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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Each question may contain from zero to three subsets of questions with marks ranging from 2 to 8 marks. The total weighting of the paper is 80 marks and constitutes 44% of the grade. Paper 2 (Duration: 2 hours 30 minutes): Questions are categorised into 3 sections: A, B and C. Section A contains 7 questions which must all be answered.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
In June 2015, students across the United Kingdom who had taken an Edexcel GCSE Maths paper expressed anger and confusion over questions that "did not make sense" and were "ridiculous", mocking the exam on Twitter. [13] [14] [15] On a Sky News segment, presenter Adam Boulton answered one of the paper's 'hardest' questions with a former maths ...
A qualification in Further Mathematics involves studying both pure and applied modules. Whilst the pure modules (formerly known as Pure 4–6 or Core 4–6, now known as Further Pure 1–3, where 4 exists for the AQA board) build on knowledge from the core mathematics modules, the applied modules may start from first principles.
Hilbert himself declared: "If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proved?" [ 11 ] In 2008, DARPA announced its own list of 23 problems that it hoped could lead to major mathematical breakthroughs, "thereby strengthening the scientific and technological ...
Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians. List of algebraic number theory topics; List of number theory topics