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Topic Review
μ-Recursive Function
In mathematical logic and computer science, the general recursive functions (often shortened to recursive functions) or μ-recursive functions are a class of partial functions from natural numbers to natural numbers that are "computable" in an intuitive sense. In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines(this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every μ-recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other equivalent classes of functions are the λ-recursive functions and the functions that can be computed by Markov algorithms. The subset of all total recursive functions with values in {0,1} is known in computational complexity theory as the complexity class R.
  • 1.8K
  • 01 Dec 2022
Biography
William Minicozzi II
William Philip Minicozzi II is an United States mathematician. He was born in Bryn Mawr, Pennsylvania, in 1967. Minicozzi graduated from Princeton University in 1990 and received his Ph.D. from Stanford University in 1994 under the direction of Richard Schoen. After graduating he spent a year at the Courant Institute of New York University as a visiting member where he began working with Tobi
  • 547
  • 12 Dec 2022
Biography
Valentina Mikhailovna Borok
Valentina Mikhailovna Borok (9 July 1931, Kharkiv, Ukraine , USSR – 4 February 2004, Haifa, Israel) was a Soviet Ukraine mathematician. She is mainly known for her work on partial differential equations.[1] Borok was born on July 9, 1931 in Kharkiv in Ukraine (then USSR), into a Jewish family.[2] Her father, Michail Borok, was a chemist, scientist and an expert in material science. Her moth
  • 273
  • 23 Dec 2022
Biography
Valentin Danilovich Belousov
Belousov Valentin Danilovich (20 February 1925 – 23 July 1988) was a Moldavian Soviet mathematician and a corresponding member of the Academy of Pedagogical Sciences of the USSR (1968).[1][2] He graduated from the Kishinev Pedagogical Institute (1947), Doctor of Physical and Mathematical Sciences (1966), Professor (1967), honored worker of science and technology of the Moldavian SSR. Since 1
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  • 23 Nov 2022
Topic Review
Two-Dimensional Space
Two-dimensional space (also known as 2D space, 2-space, or bi-dimensional space) is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point). The set [math]\displaystyle{ \mathbb{R}^2 }[/math] of pairs of real numbers with appropriate structure often serves as the canonical example of a two-dimensional Euclidean space. For a generalization of the concept, see dimension. Two-dimensional space can be seen as a projection of the physical universe onto a plane. Usually, it is thought of as a Euclidean space and the two dimensions are called length and width.
  • 3.7K
  • 28 Nov 2022
Biography
Thomas Little Heath
Sir Thomas Little Heath KCB KCVO FRS FBA (/hiːθ/; 5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English. Heath was
  • 375
  • 18 Nov 2022
Topic Review
Technology for Science Education
The COVID-19 confinement has represented both opportunities and losses for education. Rarely before has any other period moved the human spirit into such discipline or submission—depending on one’s personal and emotional points of view. Both extremes have been widely influenced by external factors on each individual’s life path. Education in the sciences and engineering has encountered more issues than other disciplines due to specialized mathematical handwriting, experimental demonstrations, abstract complexity, and lab practices. 
  • 593
  • 22 Sep 2021
Topic Review
Synthetic Datasets
With the consistent growth in the importance of machine learning and big data analysis, feature selection stands to be one of the most relevant techniques in the field. Extending into many disciplines, the use of feature selection in medical applications, cybersecurity, DNA micro-array data, and many more areas is witnessed. Machine learning models can significantly benefit from the accurate selection of feature subsets to increase the speed of learning and also to generalize the results. Feature selection can considerably simplify a dataset, such that the training models using the dataset can be “faster” and can reduce overfitting. Synthetic datasets were presented as a valuable benchmarking technique for the evaluation of feature selection algorithms.
  • 48
  • 20 Mar 2024
Topic Review
Symmetric Difference
In mathematics, the symmetric difference, also known as the disjunctive union, of two sets is the set of elements which are in either of the sets and not in their intersection. The symmetric difference of the sets A and B is commonly denoted by or or For example, the symmetric difference of the sets [math]\displaystyle{ \{1,2,3\} }[/math] and [math]\displaystyle{ \{3,4\} }[/math] is [math]\displaystyle{ \{1,2,4\} }[/math]. The power set of any set becomes an abelian group under the operation of symmetric difference, with the empty set as the neutral element of the group and every element in this group being its own inverse. The power set of any set becomes a Boolean ring with symmetric difference as the addition of the ring and intersection as the multiplication of the ring.
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  • 17 Oct 2022
Biography
Sunil Mukhi
Sunil Mukhi is an Indian theoretical physicist working in the areas of string theory, quantum field theory and particle physics. Currently he is a physics professor at IISER Pune. He is also the dean of faculty here. He obtained a B.Sc. degree at St. Xavier's College, Mumbai and a Ph.D. in Theoretical Physics in 1981 from Stony Brook University (then called the State University of New York at
  • 412
  • 16 Nov 2022
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