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[2] [3] An important open mathematics problem solved in the early 21st century is the Poincaré conjecture. Open problems exist in all scientific fields. For example, one of the most important open problems in biochemistry is the protein structure prediction problem [4] [5] – how to predict a protein's structure from its sequence.
Problem-based learning (PBL) is a teaching method in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes. This includes ...
An open-ended question is a question that cannot be answered with a "yes" or "no" response, or with a static response. Open-ended questions are phrased as a statement which requires a longer answer. They can be compared to closed-ended questions which demand a “yes”/“no” or short answer. [1]
Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. ... But many open questions remain, and new cardinals have been ...
This is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, to biology, [14] philosophy [15] and to cryptography (see P versus NP problem proof consequences).
In other words, any problem in EXPTIME is solvable by a deterministic Turing machine in O(2 p(n)) time, where p(n) is a polynomial function of n. A decision problem is EXPTIME-complete if it is in EXPTIME, and every problem in EXPTIME has a polynomial-time many-one reduction to it. A number of problems are known to be EXPTIME-complete.
Open problems around exact algorithms by Gerhard J. Woeginger, Discrete Applied Mathematics 156 (2008) 397–405. The RTA list of open problems – open problems in rewriting. The TLCA List of Open Problems – open problems in area typed lambda calculus
The pedagogy of Socratic questions is open-ended, focusing on broad, general ideas rather than specific, factual information. [12] The questioning technique emphasizes a level of questioning and thinking where there is no single right answer.