Writing
94 posts · Page 4 of 7
We prove the Bolzano-Weierstrass theorem — that every bounded sequence in Euclidean space has a convergent subsequence — and explore its central role in real analysis as a bridge between boundedness and convergence.
Why mathematical seminars are essential for learning, how to get the most out of them, and how to overcome the fear of not understanding — a guide for students at every level.
A practical guide to using SageMath and Python for mathematical computation, from basic algebra and plotting to number theory, group theory, and symbolic computation.
An honest discussion of the mental health challenges facing mathematics students and researchers — including imposter syndrome, frustration, isolation, and practical strategies for coping.
The story of John von Neumann — a polymath of staggering intellect who made foundational contributions to set theory, quantum mechanics, game theory, computing, and the atomic bomb, reshaping the modern world.
We explore the Axiom of Choice, its equivalence with Zorn's Lemma and the Well-Ordering Principle, the controversies surrounding it, and its indispensable role throughout modern mathematics.
A curated guide to the best free online mathematics courses from MIT, Stanford, Harvard, and other top institutions, organized by subject and level, with advice on how to get the most out of online learning.
A practical guide to reading mathematics research papers, covering how to approach dense notation, navigate unfamiliar territory, and extract the key ideas from a paper.
The life and vast mathematical legacy of Henri Poincaré — the last mathematician who mastered virtually all branches of mathematics and made foundational contributions to topology, dynamical systems, and mathematical physics.
The history, significance, and controversies of the Fields Medal — who wins it, why the age limit matters, and what it tells us about the culture of mathematics.
We state and prove the Central Limit Theorem — the reason the bell curve appears throughout nature, science, and statistics — and explore its assumptions, generalizations, and applications.
A catalog of the most common errors students make when writing mathematical proofs, with explanations of why each error is wrong and how to fix it.
A comprehensive guide to LaTeX and Overleaf for mathematics students: getting started, writing mathematical notation, structuring documents, collaborating, and producing professional mathematical writing.
The unique life and extraordinary mathematical legacy of Paul Erdős, who owned almost nothing, collaborated with hundreds of mathematicians around the world, and became the most prolific mathematician of the twentieth century.
A realistic look at the daily life of working mathematicians — in academia, industry, and research institutes — covering the activities, rhythms, and realities that outsiders rarely see.