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Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges
Math 55 is a two-semester freshman undergraduate mathematics course at Harvard University founded by Lynn Loomis and Shlomo Sternberg.The official titles of the course are Studies in Algebra and Group Theory (Math 55a) [1] and Studies in Real and Complex Analysis (Math 55b). [2]
Angus Ellis Taylor (October 13, 1911 – April 6, 1999) was a mathematician and professor at various universities in the University of California system. [1] He earned his undergraduate degree at Harvard summa cum laude in 1933 and his PhD at Caltech in 1936 under Aristotle Michal with a dissertation on analytic functions.
This textbook uses differential forms as a unifying approach to multivariate calculus. Most chapters are self-contained. Most chapters are self-contained. As an aid to learning the material, several important tools such as the implicit function theorem are described first in the simplified setting of affine maps before being extended to ...
A sequent calculus is often shown to have the focusing property by working in a related calculus where polarity explicitly controls which rules apply. Proofs in such systems are in focused, unfocused, or neutral phases, where the first two are characterised by hereditary decomposition; and the latter by forcing a choice of focus.
Gerald Budge Folland is an American mathematician and a professor of mathematics at the University of Washington.He is the author of several textbooks on mathematical analysis.
An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right. Coq is an interactive theorem prover first released in 1989. It allows for expressing mathematical assertions, mechanically checks proofs of these assertions, helps find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
A branch of calculus that goes beyond multivariable calculus; for this, see Calculus on Euclidean space Topics referred to by the same term This disambiguation page lists articles associated with the title Advanced calculus .