Sentence examples for include proofs of from inspiring English sources

The central topics in this theory include proofs of irrationality and transcendence of various numbers, especially those that arise as the values of special functions.

I try to include proofs of results if I think that seeing the proof will help the students to understand the material.

In his R / O / G, written prior to the lecture, one sees the conflict he perceives between what the student audience will want from him and his desire to "include proofs of results if I think that seeing the proof will help the students to understand the material".

Textbooks often include proofs of the formulas that they expect you to know; this is useful for truly understanding the material and why it works.

But Buterin recently said that Ethereum could upgrade to a hybrid scheme that includes proof-of-stake components as early as next summer.

Recent years have seen the creation of increasingly complex RNA devices, including proof-of-concept applications for in vivo three-dimensional scaffolding, imaging, computing, and control of biological behaviors.

(Past winners include "Proof of Life," with Russell Crowe and Meg Ryan, and "Volunteers," with Tom Hanks and Rita Wilson).

Be sure to include proof of the resolution of your case.

Students whose native language is not English must include proof of English proficiency.

Final official transcripts must include proof of the degree(s) awarded.

The certificates include proof of registration, enrollment status, and anticipated graduation dates.