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Based on a 1988 survey of 68 readers who scored 24 famous mathematical theorems, this article presents a ranked list with average scores and brief explanations, revealing which results are considered the most beautiful in mathematics.
This article introduces the definition of continuity for multivariable functions, distinguishes between continuous points and discontinuities, presents fundamental theorems such as boundedness, extreme value, intermediate value, and uniform continuity on closed domains, and works through illustrative examples.
Elementary matrices, derived from a single elementary row or column operation on the identity matrix, serve as building blocks for matrix transformations; the article defines three types—swap, scaling, and shear—presents two key theorems linking them to invertibility, and illustrates their use in computing an inverse.