science students, while maintaining core mathematical concepts for math majors and future teachers. It includes more interactive exercises and code explorations using Sage and Python. The book is freely available online and under a Creative Commons License.
